Infinity.J. Wallis (1655).

First encountered in the treatise of the English mathematician John Walis "On Conical Sections".

The base of natural logarithms. L. Euler (1736).

Mathematical constant, transcendental number. This number is sometimes called neperov in honor of the Scottish scientist Napier, author of the work "Description of the amazing table of logarithms" (1614). For the first time, the constant is tacitly present in the appendix to the translation into English language Napier's aforementioned work, published in 1618. The very same constant was first calculated by the Swiss mathematician Jacob Bernoulli in the course of solving the problem of the marginal value of interest income.

2,71828182845904523...

The first known use of this constant, where it was denoted by the letter b, found in Leibniz's letters to Huygens, 1690-1691. Letter e began to use Euler in 1727, and the first publication with this letter was his work "Mechanics, or the Science of Motion, Expounded Analytically" in 1736. Respectively, e commonly called Euler's number... Why was the letter chosen e, it is not known exactly. Perhaps this is due to the fact that the word begins with it exponential("Exponential", "exponential"). Another assumption is that the letters a, b, c and d were already quite widely used for other purposes, and e was the first "free" letter.

The ratio of the circumference to the diameter. W. Jones (1706), L. Euler (1736).

Mathematical constant, irrational number. The number "pi", the old name is the Ludolph number. Like any irrational number, π is represented by an infinite non-periodic decimal fraction:

π = 3.141592653589793 ...

For the first time the designation of this number by the Greek letter π was used by the British mathematician William Jones in his book "A New Introduction to Mathematics", and it became generally accepted after the works of Leonard Euler. This designation comes from initial letter the Greek words περιφερεια - circle, periphery and περιμετρος - perimeter. Johann Heinrich Lambert proved the irrationality of π in 1761, and Adrienne Marie Legendre in 1774 proved the irrationality of π 2. Legendre and Euler assumed that π could be transcendental, i.e. can not satisfy any algebraic equation with integer coefficients, which was ultimately proven in 1882 by Ferdinand von Lindemann.

Imaginary unit. L. Euler (1777, in press - 1794).

It is known that the equation x 2 = 1 has two roots: 1 and -1 ... The imaginary unit is one of the two roots of the equation x 2 = -1, denoted by a Latin letter i, one more root: -i... This designation was proposed by Leonard Euler, who took for this the first letter of the Latin word imaginarius(imaginary). He also extended all standard functions to the complex area, i.e. the set of numbers representable in the form a + ib, where a and b- real numbers. The term "complex number" was widely used by the German mathematician Karl Gauss in 1831, although the term was previously used in the same sense by the French mathematician Lazar Carnot in 1803.

Unit vectors. W. Hamilton (1853).

Unit vectors are often associated with the coordinate axes of the coordinate system (in particular, with the axes of the Cartesian coordinate system). The unit vector directed along the axis X, denoted i, the unit vector directed along the axis Y, denoted j, and the unit vector directed along the axis Z, denoted k... Vectors i, j, k are called orts, they have unit modules. The term "ort" was introduced by the English mathematician, engineer Oliver Heaviside (1892), and the notation i, j, k- Irish mathematician William Hamilton.

Whole part of the number, antje. K. Gauss (1808).

The integer part of the number [x] of the number x is the largest integer not exceeding x. So, = 5, [-3.6] = - 4. The function [x] is also called "antje of x". The symbol for the "integer part" function was introduced by Karl Gauss in 1808. Some mathematicians prefer to use the notation E (x), proposed in 1798 by Legendre, instead.

Parallelism angle. N.I. Lobachevsky (1835).

On the Lobachevsky plane - the angle between the straight linebpassing through the pointOparallel straightanot containing pointO, and perpendicular fromO on the a. α is the length of this perpendicular. As the point is removedO from straight athe parallelism angle decreases from 90 ° to 0 °. Lobachevsky gave a formula for the angle of parallelismP( α ) = 2arctg e - α / q , where q- some constant associated with the curvature of the Lobachevsky space.

Unknown or variable values. R. Descartes (1637).

In mathematics, a variable is a quantity characterized by a set of values ​​that it can take. In this case, one can mean both a real physical quantity, temporarily considered in isolation from its physical context, and some abstract quantity that has no analogues in real world... The concept of a variable originated in the 17th century. initially under the influence of the demands of natural science, which highlighted the study of motion, processes, and not just states. This concept required new forms for its expression. Alphabetic algebra and analytic geometry by Rene Descartes were just such new forms. For the first time rectangular system coordinates and designations x, y were introduced by Rene Descartes in his work "Discourse on the Method" in 1637. Pierre Fermat also contributed to the development of the coordinate method, but his works were first published after his death. Descartes and Fermat used the coordinate method only on the plane. The coordinate method for three-dimensional space was first applied by Leonard Euler already in the 18th century.

Vector. O. Koshi (1853).

From the outset, a vector is understood as an object that has magnitude, direction, and (optionally) an application point. The rudiments of vector calculus appeared along with the geometric model of complex numbers by Gauss (1831). Developed operations with vectors were published by Hamilton as part of his quaternion calculus (the vector was formed by the imaginary components of the quaternion). Hamilton coined the term itself vector(from the Latin word vector, carrier) and described some of the vector analysis operations. This formalism was used by Maxwell in his works on electromagnetism, thereby drawing the attention of scientists to a new calculus. Gibbs's Elements of Vector Analysis (1880s) soon came out, and then Heaviside (1903) gave vector analysis a modern look. The vector sign itself was introduced into use by the French mathematician Augustin Louis Cauchy in 1853.

Addition, subtraction. J. Widman (1489).

The plus and minus signs were apparently invented in the German mathematical school of "kossists" (that is, algebraists). They are used in Jan (Johannes) Widmann's textbook, A Quick and Nice Counting for All Traders, published in 1489. Before that, addition was denoted by the letter p(from latin plus"More") or Latin word et(the conjunction "and"), and subtraction is a letter m(from latin minus"Less, less"). In Widman, the plus symbol replaces not only addition, but also the conjunction "and". The origin of these symbols is unclear, but most likely they were previously used in trading as indicators of profit and loss. Both symbols soon became common in Europe - with the exception of Italy, which used the old designations for about a century.

Multiplication. W. Outred (1631), H. Leibniz (1698).

The multiplication sign in the form of an oblique cross was introduced in 1631 by the Englishman William Outred. Before him, most often the letter was used M, although other designations were proposed: the symbol of a rectangle (French mathematician Erigon, 1634), an asterisk (Swiss mathematician Johann Rahn, 1659). Later, Gottfried Wilhelm Leibniz replaced the cross with a dot (end of the 17th century) so as not to confuse it with the letter x; before him, such symbolism was found among the German astronomer and mathematician Regiomontanus (15th century) and the English scientist Thomas Harriott (1560-1621).

Division. I. Rahn (1659), G. Leibniz (1684).

William Outread used the forward slash / for the division sign. Gottfried Leibniz began to denote division with a colon. Before them, the letter was also often used D... Starting with Fibonacci, the horizontal line of the fraction is also used, which was used by Heron, Diophantus and in Arabic writings. In England and the USA, the symbol ÷ (obelus) became widespread, which was proposed by Johann Rahn (possibly with the participation of John Pell) in 1659. An attempt by the American National Mathematical Standards Committee ( National Committee on Mathematical Requirements) to take the obelus out of practice (1923) was unsuccessful.

Percent. M. de la Port (1685).

One hundredth of a whole, taken as one. The word "percent" itself comes from the Latin "pro centum", which means "per hundred". In 1685, Mathieu de la Porta's A Guide to Commercial Arithmetic was published in Paris. In one place it was about percentages, which then stood for "cto" (short for cento). However, the typesetter mistook this "cto" for a fraction and printed "%". So, due to a misprint, this sign came into use.

Degrees. R. Descartes (1637), I. Newton (1676).

The modern notation of the exponent was introduced by Rene Descartes in his " Geometries"(1637), however, only for natural degrees with exponents greater than 2. Later, Isaac Newton extended this form of notation to negative and fractional exponents (1676), the interpretation of which had already been proposed by this time: Flemish mathematician and engineer Simon Stevin, English mathematician John Wallis and French mathematician Albert Girard.

Arithmetic root n-th power of real number a≥0, is a non-negative number n-th degree of which is a... The arithmetic root of the 2nd degree is called the square root and can be written without specifying the degree: √. The arithmetic root of the 3rd degree is called the cube root. Medieval mathematicians (for example, Cardano) denoted Square root symbol R x (from Latin Radix, root). The modern designation was first used by the German mathematician Christoph Rudolph, from the Kossist school, in 1525. This character comes from the stylized first letter of the same word radix... The line above the radical expression was initially absent; it was later introduced by Descartes (1637) for a different purpose (instead of parentheses), and this feature soon merged with the root sign. The cubic root in the 16th century was designated as follows: R x .u.cu (from lat. Radix universalis cubica). Albert Girard (1629) began to use the usual designation of a root of an arbitrary degree. This format was consolidated thanks to Isaac Newton and Gottfried Leibniz.

Logarithm, decimal logarithm, natural logarithm. I. Kepler (1624), B. Cavalieri (1632), A. Prinsheim (1893).

The term "logarithm" belongs to the Scottish mathematician John Napier ( "Description of the amazing table of logarithms", 1614); it arose from a combination of the Greek words λογος (word, relation) and αριθμος (number). J. Napier's logarithm is an auxiliary number for measuring the ratio of two numbers. The modern definition of the logarithm was first given by the English mathematician William Gardiner (1742). By definition, the logarithm of a number b by reason a (a ≠ 1, a> 0) - exponent m to which the number should be raised a(called the base of the logarithm) to get b... Denoted log a b. So, m = log a b, if a m = b.

The first tables of decimal logarithms were published in 1617 by the Oxford professor of mathematics Henry Briggs. Therefore, abroad, decimal logarithms are often called brigs. The term "natural logarithm" was introduced by Pietro Mengoli (1659) and Nicholas Mercator (1668), although the London mathematics teacher John Spidell compiled a table of natural logarithms back in 1619.

Until the end of the 19th century, there was no generally accepted notation for the logarithm, the base a indicated then to the left and above the symbol log then over it. Ultimately, mathematicians came to the conclusion that the most convenient place for the base is below the line, after the symbol log... The sign of the logarithm - the result of the abbreviation of the word "logarithm" - occurs in different types almost simultaneously with the appearance of the first tables of logarithms, for example Log- I. Kepler (1624) and G. Briggs (1631), log- at B. Cavalieri (1632). Designation ln for the natural logarithm was introduced by the German mathematician Alfred Pringsheim (1893).

Sine, cosine, tangent, cotangent. W. Outred (mid. 17th century), I. Bernoulli (18th century), L. Euler (1748, 1753).

Abbreviations for sine and cosine were introduced by William Outread in the middle of the 17th century. Abbreviations for tangent and cotangent: tg, ctg introduced by Johann Bernoulli in the 18th century, they became widespread in Germany and Russia. Other countries use the names of these functions tan, cot proposed by Albert Girard even earlier, at the beginning of the 17th century. V modern shape the theory of trigonometric functions was led by Leonard Euler (1748, 1753), and we owe him the consolidation of real symbolism.The term "trigonometric functions" was introduced by the German mathematician and physicist Georg Simon Klugel in 1770.

The sine line of Indian mathematicians was originally called "Arha-jiva"("Semi-string", that is, half a chord), then the word "Archa" was dropped and the sine line was called simply Jiva... Arabic translators have not translated the word Jiva Arabic word "Vatar", denoting a bowstring and a chord, and transcribed in Arabic letters and began to call the sine line Jiba... Since in Arabic, short vowels are not indicated, but a long "and" in the word Jiba denoted in the same way as the half-vowel "y", the Arabs began to pronounce the name of the sinus line Jibe, which literally means "cavity", "sinus". When translating Arabic works into Latin, European translators translated the word Jibe Latin word sinus, having the same meaning.The term "tangent" (from lat.tangens- concerning) was introduced by the Danish mathematician Thomas Finke in his book The Geometry of the Round (1583).

Arcsine. C. Scherfer (1772), J. Lagrange (1772).

Inverse trigonometric functions are mathematical functions that are inverse to trigonometric functions. The name of the inverse trigonometric function is derived from the name of the corresponding trigonometric function by adding the prefix "arc" (from lat. arc- arc).Inverse trigonometric functions usually include six functions: arcsin, arccos, arctg, arcctg, arcsec, and arccosec. For the first time, special symbols for inverse trigonometric functions were used by Daniel Bernoulli (1729, 1736).The manner of denoting inverse trigonometric functions with the prefix arc(from lat. arcus, arc) appeared at the Austrian mathematician Karl Scherfer and was consolidated thanks to the French mathematician, astronomer and mechanic Joseph Louis Lagrange. It meant that, for example, an ordinary sine allows finding a chord that contracts it along an arc of a circle, and the inverse function solves the opposite problem. Until the end of the 19th century, the English and German mathematical schools proposed other designations: sin -1 and 1 / sin, but they are not widely used.

Hyperbolic sine, hyperbolic cosine. W. Riccati (1757).

Historians discovered the first appearance of hyperbolic functions in the works of the English mathematician Abraham de Moivre (1707, 1722). The modern definition and detailed study of them were carried out by the Italian Vincenzo Riccati in 1757 in the work "Opusculorum", he also proposed their designations: sh,ch... Riccati proceeded from the consideration of a single hyperbole. An independent discovery and further study of the properties of hyperbolic functions was carried out by the German mathematician, physicist and philosopher Johann Lambert (1768), who established a wide parallelism of the formulas of ordinary and hyperbolic trigonometry. N.I. Lobachevsky subsequently used this parallelism, trying to prove the consistency of non-Euclidean geometry, in which ordinary trigonometry is replaced by hyperbolic one.

Just as trigonometric sine and cosine are coordinates of a point on a coordinate circle, hyperbolic sine and cosine are coordinates of a point on a hyperbola. Hyperbolic functions are expressed in terms of the exponent and are closely related to trigonometric functions: sh (x) = 0.5 (e x -e -x) , ch (x) = 0.5 (e x + e -x). By analogy with trigonometric functions, hyperbolic tangent and cotangent are defined as ratios of hyperbolic sine and cosine, cosine and sine, respectively.

Differential. G. Leibniz (1675, in press 1684).

The main, linear part of the function increment.If the function y = f (x) one variable x has for x = x 0derivative, and incrementΔy = f (x 0 +? X) -f (x 0)functions f (x) can be represented asΔy = f "(x 0) Δx + R (Δx) , where is the member R infinitely small compared toΔx... First termdy = f "(x 0) Δxin this expansion is called the differential of the function f (x) at the pointx 0... V works of Gottfried Leibniz, Jacob and Johann Bernoulli word"differentia"was used in the sense of "increment", I. Bernoulli denoted it by Δ. G. Leibniz (1675, in print 1684) used the notation for the "infinitely small difference"d- the first letter of the word"differential", formed by him from"differentia".

Indefinite integral. G. Leibniz (1675, in press 1686).

The word "integral" was first used in print by Jacob Bernoulli (1690). Perhaps the term is derived from Latin integer- whole. According to another assumption, the basis was the Latin word integro- to bring to the previous state, to restore. The ∫ sign is used to denote an integral in mathematics and is a stylized image of the first letter of a Latin word summa - sum. It was first used by the German mathematician Gottfried Leibniz, the founder of differential and integral calculus, at the end of the 17th century. Another of the founders of differential and integral calculus, Isaac Newton, in his works did not offer an alternative symbolism of the integral, although he tried various options: a vertical bar over a function or a square symbol that stands in front of a function or borders it. Indefinite integral for a function y = f (x) Is a collection of all the antiderivatives of a given function.

A definite integral. J. Fourier (1819-1822).

The definite integral of a function f (x) with lower limit a and the upper limit b can be defined as the difference F (b) - F (a) = a ∫ b f (x) dx , where F (x)- some antiderivative of the function f (x) ... Definite integral a ∫ b f (x) dx numerically equal to the area figures bounded by the abscissa axis, straight lines x = a and x = b and the function graph f (x)... Registration definite integral in our usual form was proposed by the French mathematician and physicist Jean Baptiste Joseph Fourier in early XIX century.

Derivative. G. Leibniz (1675), J. Lagrange (1770, 1779).

Derivative is the basic concept of differential calculus that characterizes the rate of change of a function f (x) on argument change x ... It is defined as the limit of the ratio of the increment of a function to the increment of its argument when the increment of the argument tends to zero, if such a limit exists. A function that has a finite derivative at some point is called differentiable at this point. The process of calculating a derivative is called differentiation. The reverse process is integration. In the classic differential calculus the derivative is most often defined through the concepts of the theory of limits, however, historically, the theory of limits appeared later than differential calculus.

The term "derivative" was introduced by Joseph Louis Lagrange in 1797; dy / dx- Gottfried Leibniz in 1675. The manner in which the time derivative is denoted by a dot over a letter comes from Newton (1691).The Russian term "derivative of a function" was first used by a Russian mathematicianVasily Ivanovich Viskovatov (1779-1812).

Partial derivative. A. Legendre (1786), J. Lagrange (1797, 1801).

For functions of many variables, partial derivatives are determined - derivatives with respect to one of the arguments, calculated under the assumption that the other arguments are constant. Designations ∂f / ∂ x, ∂ z / ∂ y introduced by the French mathematician Adrienne Marie Legendre in 1786; fx ",z x "- Joseph Louis Lagrange (1797, 1801) ∂ 2 z / ∂ x 2, ∂ 2 z / ∂ x ∂ y- partial derivatives of the second order - German mathematician Carl Gustav Jacob Jacobi (1837).

Difference, increment. I. Bernoulli (late 17th century - first half of the 18th century), L. Euler (1755).

The notation of increment by the letter Δ was first used by the Swiss mathematician Johann Bernoulli. V general practice The delta symbol came into use after the work of Leonard Euler in 1755.

Sum. L. Euler (1755).

The sum is the result of adding values ​​(numbers, functions, vectors, matrices, etc.). To denote the sum of n numbers a 1, a 2, ..., a n, the Greek letter "sigma" Σ is used: a 1 + a 2 + ... + a n = Σ n i = 1 a i = Σ n 1 a i. The Σ sign for the sum was introduced by Leonard Euler in 1755.

Work. K. Gauss (1812).

The product is the result of multiplication. To denote the product of n numbers a 1, a 2, ..., a n, the Greek letter "pi" Π is used: a 1 · a 2 · ... · a n = Π n i = 1 a i = Π n 1 a i. For example, 1 · 3 · 5 · ... · 97 · 99 =? 50 1 (2i-1). The Π sign for the work was introduced by the German mathematician Karl Gauss in 1812. In Russian mathematical literature, the term "work" was first encountered by Leonty Filippovich Magnitsky in 1703.

Factorial. K. Crump (1808).

The factorial of the number n (denoted by n !, pronounced "ento-factorial") is the product of all natural numbers up to n inclusive: n! = 1 · 2 · 3 · ... · n. For example, 5! = 1 · 2 · 3 · 4 · 5 = 120. By definition, it is assumed 0! = 1. Factorial is defined only for non-negative integers. The factorial of the number n is equal to the number of permutations of n elements. For example, 3! = 6, indeed,

♣ ♦

♣ ♦

♣ ♦

♦ ♣

♦ ♣

♦ ♣

All six and only six permutations of three elements.

The term "factorial" was introduced by the French mathematician and politician Louis Francois Antoine Arbogast (1800), the designation n! - French mathematician Christian Crump (1808).

Modulus, absolute value. K. Weierstrass (1841).

Modulus, the absolute value of a real number x is a non-negative number defined as follows: | x | = x for x ≥ 0, and | x | = -x for x ≤ 0. For example, | 7 | = 7, | - 0.23 | = - (- 0.23) = 0.23. The modulus of a complex number z = a + ib is a real number equal to √ (a 2 + b 2).

It is believed that the term "module" was suggested to be used by the English mathematician and philosopher, a student of Newton, Roger Coots. Gottfried Leibniz also used this function, which he called "module" and denoted: mol x. The generally accepted designation for the absolute value was introduced in 1841 by the German mathematician Karl Weierstrass. For complex numbers, this concept was introduced by the French mathematicians Augustin Cauchy and Jean Robert Argan at the beginning of the 19th century. In 1903 the Austrian scientist Konrad Lorenz used this same symbolism for the length of a vector.

Norm. E. Schmidt (1908).

Norm is a functional defined on a vector space and generalizing the concept of the length of a vector or modulus of a number. The sign "norms" (from the Latin word "norma" - "rule", "sample") was introduced by the German mathematician Erhard Schmidt in 1908.

Limit. S. Luillier (1786), W. Hamilton (1853), many mathematicians (up to the beginning of the XX century)

Limit is one of the basic concepts mathematical analysis, meaning that a certain variable value in the considered process of its change approaches infinitely to a certain constant value. The concept of a limit on an intuitive level was used as early as the second half of the 17th century by Isaac Newton, as well as by mathematicians of the 18th century, such as Leonard Euler and Joseph Louis Lagrange. The first strict definitions of the sequence limit were given by Bernard Bolzano in 1816 and Augustin Cauchy in 1821. The lim symbol (the first 3 letters from the Latin word limes - border) appeared in 1787 by the Swiss mathematician Simon Antoine Jean Luillier, but its use did not yet resemble the modern one. The expression lim, in a more familiar form for us, was first used by the Irish mathematician William Hamilton in 1853.Weierstrass introduced a designation close to the modern designation, however, instead of the usual arrow, he used the equal sign. The arrow appeared at the beginning of the 20th century at once by several mathematicians - for example, by the English mathematician Godfried Hardy in 1908.

Zeta function, d Riemann's zeta function... B. Riemann (1857).

The analytical function of the complex variable s = σ + it, for σ> 1, is determined absolutely and uniformly by the Dirichlet series:

ζ (s) = 1 -s + 2 -s + 3 -s + ....

For σ> 1, the representation in the form of a Euler product is valid:

ζ (s) = Π p (1-p -s) -s,

where the product is taken over all primes p. The zeta function plays an important role in number theory.As a function of a real variable, the zeta function was introduced in 1737 (published in 1744) by L. Euler, who indicated its expansion into a product. Then this function was considered by the German mathematician L. Dirichlet and, especially successfully, by the Russian mathematician and mechanic P.L. Chebyshev when studying the law of distribution of prime numbers. However, the most profound properties of the zeta function were discovered later, after the work of the German mathematician Georg Friedrich Bernhard Riemann (1859), where the zeta function was considered as a function of a complex variable; he also introduced the name "zeta function" and the notation ζ (s) in 1857.

Gamma function, Euler Γ-function. A. Legendre (1814).

The gamma function is a mathematical function that extends the concept of factorial to the field of complex numbers. Usually denoted by Γ (z). The r-function was first introduced by Leonard Euler in 1729; it is determined by the formula:

Γ (z) = limn → ∞ n! n z /z(z+1)...(z+n).

The Γ-function is expressed big number integrals, infinite products and sums of series. It is widely used in analytical number theory. The name "Gamma function" and the notation Γ (z) were proposed by the French mathematician Adrien Marie Legendre in 1814.

Beta function, B function, Euler B function. J. Binet (1839).

A function of two variables p and q, defined for p> 0, q> 0 by the equality:

B (p, q) = 0 ∫ 1 x p-1 (1-x) q-1 dx.

The beta function can be expressed in terms of the Γ-function: B (p, q) = Γ (p) Г (q) / Г (p + q).Just as the gamma function for integers is a generalization of the factorial, the beta function is, in a sense, a generalization of the binomial coefficients.

Many properties are described using the beta functionelementary particles participating in strong interaction... This feature was noticed by the Italian theoretical physicistGabriele Veneziano in 1968. This marked the beginning string theory.

The name "beta function" and the notation B (p, q) were introduced in 1839 by the French mathematician, mechanic and astronomer Jacques Philippe Marie Binet.

Laplace operator, Laplacian. R. Murphy (1833).

Linear differential operator Δ, which assigns the function φ (x 1, x 2, ..., x n) in n variables x 1, x 2, ..., x n:

Δφ = ∂ 2 φ / ∂х 1 2 + ∂ 2 φ / ∂х 2 2 + ... + ∂ 2 φ / ∂х n 2.

In particular, for a function φ (x) of one variable, the Laplace operator coincides with the operator of the 2nd derivative: Δφ = d 2 φ / dx 2. The equation Δφ = 0 is usually called the Laplace equation; hence the names "Laplace operator" or "Laplacian" originated. The notation Δ was introduced by the English physicist and mathematician Robert Murphy in 1833.

Hamilton operator, nabla operator, Hamiltonian. O. Heaviside (1892).

Vector differential operator of the form

∇ = ∂ / ∂x i+ ∂ / ∂y j+ ∂ / ∂z k,

where i, j, and k- coordinate unit vectors. The basic operations of vector analysis, as well as the Laplace operator, are expressed in a natural way through the nabla operator.

In 1853, the Irish mathematician William Rowan Hamilton introduced this operator and coined the symbol ∇ for it in the form of an inverted Greek letter Δ (delta). In Hamilton, the tip of the symbol pointed to the left; later, in the works of the Scottish mathematician and physicist Peter Guthrie Tate, the symbol acquired its modern form. Hamilton called this symbol the word "atled" (the word "delta", read the other way around). Later, English scientists, including Oliver Heaviside, began to call this symbol "nabla", after the name of the letter ∇ in the Phoenician alphabet, where it occurs. The origin of the letter is associated with a musical instrument of the harp type, ναβλα (nabla) in ancient Greek means "harp". The operator was called the Hamilton operator, or the nabla operator.

Function. I. Bernoulli (1718), L. Euler (1734).

A mathematical concept that reflects the relationship between the elements of a set. We can say that a function is a "law", a "rule" according to which each element of one set (called the domain of definition) is associated with some element of another set (called the domain of values). The mathematical concept of a function expresses an intuitive idea of ​​how one quantity completely determines the value of another quantity. Often the term "function" refers to a numeric function; that is, a function that assigns one number to another. For a long time, mathematicians have given arguments without parentheses, for example, so - φх. For the first time such a designation was used by the Swiss mathematician Johann Bernoulli in 1718.Parentheses were only used in the case of many arguments, and also if the argument was complex expression... Records that are still in use today are an echo of those times.sin x, lg xand others. But gradually the use of parentheses, f (x), became a general rule. And the main merit in this belongs to Leonard Euler.

Equality. R. Record (1557).

The equal sign was proposed by the Welsh physician and mathematician Robert Record in 1557; the shape of the symbol was much longer than the current one, since it imitated the image of two parallel segments. The author explained that there is nothing more equal in the world than two parallel line the same length. Prior to that, in ancient and medieval mathematics, equality was denoted verbally (for example est egale). Rene Descartes in the 17th century began to use æ (from lat. aequalis), and he used the modern equal sign to indicate that the coefficient could be negative. François Viette denoted subtraction with an equal sign. The Record symbol did not spread immediately. The spread of the Record symbol was hindered by the fact that since ancient times the same symbol has been used to denote the parallelism of straight lines; in the end it was decided to make the parallelism symbol vertical. In continental Europe, the "=" sign was introduced by Gottfried Leibniz only at the turn of the 17th-18th centuries, that is, more than 100 years after the death of Robert Record, who first used it for this.

Approximately equal, approximately equal. A. Gunther (1882).

Sign " ≈ "introduced into use as a symbol of the relationship" approximately equal to "the German mathematician and physicist Adam Wilhelm Sigmund Gunther in 1882.

More less. T. Garriott (1631).

These two signs were introduced into use by the English astronomer, mathematician, ethnographer and translator Thomas Garriot in 1631, before that the words "more" and "less" were used.

Comparability. K. Gauss (1801).

Comparison is a ratio between two integers n and m, meaning that difference n-m these numbers are divided by a given integer a, called the comparison module; written: n≡m (mod a) and read "numbers n and m are comparable mod a". For example, 3≡11 (mod 4), since 3-11 is divisible by 4; the numbers 3 and 11 are comparable modulo 4. Comparisons have many properties similar to those of equalities. So, the term in one part of the comparison can be transferred with the opposite sign to the other part, and comparisons with the same module can be added, subtracted, multiplied, both parts of the comparison can be multiplied by the same number, etc. For example,

3≡9 + 2 (mod 4) and 3-2≡9 (mod 4)

Simultaneously correct comparisons. And from a pair of correct comparisons 3≡11 (mod 4) and 1≡5 (mod 4) the following are correct:

3 + 1≡11 + 5 (mod 4)

3-1≡11-5 (mod 4)

3 1≡11 5 (mod 4)

3 2 ≡11 2 (mod 4)

3 23≡11 23 (mod 4)

Methods for solving various comparisons are considered in number theory, i.e. methods for finding integers that satisfy comparisons of one kind or another. Modulus comparisons were first used by the German mathematician Karl Gauss in his 1801 book "Arithmetic Investigations". He also proposed the symbolism established in mathematics for comparisons.

Identity. B. Riemann (1857).

Identity - equality of two analytical expressions, valid for any admissible values ​​of the letters included in it. The equality a + b = b + a is true for all numerical values ​​of a and b, and therefore is an identity. To write identities in some cases, since 1857, the sign "≡" (read "identically equal") has been used, the author of which in this use is the German mathematician Georg Friedrich Bernhard Riemann. You can write a + b ≡ b + a.

Perpendicularity. P. Erigon (1634).

Perpendicularity - mutual arrangement two straight lines, planes or a straight line and a plane, in which the specified figures form a right angle. The ⊥ sign to denote perpendicularity was introduced in 1634 by the French mathematician and astronomer Pierre Erigon. The concept of perpendicularity has a number of generalizations, but all of them, as a rule, are accompanied by the ⊥ sign.

Parallelism. W. Outred (posthumous edition 1677).

Parallelism is a relationship between some geometric shapes; for example, straight lines. Defined differently depending on different geometries; for example, in the geometry of Euclid and in the geometry of Lobachevsky. The sign of parallelism has been known since ancient times; it was used by Heron and Pappus of Alexandria. At first, the symbol was similar to the current equal sign (only longer), but with the appearance of the latter, to avoid confusion, the symbol was rotated vertically ||. As such, he first appeared in the posthumous edition of the works of the English mathematician William Outread in 1677.

Intersection, unification. J. Peano (1888).

The intersection of sets is a set to which those and only those elements belong that simultaneously belong to all given sets. Union of sets - a set containing all the elements of the original sets. Intersection and union are also called operations on sets that associate new sets with certain sets according to the above rules. ∩ and ∪ are denoted, respectively. For example, if

A = (♠ ♣) and B = (♣ ♦),

That

А∩В = {♣ }

А∪В = {♠ ♣ ♦ } .

Contains, contains. E. Schroeder (1890).

If A and B are two sets and there are no elements in A that do not belong to B, then A is said to be contained in B. They write A⊂B or B⊃A (B contains A). For instance,

{♠}⊂{♠ ♣}⊂{♠ ♣ ♦ }

{♠ ♣ ♦ }⊃{ ♦ }⊃{♦ }

The symbols "contains" and "contains" appeared in 1890 by the German mathematician logician Ernst Schroeder.

Affiliation. J. Peano (1895).

If a is an element of the set A, then they write a∈A and read "a belongs to A". If a is not an element of the set A, write a∉A and read "and does not belong to A". Initially, the relationship "contains" and "belongs" ("is an element") was not distinguished, but over time these concepts demanded a distinction. The ∈ was first used by the Italian mathematician Giuseppe Peano in 1895. The symbol ∈ comes from the first letter of the Greek word εστι - to be.

The quantifier of universality, the quantifier of existence. G. Genzen (1935), C. Pearce (1885).

Quantifier is a general name for logical operations that indicate the area of ​​truth of a predicate (mathematical statement). Philosophers have long paid attention to logical operations that limit the scope of truth of a predicate, but did not single them out as a separate class of operations. Although quantifier-logical constructions are widely used both in scientific and everyday speech, their formalization took place only in 1879, in the book of the German logician, mathematician and philosopher Friedrich Ludwig Gotlob Frege "The Calculus of Concepts". Frege's designations looked like bulky graphic constructions and were not accepted. Subsequently, many more successful symbols were proposed, but the generally accepted notation became ∃ for the existential quantifier (read "exists", "will be found"), proposed by the American philosopher, logician and mathematician Charles Pearce in 1885, and ∀ for the universal quantifier (read "any" , "everyone", "everyone"), formed by the German mathematician and logician Gerhard Karl Erich Gentzen in 1935 by analogy with the existential quantifier symbol (inverted first letters English words Existence and Any). For example, the entry

(∀ε> 0) (∃δ> 0) (∀x ≠ x 0, | x-x 0 |<δ) (|f(x)-A|<ε)

reads as follows: "for any ε> 0, there is δ> 0 such that for all x not equal to x 0 and satisfying the inequality | x-x 0 |<δ, выполняется неравенство |f(x)-A|<ε".

Empty set. N. Burbaki (1939).

A set containing no elements. The empty set sign was introduced in the books of Nicolas Bourbaki in 1939. Bourbaki is a collective pseudonym for a group of French mathematicians created in 1935. One of the members of the Bourbaki group was André Weil, the author of the Ø symbol.

Q.E.D. D. Knuth (1978).

In mathematics, a proof is understood as a sequence of reasoning, built on certain rules, showing that a certain statement is true. Since the Renaissance, the end of the proof was denoted by mathematicians by the abbreviation "Q.E.D.", from the Latin expression "Quod Erat Demonstrandum" - "What was required to prove." When creating a typesetting system ΤΕΧ in 1978, the American computer science professor Donald Edwin Knuth used a symbol: a filled square, the so-called "Halmos symbol", named after the American mathematician of Hungarian origin Paul Richard Halmos. Today, the completion of a proof is usually denoted by the Halmos Symbol. Alternatively, other signs are used: an empty square, a right triangle, // (two slashes), as well as the Russian abbreviation "ch.t.d."

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Balagin Victor

With the discovery of mathematical rules and theorems, scientists came up with new mathematical notation, signs. Mathematical signs are symbols used to write mathematical concepts, sentences, and calculations. In mathematics, special symbols are used to shorten the notation and more accurately express the statement. In addition to numbers and letters of various alphabets (Latin, Greek, Hebrew), the mathematical language is used by many special characters invented over the past few centuries.

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MATHEMATICAL SYMBOLS.

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MATHEMATICAL SYMBOLS.

1. Introduction

The word mathematician came to us from ancient Greek, where μάθημα meant "to learn", "to acquire knowledge." And the one who says: "I do not need mathematics, I am not going to become a mathematician" is not right. Everybody needs math. Revealing the amazing world of the numbers around us, she teaches us to think more clearly and more consistently, develops thought, attention, fosters perseverance and will. MV Lomonosov said: "Mathematics puts the mind in order." In short, mathematics teaches us to learn to acquire knowledge.

Mathematics is the first science that a person could master. The oldest activity was counting. Some primitive tribes counted the number of objects using their fingers and toes. The rock drawing, preserved to our times from the Stone Age, depicts the number 35 in the form of 35 sticks drawn in a row. We can say that 1 stick is the first mathematical symbol.

The mathematical "writing" that we now use - from the notation of the unknown by the letters x, y, z to the integral sign - has evolved gradually. The development of symbolism simplified the work with mathematical operations and contributed to the development of mathematics itself.

From the ancient Greek "symbol" (Greek. symbolon - sign, omen, password, emblem) - a sign that is associated with the objectivity it denotes in such a way that the meaning of the sign and its object are represented only by the sign itself and are revealed only through its interpretation.

With the discovery of mathematical rules and theorems, scientists came up with new mathematical notation, signs. Mathematical signs are symbols used to write mathematical concepts, sentences, and calculations. In mathematics, special symbols are used to shorten the notation and more accurately express the statement. In addition to numbers and letters of various alphabets (Latin, Greek, Hebrew), the mathematical language is used by many special characters invented over the past few centuries.

2. Signs of addition, subtraction

The history of mathematical notation begins in the Paleolithic. Stones and bones with notches used for counting date from this time. The most famous example isIshango bone... The famous bone from Ishango (Congo), dating from about 20 thousand years BC, proves that already at that time a person performed quite complex mathematical operations. The notches on the bones were used for addition and were applied in groups, symbolizing the addition of numbers.

Ancient Egypt already had a much more advanced designation system. For example, inAhmes papyrusas a symbol for addition, the image of two legs going forward along the text is used, and for subtraction, two legs going backward.The ancient Greeks referred to addition by writing side by side, but from time to time they used the slash “/’ ”and the semi-elliptic curve for subtraction.

Symbols for the arithmetic operations of addition (plus “+’ ’”) and subtraction (minus “-‘ ’) are so common that we almost never think that they did not always exist. The origin of these symbols is unclear. One of the versions is that they were previously used in trading as signs of profit and loss.

It is also believed that our signcomes from one of the forms of the word "et", which in Latin means "and". Expression a + b it was written in Latin like this: a et b ... Gradually, due to frequent use, from the sign " et " remains only " t "which, over time, turned into"+ ". The first person who may have used the signas an abbreviation for et, was the astronomer Nicole D'Orem (author of The Book of the Sky and the World '') in the middle of the fourteenth century.

In the late fifteenth century, the French mathematician Schiquet (1484) and the Italian Pacioli (1494) used “'' or " ’’ (Denoting “plus”) for addition and “'' or " '' (Denoting 'minus') for subtraction.

Subtraction notation was more confusing because instead of the simple “”In German, Swiss and Dutch books, the symbol“ ÷ ’” was sometimes used, which we now denote division. Several books of the seventeenth century (eg Descartes and Mersenne) use two dots “∙ ∙’ ”or three dots“ ∙ ∙ ∙ ’’ ”to denote subtraction.

The first use of the modern algebraic sign “”Refers to a 1481 German manuscript on algebra that was found in the Dresden library. In a Latin manuscript from the same time (also from the Dresden library), there are both symbols: “" and " - " . The systematic use of the signs ""And" - "for addition and subtraction occurs inJohann Widmann. German mathematician Johann Widmann (1462-1498) was the first to use both signs to mark the presence and absence of students in his lectures. True, there is information that he "borrowed" these signs from a little-known professor at the University of Leipzig. In 1489, he published in Leipzig the first printed book (Mercantile Arithmetic - "Commercial arithmetic"), in which both signs were present and , in the work "A quick and pleasant account for all traders" (c. 1490)

As a historical curiosity, it is worth noting that even after the adoption of the signnot everyone used this symbol. Widmann himself introduced it as a Greek cross(the sign we use today), where the horizontal bar is sometimes slightly longer than the vertical one. Some mathematicians, such as Record, Harriot, and Descartes, used the same sign. Others (such as Hume, Huygens, and Fermat) used the Latin cross "†", sometimes horizontal, with a bar at one end or the other. Finally, some (like Halley) used a more decorative look. " ».

3.Equality sign

An equal sign in mathematics and other exact sciences is written between two expressions that are identical in size. Diophantus was the first to use the equal sign. He designated equality with the letter i (from the Greek isos - equal). Vancient and medieval mathematicsequality was denoted verbally, for example, est egale, or they used the abbreviation “ae” from the Latin aequalis - “equal”. Other languages ​​also used the first letters of the word "equal", but this was not generally accepted. The equal sign "=" was introduced in 1557 by a Welsh physician and mathematicianRobert Record(Recorde R., 1510-1558). In some cases, the symbol II served as a mathematical symbol for denoting equality. The record introduced the '=' symbol with two identical horizontal parallel lines, much longer than those used today. English mathematician Robert Record was the first to use the symbol "equality", arguing with the words: "no two objects can be equal to each other more than two parallel segments." But back in17th centuryRene Descartesused the abbreviation "ae".Francois Vietthe equal sign denotes subtraction. For some time, the spread of the Record symbol was hindered by the fact that the same symbol was used to denote the parallelism of straight lines; in the end it was decided to make the parallelism symbol vertical. The sign got widespread only after the works of Leibniz at the turn of the 17th-18th centuries, that is, more than 100 years after the death of the one who first used it for thisRoberta Record... There are no words on his tombstone - just an equal sign carved.

Related symbols for approximate equality "≈" and identity "" are very young - the first was introduced in 1885 by Gunther, the second - in 1857Riemann

4. Signs of multiplication and division

The multiplication sign in the form of a cross ("x") was introduced by an Anglican mathematician priestWilliam Oughtred v 1631 year... Before him, the letter M was used for the multiplication sign, although other designations were proposed: the rectangle symbol (Erigon,), asterisk ( Johann Rahn, ).

Later Leibnizreplaced the cross with a dot (end17th century) so as not to confuse it with the letter x ; before him, such symbolism was found inRegiomontana (XV century) and an English scientistThomas Harriott (1560-1621).

To indicate the action of divisionOtredpreferred the forward slash. Colon began to denote divisionLeibniz... Before them, the letter D was also often used. Starting withFibonacci, is also used a line of fraction, which was used in Arabic writings. Division in the form obelus ("÷") introduced by a Swiss mathematicianJohann Rahn(about 1660)

5. Percentage sign.

One hundredth of a whole, taken as one. The word "percent" itself comes from the Latin "pro centum", which means "per hundred". In 1685, the book "A Guide to Commercial Arithmetic" by Mathieu de la Porta (1685) was published in Paris. In one place it was about percentages, which then stood for "cto" (short for cento). However, the typesetter mistook this "cto" for a fraction and printed "%". So, due to a misprint, this sign came into use.

6 the infinity sign

The current infinity symbol "∞" was introducedJohn Wallis in 1655. John Wallispublished a large treatise "Arithmetic of the Infinite" (lat.Arithmetica Infinitorum sive Nova Methodus Inquirendi in Curvilineorum Quadraturam, aliaque Difficiliora Matheseos Problemata), where he entered the symbol he inventedinfinity... It is still not known why he chose this particular sign. One of the most authoritative hypotheses connects the origin of this symbol with the Latin letter "M", which the Romans used to designate the number 1000.The infinity symbol was named "lemniscus" (Latin tape) by the mathematician Bernoulli about forty years later.

Another version says that the figure of the "figure of eight" conveys the main property of the concept of "infinity": movement endlessly ... On the lines of number 8, you can make endless movement, like on a cycle track. In order not to confuse the entered sign with the number 8, mathematicians decided to place it horizontally. Happened... This designation has become standard for all mathematics, not just algebra. Why is infinity not denoted by zero? The answer is obvious: do not turn the number 0 - it will not change. Therefore, the choice fell on 8.

Another option is a serpent devouring its own tail, which, one and a half thousand years BC in Egypt, symbolized various processes that have no beginning or end.

Many believe that the Mobius leaf is the progenitor of the symbol.infinity, because the infinity symbol was patented after the invention of the Mobius strip device (named after the nineteenth-century mathematician Moebius). A Mobius strip is a strip of paper that is curved and joined at its ends to form two spatial surfaces. However, according to available historical information, the infinity symbol began to be used to denote infinity two centuries before the discovery of the Mobius strip.

7. Signs coal and and perpendicular sti

The symbols " injection" and " perpendicular»Came up with 1634 yearFrench mathematicianPierre Erigon... The symbol of perpendicularity was inverted, resembling the letter T. The symbol of the angle resembled an icon, gave it a modern formWilliam Oughtred ().

8. Sign parallelism and

Symbol " parallelism»Known since ancient times, it was usedHeron and Pappus of Alexandria... At first, the symbol was similar to the current equal sign, but since the appearance of the latter, to avoid confusion, the symbol has been rotated vertically (Otred(1677), Kersey (John Kersey ) and other mathematics of the 17th century)

9. Number pi

The generally accepted designation of a number equal to the ratio of the circumference of a circle to its diameter (3.1415926535 ...) was first formed byWilliam jones v 1706 year, taking the first letter of the Greek words περιφέρεια -circle and περίμετρος - perimeter, that is, the circumference. I liked this cutEuler, whose works finally consolidated the designation.

10. Sine and cosine

The appearance of sine and cosine is interesting.

Sinus from Latin - sinus, depression. But this name has a long history. Indian mathematicians advanced far in trigonometry around the 5th century. The word "trigonometry" itself was not, it was introduced by Georg Klugel in 1770.) What we now call a sine, roughly corresponds to what the Indians called ardha-jiya, in translation - a half-string (ie half-chord). For brevity, they were called simply - jiya (bowstring). When the Arabs translated the works of the Hindus from Sanskrit, they did not translate the "bowstring" into Arabic, but simply transcribed the word in Arabic letters. It turned out to be a jiba. But since in the syllabic Arabic writing short vowels are not indicated, it really remains jb, which is similar to another Arabic word - jayb (cavity, sinus). When Gerard of Cremona translated the Arabs into Latin in the 12th century, he translated this word as sinus, which in Latin also means a bosom, a depression.

The cosine appears automatically, because the Hindus called him koti-jiya, or ko-jiya for short. Kochi is the curved end of a bow in Sanskrit.Modern short notation and introduced By William Oughtredand enshrined in the writings Euler.

The tangent / cotangent designations are of much later origin (the English word tangent comes from the Latin tangere - to touch). And even until now there is no unified designation - in some countries the designation tan is more often used, in others - tg

11. Abbreviation "What was required to be proved" (etc.)

Quod erat demonstrandum "(Quol erat lemonstranlum).
The Greek phrase means "what needed to be proved", and the Latin means "what needed to be shown." This formula ends every mathematical argument of the great Greek mathematician of Ancient Greece Euclid (III century BC). Translated from Latin - which was required to be proved. In medieval scientific treatises, this formula was often written in an abbreviated form: QED.

12. Mathematical notation.

13. Conclusion

Mathematical science is essential for a civilized society. Mathematics is found in all sciences. The language of mathematics is mixed with the language of chemistry and physics. But we still understand it. We can say that we begin to learn the language of mathematics together with our native speech. This is how mathematics inseparably entered our life. Thanks to the mathematical discoveries of the past, scientists create new technologies. The surviving discoveries make it possible to solve complex mathematical problems. And the ancient mathematical language is clear to us, and the discoveries are interesting to us. Thanks to mathematics, Archimedes, Plato, Newton discovered physical laws. We study them in school. In physics, there are also symbols, terms inherent in physical science. But the mathematical language is not lost among physical formulas. On the contrary, these formulas cannot be written without knowledge of mathematics. History preserves knowledge and facts for future generations. Further study of mathematics is necessary for new discoveries. To use the preview of presentations, create yourself a Google account (account) and log into it: https://accounts.google.com

Slide captions:

Mathematical symbols The work was completed by a 7th grade student of school No. 574 Balagin Viktor

A symbol (Greek symbolon - sign, omen, password, emblem) is a sign that is associated with the objectivity it denotes in such a way that the meaning of the sign and its object are represented only by the sign itself and are revealed only through its interpretation. Signs are mathematical conventions for recording mathematical concepts, sentences, and calculations.

Ishango Bone Part of Ahmes Papyrus

+ - Plus and minus signs. Addition was denoted by the letter p (plus) or the Latin word et (the conjunction "and"), and subtraction was denoted by the letter m (minus). The expression a + b was written in Latin like this: a et b.

Subtraction notation. ÷ ∙ ∙ or ∙ ∙ ∙ Rene Descartes Maren Mersenne

A page from the book of Johann Widmann na. In 1489, Johann Widmann published in Leipzig the first printed book (Mercantile Arithmetic - "Commercial arithmetic"), in which both signs + and - were present

Addition notation. Christian Huygens David Hume Pierre de Fermat Edmund (Edmond) Halley

The equal sign Diophantus was the first to use the equal sign. He designated equality with the letter i (from the Greek isos - equal).

The equal sign Proposed in 1557 by the English mathematician Robert Record “No two objects can be equal to each other more than two parallel segments.” In continental Europe, the equal sign was introduced by Leibniz

× ∙ The sign of multiplication Introduced in 1631 by William Oughtred (England) in the form of an oblique cross. Leibniz replaced the cross with a dot (late 17th century) so as not to confuse it with the letter x. William Oughtred Gottfried Wilhelm Leibniz

Percent. Mathieu de la Port (1685). One hundredth of a whole, taken as one. "Percentage" - "pro centum", which means - "one hundred". "Cto" (short for cento). The typesetter mistook "cto" for a fraction and typed "%".

Infinity. John Wallis John Wallis introduced the symbol he invented in 1655. The serpent devouring its tail symbolized various processes that have no beginning or end.

The infinity symbol began to be used to denote infinity two centuries before the discovery of the Mobius strip. The Mobius strip is a strip of paper that is curved and joined at its ends to form two spatial surfaces. August Ferdinand Möbius

Angle and perpendicular. The symbols were invented in 1634 by the French mathematician Pierre Erigon. Erigon's angle symbol resembled an icon. The perpendicularity symbol has been reversed to resemble the letter T. These signs were given their modern form by William Oughtred (1657).

Parallelism. The symbol was used by Heron of Alexandria and Pappus of Alexandria. At first, the symbol was similar to the current equal sign, but since the appearance of the latter, to avoid confusion, the symbol has been rotated vertically. Heron of Alexandria

Pi. π ≈ 3.1415926535 ... William Jones in 1706 π εριφέρεια is a circle and π ερίμετρος is a perimeter, that is, the length of a circle. This abbreviation was liked by Euler, whose works finally consolidated the designation. William jones

sin Sine and cosine cos Sinus (from Latin) - sinus, cavity. koti-jiya, or ko-jiya for short. Kochi - the curved end of the bow Modern abbreviations introduced by William Otred and enshrined in the writings of Euler. "Arha-jiva" - among the Indians - "half-string" Leonard Euler William Otred

Which is what was required to prove (etc.) "Quod erat demonstrandum" QED. This formula ends every mathematical argument of the great mathematician of Ancient Greece Euclid (III century BC).

The ancient mathematical language is clear to us. In physics, there are also symbols, terms inherent in physical science. But the mathematical language is not lost among physical formulas. On the contrary, these formulas cannot be written without knowledge of mathematics.

Continuation of the first part: Occult and mystical symbols and their meaning. Geometric Symbols, Universal Image Symbols and Concept Symbols. Emblems of modern religions. Crosses: the most common shapes. Images of time. Symbols of the kingdom of plants and animals. Mythical creatures.

Encyclopedia of symbols

Swastika straight (left-sided)

Swastika as a solar symbol

A straight (left-handed) swastika is a cross with ends bent to the left. Rotation is considered to occur clockwise (opinions sometimes differ in determining the direction of movement).

A straight swastika is a symbol of blessing, a good omen, prosperity, good luck and aversion to trouble, as well as a symbol of fertility, longevity, health and life. It is also a symbol of the masculine principle, spirituality, which inhibits the flow of lower (physical) forces and allows the energies of a higher, divine nature to manifest.

Reverse swastika (right-sided)

Swastika on a Nazi military medal

The reverse (right-handed) swastika is a cross with the ends bent to the right. Rotation is considered to be counterclockwise.

The reverse swastika is usually associated with the feminine principle. Sometimes it is associated with the launching of negative (physical) energies, blocking the passage to the exalted forces of the spirit.

The Sumerian swastika, formed by four women and their hair, symbolizes the female generative power

Pentagram (pentacle): the general meaning of the symbol

Pentagram sign

The pentagram, written in one line, is the oldest of all symbols that we own. Had different interpretations in different historical times of mankind. She became the Sumerian and Egyptian star sign.

Later symbolism: five senses; masculine and feminine principles, expressed by five points; harmony, health and mystical powers. The pentagram is also a symbol of the victory of the spiritual over the material, a symbol of security, protection, and a safe return home.

Pentagram as a magic symbol

Pentagrams of the White and Black Magicians

The pentacle with one end up and two down is a sign of white magic known as the "druid's foot"; with one end down and two up, it represents the so-called "goat's hoof" and the devil's horns - a characteristic symbolism change of sign from positive to negative when it is turned over.

The Pentagram of the White Magician is a symbol of magical influence and the domination of disciplined Will over the phenomena of the world. The will of the Black Magician is directed towards destruction, towards refusal to fulfill a spiritual task, therefore the inverted pentagram is regarded as a symbol of evil.

Pentagram as a symbol of a perfect person

The pentagram symbolizing the perfect person

The pentagram, a five-pointed star, is a symbol of a perfect man standing on two legs with his arms outstretched. We can say that a person is a living pentagram. This is true both physically and spiritually - a person has five virtues and manifests them: love, wisdom, truth, justice and kindness.

Truth belongs to the spirit, love to the soul, wisdom to the intellect, kindness to the heart, justice to the will.

Double pentagram

Double pentagram (man and the universe)

There is also a correspondence between the human body and the five elements (earth, water, air, fire and ether): will corresponds to earth, heart to water, intellect to air, soul to fire, spirit to ether. Thus, by his will, intellect, heart, soul, spirit, a person is connected with the five elements working in space, and he can consciously work in harmony with them. This is the meaning of the symbol of the double pentagram, in which the small is inscribed in the large: a person (microcosm) lives and acts inside the Universe (macrocosm).

Hexagram

Hexagram image

Hexagram is a figure made up of two polar triangles, a six-pointed star. It is a complex and one-piece symmetrical shape in which six small individual triangles are grouped around a large central hexagon. The result is a star, although the original triangles retain their identity. Since the upward-facing triangle is a heavenly symbol, and the downward-facing triangle is a symbol of the earthly, together they are a symbol of a person who unites these two worlds. It is a symbol of a perfect marriage that connects a man and a woman.

Solomon's seal

Solomon's Seal, or Star of David

This is the famous magic seal of Solomon, or the Star of David. The top triangle in her image is white and the bottom triangle is black. It symbolizes, first of all, the absolute law of analogy, expressed by the mystical formula: "That which is below is similar to that which is above."

Solomon's seal is also a symbol of human evolution: one must learn not only to take, but also to give, absorb and radiate at the same time, to radiate - for the Earth, to receive - from Heaven. We receive and are filled only when we give to others. This is the perfect union of spirit and matter in man - the union of the solar plexus and the brain.

Five pointed star

Five pointed star

Star of bethlehem

The five-pointed star is interpreted in different ways, including it symbolizes joy and happiness. It is also the emblem of the Semitic goddess Ishtar in her warlike incarnation, and in addition, the Star of Bethlehem. Among the Masons, the five-pointed star symbolizes the mystical center.

The Egyptians attached great importance to the five- and six-pointed stars, as is evident from the text preserved on the wall of the burial temple of Hatshepsut.

Seven pointed star

Seven-pointed star of magicians

The seven-pointed star repeats the characteristic features of the five-pointed one. The Gnostic star has seven rays.

Seven- and nine-pointed stars, drawn in one line, are mystical stars in astrology and magic.

The star of the magicians is read in two ways: sequentially along the course of the rays (along the line of the outline of the star) and along the circumference. In the course of the rays are the planets that control the days of the week: the Sun - Sunday, the Moon - Monday, Mars - Tuesday, Mercury - Wednesday, Jupiter - Thursday, Venus - Friday, Saturn - Saturday.

Nine pointed star

The nine-pointed star of the magicians

Nine-pointed stars, like seven-pointed stars, if they are drawn in one line, are mystical stars in astrology and magic.

The nine-pointed star, made up of three triangles, symbolizes the Holy Spirit.

Monad

The four constituent parts of the monad

It is a magical symbol named by the monad John Dee (1527-1608), counselor and astrologer to Queen Elizabeth I of England.

Dee presents the nature of magic symbols in terms of geometry and tests the monad in a number of theorems.

Dee researches the monad at such a deep level that he finds connections between his theory and Pythagorean harmony, biblical knowledge, and mathematical proportions.

Spiral

Spiral structure of the milky way

Spiral shapes are very common in nature, ranging from spiral galaxies to whirlpools and tornadoes, from shellfish to drawings on human fingers, and even the DNA molecule has the shape of a double helix.

The spiral is a very complex and ambiguous symbol. But above all, it is a symbol of the great creative (life) force both at the level of the cosmos and at the level of the microcosm. The spiral is a symbol of time, cyclical rhythms, changing seasons of the year, birth and death, phases of "aging" and "growth" of the Moon, as well as the Sun itself.

Tree of life

The tree of life in a human being

Tree of life

The Tree of Life does not belong to any culture - not even the Egyptians. It is beyond races and religions. This image is an integral part of nature ... Man himself is a miniature Tree of Life. He possessed immortality when associated with this tree. The Tree of Life can be thought of as the arteries of a large cosmic body. Through these arteries, as through channels, the life-giving forces of the cosmos flow, which feed all forms of existence, and the cosmic pulse of life beats in them. The Tree of Life is a separate section, part of the universal life code scheme.

Sphere

Armillary sphere (engraving from the book by Tycho Brahe)

A symbol of fertility (like a circle), as well as integrity. In ancient Greece, the sign of the sphere was a cross in a circle - an ancient emblem of power. A sphere made up of several metal rings, illustrating the cosmogonic theory of Ptolemy, who believed that the Earth was at the center of the universe, is an ancient emblem of astronomy.

Platonic solids

Platonic solids inscribed in a sphere

Platonic Solids - Five Unique Shapes. Long before Plato, Pythagoras used them, calling them ideal geometric bodies. Ancient alchemists and such great minds as Pythagoras believed that these bodies are associated with certain elements: cube (A) - earth, tetrahedron (B) - fire, octahedron (C) - air, icosahedron (D) - water, dodecahedron ( E) is ether, and the sphere is emptiness. These six elements are the building blocks of the universe. They create the qualities of the universe.

Symbols of planets

Symbols of planets

The planets are depicted by a combination of the simplest geometric symbols. It is a circle, a cross, an arc.

Consider, for example, the symbol for Venus. The circle is located above the cross, which personifies a kind of "spiritual attraction" that pulls the cross upward into the elevated areas belonging to the circle. The cross, subject to the laws of generation, decay and death, will find its redemption if it is lifted up inside this great circle of spirituality. The symbol as a whole represents the feminine principle in the world, which is trying to spiritualize and protect the material sphere.

Pyramid

Great pyramids of Cheops, Khafre and Mikerin

The pyramid is a symbol of the hierarchy that exists in the Universe. In any area, the pyramid symbol can help move from the lower plane of plurality and fragmentation to the higher plane of oneness.

It is believed that the initiates chose the shape of a pyramid for their sanctuaries because they wanted the lines converging to the top, rushing towards the Sun to teach humanity a lesson in unity.

Star tetrahedron

Star tetrahedron

A star tetrahedron is a figure consisting of two intersecting tetrahedrons. This figure can also be thought of as a 3D Star of David.

Tetrahedrons appear as two opposite laws: the law of the spirit (radiation, bestowal, selflessness, selflessness) and the law of matter (being pulled inward, cooling, freezing, paralysis). Only a person can consciously combine these two laws, since he is a connecting link between the world of spirit and the world of matter.

Thus, the star tetrahedron represents the two poles of creation in complete equilibrium.

Generic Image Symbols

A thing is just not because God wants it, but God wants it precisely because it is just.

Symbols-images are often objects (things) or graphic images that imitate the form of the creature or object with which they are associated. Their meanings are sometimes unexpected, but more often obvious, since they are based on a certain quality that is inherent in these objects or creatures: lion - courage, rock - stamina, etc.

Arch, arc

Sacrifice to an Astral Deity (from a 13th century Arabian manuscript)

Arch (arc), first of all, is a symbol of the firmament, the God of Heaven. In initiation rites, passing through the arch means rebirth after completely abandoning one's old nature. In ancient Rome, an army passed through the triumphal arch after defeating the enemy.

Arch and arch are common elements in the culture of Islam. Mosques often have arched entrances. It is believed that a person entering the mosque through an arched door will be protected by the symbolic forces of the spiritual (higher) sphere.

Ba-gua

Ba-gua and the Great Monad (charm against evil forces, China)

Ba-gua (in some sources pa-kua) - eight trigrams and pairs of opposites, usually arranged in a circle, which symbolizes time and space.

scales

Weighing scales. The lung gives way. Heavy pulls

Libra symbolizes justice, impartiality, judgment, assessment of the merits and demerits of a person. A symbol of the balance of all opposites and complementary factors. The attribute of Nemesis is the goddess of fate.

Disk

Solar winged disc (Egypt)

The disc is a multidimensional symbol: the symbol of creation, the center of the Void, the Sun, Heaven, deity, spiritual and heavenly perfection. The disc of the rising sun is a symbol of the renewal of life, life after death, resurrection. The disc of the Sun with a horned moon or horns means a combination of solar and lunar deities, the unity of two in one.

The winged disk is a solar deity, the fire of Heaven, the combination of the solar disk and the wings of a falcon or eagle, the movement of the celestial sphere around its axis, transformation, immortality, producing the power of nature and its duality (protective and deadly aspects).

Wand, staff, scepter

Tutankhamun's hook and flail staff

The wand, staff and scepter are ancient emblems of supernatural power.

The wand is a symbol of transformation associated with witchcraft and mysterious creatures. The staff is a symbol of masculine strength and power, often associated with the energy of trees, phallus, snake, hand (pointing finger). It is also an attribute of pilgrims and saints, but it can also mean knowledge, which is the only support of a person. The scepter is more ornate and associated with supreme deities and rulers, with spiritual authority and at the same time compassionate wisdom.

Mirror

The divination scene depicted on the back of a bronze mirror (Greece)

Symbolizes truth, self-realization, wisdom, mind, soul, a reflection of the supernatural and divine intellect reflected in the Sun, Moon and stars, the clearly shining surface of divine truth.

It is believed that the mirror has magical properties and is the entrance to the looking glass world. If a mirror hangs with a reflective surface down in a temple or above a tomb, it opens the way for the ascent of the soul. In magic, mirrors serve to develop the gaze.

Snake Ourobor (Oroboro, Ouroboros)

A snake biting its own tail

The ring-shaped figure depicting a snake biting its own tail is a symbol of eternity, indivisibility, cyclical time, alchemy. The symbolism of this figure is interpreted in different ways, as it combines the creative symbolism of the egg (the space within the figure), the earthly symbolism of the snake and the heavenly symbolism of the circle. In addition, the snake biting its tail is a symbol of the law of karma, the wheels of samsara are the wheels of the Incarnation.

Caduceus

Caduceus

Caduceus (Greek - "messenger's staff") is often called the rod of Hermes (Mercury), the ancient god of wisdom. This is a "magic" wand with small wings, which is entwined by two snakes, intertwined so that the bodies of the snakes form two circles around the rod, symbolizing the fusion of two polarities: good - evil, right - left, light - darkness, etc., which corresponds to the nature of the created world.

All messengers wear a caduceus as a sign of peace and protection, and it is their main attribute.

Key

Saint Peter with the keys to the gates of paradise (detail of the stone image, Notre Dame, Paris, XII century)

The key is a very powerful symbol. This is power, power of choice, breath, freedom of action, knowledge, initiation. The crossed gold and silver keys are the emblem of the papal power, the symbolic “keys to the Kingdom of Heaven” that Christ gave to the Apostle Peter. While keys can both lock and unlock doors, they are almost always symbols of access, liberation, and (in initiation rites) initiation, a progressive progression from one stage of life to the next. In Japan, the keys to the rice storage are a symbol of prosperity.

Wheel

Wheel of law

The wheel of existence (samsara)

The wheel is a symbol of solar energy. The sun is the center, the spokes of the wheel are the rays. The wheel is an attribute of all solar gods and earthly rulers. It also symbolizes the life cycle, rebirth and renewal, nobility, variability and changes in the material world (a circle is the limit of the material world, and the center is a "stationary engine", a cosmic source of light and power).

The spinning wheel is associated with the cycles of manifestation (birth, death and rebirth) and the fate of a person.

At the ordinary level, the wheel of Lady Luck (the wheel of fortune) is a symbol of ups, downs and the unpredictability of fate.

Chariot

Ancient hero on a chariot symbolizing his readiness for battle

A dynamic symbol of power, power and speed of movement of gods, heroes or allegorical figures. The chariot is also a symbol of human nature: the charioteer (consciousness), using the reins (willpower and mind), controls the horses (vital forces), carrying the cart (body).

The chariot (in Hebrew - Merkaba) is also a symbol of the chain of descent from God through man into the world of phenomena and then the triumphant ascent of the spirit. The word "Merkaba" also means the human body of light.

Cauldron, bowl

Ritual Cauldron (China, 800 BC)

Carl Jung views the cup as a feminine symbol that accepts and gives. On the other hand, the cup can be a symbol of a difficult fate ("bitter cup"). The so-called poisoned cup promises hope, but brings trouble.

The cauldron is a more powerful symbol and is often associated with ritual and magic, representing transformative power. The cauldron is also a symbol of abundance, an inexhaustible source of life support, the forces of revitalization, the reproductive forces of the earth, the revival of warriors for a new battle.

Blood

Detail of the painting by Fey Pomeranes "The Sixth Palace of the Underworld": from a glass resembling the shape of an ankh, the last drops of blood flow - a symbol of life

Ritual symbol of vitality. In many cultures, blood is believed to contain some of the divine energy or, more generally, the spirit of the individual.

Blood is red solar energy. It personifies the principle of life, soul, strength, including rejuvenating. Drinking someone's blood means becoming related, but you can also absorb the strength of the enemy and thereby protect him after death. The mixing of blood is a symbol of union in popular customs (for example, brotherhood by blood) or an agreement between people, as well as between man and God.

Maze

Plan of a medieval dance-labyrinth on the marble floor of the Cathedral in Chartres (France)

The labyrinth symbolizes the world, the Universe, incomprehensibility, movement, a complex problem, an enchanted place. This is a symbol of mystery, enigma, which has many different interpretations, often contradictory, sometimes frightening.

Images of the labyrinth on houses are considered an amulet to protect against hostile forces and evil spirits.

Burials, burial caves and labyrinthine burial mounds protect the dead and prevent them from returning.

Lotus

Vishnu and Lakshmi overseeing creation: Brahma grows from a lotus flower originating from Vishnu's navel

The amazing veneration of the lotus in various cultures is explained both by the extraordinary beauty of the flower and by the analogy between it and the idealized form of the vulva as the divine source of life. Therefore, the lotus, first of all, is a symbol of fertility, birth and rebirth. Lotus is the source of cosmic life, a symbol of the gods who created the world, as well as the sun gods. The lotus symbolizes the past, present and future, as each plant has buds, flowers and seeds at the same time. This is a symbol of a noble man who has grown out of mud, but not soiled by it.

moon

Above - the waxing moon and the full moon; below - the waning moon and new moon

The moon is the mistress of the feminine principle. It symbolizes abundance, cyclical renewal, rebirth, immortality, occult power, mutability, intuition and emotion. The ancients measured time by the cycles of the moon; determined the timing of the onset of ebbs and flows; predicted what the future harvest would be.

Although the symbolism of the moon is usually positive, in some cultures it is represented as an evil eye watching what is happening, associated with death and the ominous darkness of the night.

Magic circle

Dr. Johann Faust and Mephistopheles (from Christopher Mardlowe's book The Tragic Story of Dr. Faustus, 1631)

The magic circle is the basis of ceremonial magic. It serves as a symbol of the magician's will and at the same time as a protective barrier that protects the magician from the negative influence of the invisible world. All magical operations are performed in such a circle. Different circles are used for different purposes. The drawing of a circle is a certain magical ritual that must be performed according to all the established rules. In addition, the tracing of magic circles and inscriptions is believed to contribute to the development of self-control and gait.

Mandala

The circle and square of the mandala represent the spherical shape of Heaven and the rectangular shape of the Earth. Together they symbolize the order of things in space and in the world of people.

It is a geometric composition that symbolizes a spiritual, cosmic or psychic order. In Sanskrit, mandala means circle. Even when this geometric composition is based on squares or triangles, it still has a concentric structure. The overall meaning of the composition remains unchanged and symbolizes a guiding mind, supernatural structures, clarity of enlightenment.

Mandorla, or Vesica Piscis (surrounds the entire body of the persona)

Mandorla, or Vesica Piscis

The image of an almond-shaped halo (radiance), which was used in medieval Christian art to highlight the figure of Christ ascending into heaven, and sometimes ascending saints.

In mysticism "almond" (in Italian - mandorla) is a symbol of purity and chastity. Mandorla, due to its oval shape, was in ancient times a symbol of the vulva. It is also a graphic representation of a flame, a symbol of spirituality. On the other hand, it symbolizes the dualistic unity of Heaven and Earth, depicted as two intersecting arcs.

Halo

Halo of Buddha

A kind of halo: a luminous circle that surrounds a person's head. The golden halo symbolizes the sanctity of the person or confirms the fact that a person directly communicates with a higher plane.

The image of the halo is borrowed from the magical symbolism of the Egyptians, as evidenced by images from the ancient Egyptian "Book of the Dead".

Nimbus

Halos and halos surrounding the heads of the saints symbolize the Light of God emanating from them.

Halo is a type of halo: a luminous ring around the head. It symbolizes spiritual power, as opposed to the secular power represented by the crown. Sometimes the halo is used as an attribute of the Phoenix bird as a symbol of solar power and immortality.

Halo can be blue, yellow, or iridescent. In Greek mythology, the blue halo is an attribute of Zeus as the god of Heaven. The Romans have a blue halo - an attribute of Apollo and Jupiter. A triangular halo or a rhombus-shaped halo means God the Father.

Sword

Inlaid swords found by Schliemann at Mycenae (Athens, National Museum)

The sword is one of the most complex and most common symbols. On the one hand, the sword is a formidable weapon that carries life or death, on the other, it is the most ancient and powerful force that arose simultaneously with the Cosmic Balance and was its opposite. The sword is also a powerful magical symbol, the emblem of witchcraft. In addition, the sword is a symbol of power, justice, higher justice, all-pervading reason, discernment, phallic power, light. The sword of Damocles is a symbol of fate. Broken sword - defeat.

Bird feather

Aztec Feather Headpiece (Drawing from Codex Mendoza)

The bird's feather symbolizes truth, lightness, Heaven, height, speed, space, soul, the element of wind and air, opposed to the principle of humidity, dryness, travel outside the material world. In a broader sense, the feathers worn by shamans, priests, or rulers symbolized a magical connection with the spirit world or divine authority and protection. Wearing feathers or feathered hairstyles means taking on the power of a bird. Two feathers symbolize light and air, two poles, resurrection. The white feather symbolizes clouds, sea foam and cowardice.

Horns

Image of the Persian king of the Sassanian period

The horns symbolize supernatural power, deity, soul power or life principle that arises from the head. Horns are both solar and lunar symbols. Sharp and stabbing, the horns are a phallic and masculine symbol; being hollow, they signify femininity and receptivity. The horned gods symbolize warriors, fertility for both humans and animals. The horns with a long ribbon falling from them represent the god of the storm. In later times, the horns became a symbol of shame, contempt, depravity, and a deceived husband.

Hand

"Hand of Fatima" (Muslim carved pendant)

Power (secular and spiritual), action, strength, domination, protection - these are the main symbols that reflect the important role of the hand in a person's life and the belief that it is capable of transmitting spiritual and physical energy.

The hands of kings, religious leaders, and miracle workers are believed to have healing powers; hence the laying on of hands in a religious blessing, at confirmation and ordination. They bless with their right hand, with their left they curse. In Islam, the open palm of Fatima, the daughter of Muhammad, symbolizes five principles: faith, prayer, pilgrimage, fasting, mercy.

The sun

Variants of the image of the solar disk

The sun is one of the twelve symbols of power, the main symbol of creative energy.

As a source of warmth, the Sun represents vitality, passion, courage and eternal youth. As a source of light, it symbolizes knowledge, intelligence. In most traditions, the Sun is a symbol of the masculine principle. The sun is also life, vitality, the embodied character of the person, the heart and his aspirations. The sun and the moon are gold and silver, king and queen, soul and body, etc.

Tetramorphs

Image of Christ with tetramorphs in the corners (from the manuscript of the XII-XIII centuries)

Tetramorphs are considered a synthesis of the forces of the four elements. In some cults, these are four-headed guards of the four cardinal points. In many traditions, they symbolize the universality of divine protection and protection from the return of the primordial chaos.

The four biblical tetramorphs have the heads of a man, a lion, an ox, and an eagle. Subsequently, in Christianity, these images began to be identified with the apostles - Saints Matthew, Mark, Luke and John, as well as with the incarnation of Jesus Christ, his resurrection and ascension.

Thyrsus

Thyrsus

Thyrsus is the rod of the Greek god of wine Dionysus (in Roman mythology Bacchus). It is a spear-shaped pole (originally of a hollow dill stalk) topped with a pine cone or bunch of grapes and entwined with grapevines or ivy. Symbolizes the fertilizing, fertile power - both sexual and plant.

The cone is present on the thyrsus, probably because fermented pine resin was mixed with the wine that was drunk during the bacchanalia - it was believed that this enhances the sexual sensations.

Ax (poleaxe)

Great Mother with a double ax in her hands (the ax here is a phallic symbol)

The ax is a symbol of power, thunder, fertility, rain brought by the heavenly gods, and storm winds, correction of mistakes, sacrifice, support, help. It is also a common symbol of sovereignty associated with the ancient sun gods.

The double ax (double-sided ax) denotes the sacred union of the god of Heaven and the goddess of Earth, thunder and lightning. Sometimes the crescent-shaped blades of a double-sided ax symbolize the Moon or the unity of opposites. It is also a symbol of supreme power and strength.

Trident

Vishnu's trident as a symbol of his triune essence: creator, guardian and destroyer (from a picture from Rajasthan, 18th century)

The trident is the most famous symbol of power over the sea and an attribute of the ancient Greek god Poseidon (in Roman mythology - Neptune).

The trident symbolizes thunder and lightning, three tongues of flame, a triple weapon - the forces of heaven, air and water. It is a weapon and attribute of all heavenly, thunderous gods and storm goddesses, as well as all water gods, power and fertility of waters. Can symbolize the Heavenly Triad, as well as past, present and future.

Trigrams

The Eight Trigrams Underlying The Book of Changes

Trigrams are a triple combination of continuous (yang) and discontinuous (yin) lines. There are eight of them, and they formed the basis of the great Chinese book of predictions "The Book of Changes" ("I-Ching"). Trigrams symbolize the Taoist doctrine that the cosmos is based on constant streams of complementary forces: masculine (active, yang) and feminine (passive, yin).

Trigrams also personify the three essences of man - his body, soul and spirit; irrational emotions, rational mind and super-rational intelligence.

Trikvetra (three-pointed swastika)

Trikvetra

Trikvetra has a lot of swastika symbolism. It is also the movement of the Sun: at sunrise, at zenith and at sunset. Suggestions were made about the connection of this symbol with the lunar phases and the renewal of life. Like the swastika, it is a symbol that brings good luck. He often appears with solar symbols; it can be seen on ancient coins, on Celtic crosses, where it is believed to symbolize the triad and is the symbol of the sea god Manannan. It is also found in Teutonic symbolism, where it is associated with Thor.

Triskelion

Triskelion

Dynamic energy symbol in the form of three legs connected together. It is similar to a swastika, but with three rather than four bent beams, creating the effect of a cyclical movement. As a motif in Celtic art and on Greek coins and shields, the triskelion has less to do with the solar and lunar phases (one of the suggested meanings), but with power and physical strength. In addition, the triskelion is a symbol of victory and progress.

Shamrock

Shamrock

Heraldic shamrock

The shamrock clover symbolizes unity, balance, and destruction. The oxalis shamrock, which the Arabs call shamrah, symbolizes the Persian triads. The shamrock is generally a symbol of triads, it is the Mystical Tree, the "sun wheel". In Christianity - the symbol of the Trinity, as well as the emblem of St. Patrick and the coat of arms of Ireland.

To always be profitable, carry a dried shamrock with you.

Trimurti

Trimurti - Indian Trinity (sketch of a very ancient image on granite, India House Museum)

The sacred Hindu Trinity is Brahma, Vishnu and Shiva. It symbolizes three cycles of being: creation, preservation and destruction. Despite similarities to the Christian Trinity, Trimurti is not a monotheistic concept of a "triune god."

Trimurti is sometimes depicted as a turtle. She also symbolizes the Great Mother - both in her terrible manifestation (with symbols of flame and skulls) and in her wholesome (like Lotus, Sophia, Tara, as wisdom and compassion).

Trinity

Trinity Symbol - Father, Son and Holy Spirit - as One God

The Trinity differs from the triad in that it is unity, the union of three in one and one in three. It is a symbol of unity in diversity.

In Christianity, these are Father, Son and Holy Spirit or Mary, Joseph and Jesus. The symbols of the Trinity are the hand (the symbol of the Father), the lamb (the symbol of the Son) and the dove (the symbol of the Holy Spirit).

The Trinity is symbolized by yellow, red and green colors; three qualities - Love, Faith and Hope.

Person

Symbolic representation of man as the Universe: a square in a circle (China)

The crown of all living things. A symbol of what is capable of improvement. Created in the image and likeness of God, it combines material and spiritual, heavenly and earthly. It is a microcosm that symbolically contains all the elements of the universe (macrocosm). The human body in the Pythagorean tradition is depicted as a pentagram, consisting of arms, legs, head. In a person, three principles are combined together, which modern scientists call body, life and will. Symbolically, this can be depicted by three points (beginnings) enclosed in a circle.

Universal symbols-concepts

Cognition of ideas reveals their timelessly eternal meaning in temporary phenomena.

Andrey Bely

Concept symbols are numbers or geometric shapes that reflect ideas, feelings or abstract qualities of something directly related to the inner world of a person.

The duality of the world

Diagram "Double Triangle of Solomon": God of Light and God of Reflection

The duality of the world - the interaction of two polarities behind the created universe (light and darkness, good and evil, etc.) - is reflected in many symbols. The most famous of them is the yin-yang symbol. Also interesting are the symbols presented by the famous occultist Eliphas Levi, for example, the diagram "Double Triangle of Solomon".

The main symbol used by people far from occultism to depict duality is the most common number two, although, nevertheless, it also has a magical nature.

Yin-yang (principle)

Yin-yang sign

The Chinese call the symbol "yin-yang" Tai Shi - the circle of existence. The circle is divided into two equal parts by an S-shaped curve: dark, female (yin), and light, male (yang). The circle seems to revolve, darkness is replaced by light, and then light is replaced by darkness. The Chinese claim that even in the purest light there is an element of darkness, and vice versa. Therefore, in the center of each part, a small circle of the opposite color is depicted: black on a white background and white on black. This image symbolizes the balanced dynamism of opposing forces and principles in space.

Beams

Sun with zigzag rays (golden mask of the Incas)

It is a symbol of fertilizing power, holiness, spiritual enlightenment and creative energy, creative power. The rays can represent the hair of the sun god, the manifestation of the divine essence, or the radiance (halo) emanating from the saints. In solar symbolism, the seventh ray is the main path to heaven.

Wisdom

Ancient Greek goddess of wisdom Athena (in Roman mythology Minerva) with a coiled snake at her feet

The main symbols of wisdom are the snake (daytime, solar, but femininely flexible masculine sign) and the owl (nocturnal, lunar, acting imperceptibly, silently, but masculinely decisively and quickly feminine sign). It is the combination in each of them of the most important properties of the masculine and feminine principles that very accurately corresponds to wisdom. Other symbols of wisdom: dragon, griffin, peacock, sphinx, unicorn, bird, bee, rat, lotus, heart, number seven, scepter, scroll, ring, etc.

“From many roses - a drop of oil, from many torments - a drop of wisdom” (Persian saying).

Axis of the world

Tet Osiris

In the esoteric tradition, the symbols of the axis of the world, the World Tree, are the spear, sword, key and scepter.

The Egyptians use Tat (or Tet) as a symbol of the world axis and the North Pole - the spine of Osiris, which, in addition, personifies stability, strength, immutability, preservation.

Light

Light emanating from Buddha

Light is the first creation. It is associated with the beginning and the end. Light and darkness are two aspects of the Great Mother: life and love, death and burial, creation and destruction.

The light of the Sun personifies spiritual knowledge, and the reflected light of the Moon represents rational, analytical knowledge.

Light is usually depicted as straight or wavy rays, the disk of the sun or a halo. Typically, a straight line represents light, and a wavy line represents heat. Light and heat symbolically complement each other and are the two poles of the Fire element.

Death and rebirth

Death and rebirth of human beings. Detail of the symbolism on the gravestone in Dieste (Belgium)

This image in Christianity is expressed by ancient complex symbols. The given composition unites two pairs "circle-cross", each pair personifies death and rebirth. The lower pair is represented by crossed bones and a rounded skull (symbol of death). From the lower circle (skull) a cross grows, similar to the one on which Christ died - the cross of resurrection, rebirth. This whole allegory is inscribed in a larger circle - a sign that the death and rebirth of human beings are within the great spiritual sphere of the cosmos.

Consciousness (three aspects)

Symbols representing the three aspects of consciousness

Usually three aspects of consciousness are depicted in the form of three animals: one of them lives underground, the other on the ground, and the third flies above the ground. The underground animal is a microcosm; that which flies in the air is the macrocosm; and the animal that walks on the Earth represents the middle step between the first two - like us, for example. The most common symbols: in Egypt - cobra, Horus's right eye, hawk; in Peru, the rattlesnake, puma and condor; the American Indians have the rattlesnake, mountain lion and eagle; in Tibet - a snake, a pig and a rooster.

Dance

The dance of the dervishes (the grace of God descends to the dancer through the raised hand, penetrates through his body and spirit and, leaving him, connects to the earth through the lowered hand)

The main symbolism of the dance: cosmic creative energy, transformation of space in time, the rhythm of the universe, imitation of the divine "game" of creation, maintaining strength, emotions, activity.

Circular dances are an imitation of the movement of the Sun in the sky. Dancing in a chain is a symbol of the connection between man and woman, Heaven and Earth. When a dance is performed around an object, it is thereby closed, enclosed in a magic circle, protecting and giving strength.

Shadow

Priestly esotericism: the sign of Anathema (from Eliphas Levi's book "Transcendental Magic", 1896)

The symbol of the negative beginning, as opposed to the positive solar. In some primitive tribes, the shadow symbolizes the human soul, the same in witchcraft and conspiracies. Falling into the shadow of another person is a bad omen.

The above engraving shows a human hand performing an act of blessing. A strong beam of light casts a shadow from the blessing hand on the wall, and this shadow is the image of the horned head of the Devil. The main idea of ​​the allegory is this: evil and good are intertwined, and darkness and light confront each other in a kind of moral duel.

Emblems of modern religions

It is difficult to find the Creator and Father of this universe, but even having found Him, it is impossible to express about Him in a language that is understandable for everyone.

In our time, there are three world religions on the globe - Christianity, Islam (Islam) and Buddhism. Each of them is accepted in many countries. They arose a long time ago: Christianity is 2,000 years old, Islam is almost 1,400, and Buddhism is about 2,500 years old.

There are other religions, which, although not world-wide, are also widespread.

Christianity

Bowl and cross

One of the symbols of Christ's love is the combination of a cup and a cross. The cup, or goblet, in this case indicates the great sufferings that Jesus endured, calling them "the cup."

The image of the cup indicates the prayer of Jesus in the Garden of Gethsemane: “Father! oh, if you were pleased to carry this cup past me! however, not my will, but yours be done. "

The cross is depicted as pointed; its sharp ends, like swords of sorrow and pain, pierce the suffering soul.

Islam

Star and Crescent of Islam

The main emblem of the youngest world religion, Islam, founded by the Prophet of Allah, Muhammad (570-632), is a crescent moon with a star inside. The emblem denotes divine protection, growth, rebirth and, together with the star, paradise. The star is a traditional symbol of independence and divinity. The crescent moon is one of the faithful forces capable of resisting evil, a powerful talisman.

The crescent moon in Islamic countries replaces the cross in the Red Cross organizations.

Buddhism

Maitreya

In Buddhism, Maitreya is the name of the Buddha of the coming world order. This is the only Bodhisattva ("whose essence became the mind"), who is recognized by all major branches of Buddhism. The essence of a Bodhisattva is an act of sacrifice: giving up the bliss of nirvana in order to help humanity within the limits of karmic limitations.

Maitreya is depicted sitting on a throne in a "European pose" (with his legs down), which indicates a sign of the haste of his arrival; it is golden in color. Next to Maitreya, it is customary to depict the wheel of dharma, stupa and vase.

Judaism

Mogendovid, or Shield of David

Judaism is the oldest of the monotheistic world religions (originated in the 1st millennium BC in Palestine 4000 years ago). The main provisions of Judaism were later laid down in Christianity and Islam.

The symbol of Judaism is Mogendovid, or the Shield of David. Most often associated with the six-pointed Star of David. A less commonly used name is the Star of the Creator; each end of the star symbolizes one of the six days of creation, and the central hexagon represents the Sabbath (sacred day of rest).

Zoroastrianism

Ahura Mazda

Zoroastrianism is the oldest spiritual tradition, founded about 2500 years ago by the prophet Zoroaster, and now, unfortunately, forgotten. The supreme god is Ahura Mazda. The sacred canon is the Avesta ("law").

Zoroastrianism proceeds from the doctrine of the justice of the world order and the triumph of justice in the world struggle between good and evil, in which a person's free choice and his active participation play a decisive role. Zoroastrian morality contains an ethical triad: a good thought, a good word, a good deed.

Hinduism

One of the symbols of Trimurti

Hinduism combines elements of different faiths, rooted in the depths of the centuries. Sacred books - Vedas (Rigveda, Samaveda, Yajurveda, Atharvaveda). The three main gods make up the Trimurti (triad): Brahma is the creator of the world, Vishnu is the keeper of the world and Shiva is the destroyer. Their images symbolize the fundamental processes of change in nature (prakriti).

The basis of Hinduism is the doctrine of the reincarnation of souls (samsara), which occurs in accordance with the law of retribution (karma) for virtuous or bad behavior.

Confucianism

The symbol of Confucianism is the figure of the "Highest Saint"

Confucianism and Taoism are the most famous of the philosophical movements that existed in China even before its unification (221 BC). Gradually intertwining with the traditions of Buddhists and Taoists, the teachings of Confucius acquired a religious connotation. According to Confucius, one must live in such a way that human behavior reflects the laws of the Universe, which exists according to a certain order. “The Master teaches the students four disciplines: culture, behavior, loyalty and faith” (Lunyu book, 7.25).

Taoism

Tai Shi (yin-yang circle)

Taoism is literally "Tao School". (Tao is "the way"). It is an integral part of the philosophical and religious triad (Buddhism, Confucianism, Taoism). The Chinese apply in practice all three teachings, depending on the life situation. Within the framework of his personal life, a Chinese person professes Taoism, but when it comes to social norms of behavior, he becomes a Confucian, and when faced with troubles and hardships of life, he turns to Mahayana Buddhism.

The concept of Taoism is graphically expressed by Tai Chi (in some sources - Tai Shi) - a symbol of a single limit.

Shinto (Shinto)

Horin-rimbo - wheel of law (Japan)

Shinto is the Japanese national religion, its name comes from the Chinese word "sheng-dao" ("sacred path" or "path of the gods"). At the heart of Shinto is the cult of the deities of nature and ancestors. The highest deities are Amaterasu (the sun goddess) and her descendant Jimmu. Jimmu is the first emperor of Japan, the mythical ancestor of the Japanese emperors. Day 11 February, when, according to myths, in 660 BC. e. Jimmu ascended the throne, is considered the founding day of the empire and is celebrated as a holiday.

Crosses: the most common forms

The cross is a cosmic symbol that should be studied and treated with the greatest respect.

The Science of Initiation

The cross is the common symbol of humanity. It can be found in the most ancient religions, among the most ancient civilizations: in Mesopotamia, Egypt, China, etc. Who invented the cross? Nobody - for he exists in nature. This is an ancient universal symbol and, above all, a symbol of the connection between the micro- and macrocosm, spirit and matter in their combination. The cross symbolizes the involvement of the spirit (vertical line) during time (horizontal line).

The forms of the cross are varied. They differ in the number of crossbeams, and the number of ends of the cross, and proportions.

Greek cross

Greek cross

The cross is of the simplest form: square, with ends of equal length, the horizontal bar is located in the middle of the vertical one. Cross of St. George. This sign, also called crux quadrata, has been used since prehistoric times in a variety of ways - as a symbol of the sun god, the rain god, the elements from which the world is created: air, earth, fire and water. In early Christianity, the Greek cross symbolized Christ. It is also a symbol of secular, earthly power, but received from God. Used in medieval heraldry.

Hammer cross

Hammer cross

The hammer cross is a variation of the Greek cross. One of the main heraldic crosses is named after the French potenee - "support", because its shape is similar to the supports used in antiquity.

Latin cross

Latin cross

Another name for the Latin cross is the long cross. Its horizontal bar is located above the middle of the vertical bar. It is the most common Christian symbol in the Western world. It is believed that it was from such a cross that Christ was removed, hence its other names: the cross of the Crucifixion, the cross of the West, the cross of Life, the cross of Suffering. This form, so similar to the man with his arms outstretched, symbolized God in Greece and China long before the advent of Christianity. For the Egyptians, the cross rising from the heart symbolized kindness.

Cross of st peter

Cross of st peter

St. Peter's Cross is an inverted Latin cross. Since the 4th century, it has been one of the symbols of St. Peter, who is believed to have been crucified head down on an inverted cross in 65 AD. e. during the reign of Emperor Nero in Rome.

An inverted Latin cross, that is, the cross of St. Peter, with pointed ends - the emblem of the Knights Templar.

St. Andrew's cross (oblique cross)

St. Andrew's cross (oblique cross)

It is also called diagonal or oblique. On such a cross the Apostle Saint Andrew accepted a martyr's death. The Romans used this symbol to denote a border beyond which passage was prohibited. The oblique cross also symbolizes perfection, number 10. In heraldry, this cross is called saltir.

Saint Andrew is the patron saint of Russia, and when Peter the Great was creating the Russian navy (in the 1690s), he adopted a blue oblique cross on a white background for the flag of the fleet.

Tau cross (cross of St. Anthony)

Tau cross

Cross of St. Anthony

The tau cross is so named because of its resemblance to the Greek letter "T" (tau). It symbolizes life, the key to supreme power, the phallus. In ancient Egypt, it is a sign of fertility and life. In biblical times - a symbol of protection. The Scandinavians have Thor's hammer. In Christian churches - the cross of St. Anthony (the founder of Christian monasticism, IV century). Since the beginning of the XIII century - the emblem of Francis of Assisi. In heraldry, it is the Almighty Cross. It is also known as the "cross of the gallows" due to its resemblance to the gallows as it was done in antiquity.

Ankh (Egyptian cross)

Ankh - the key to the gates of death

The ankh is the most significant symbol among the ancient Egyptians, also known as the "cross with a handle". This cross combines two symbols: a circle (as a symbol of eternity) and a tau-cross suspended from it (as a symbol of life); together they denote immortality, eternal life. Ankh also personifies "life that will come", "time that will come", hidden wisdom, the key to the secrets of life and knowledge, as well as the key that opens the gates of death. Perhaps it symbolizes the Tree of Life, as well as the sun rising over the horizon.

Maltese cross

Maltese cross

The Maltese cross is also called the eight-pointed cross. It symbolizes the four great gods of Assyria: Ra, Anu, Belus and Hea. The emblem of the Knights of the Order of Malta. From the very beginning, the white cross of this form on a black background was the emblem of the military and religious order of the Hospitallers (Johannites), who moved their headquarters to Malta (in 1529) - hence the name.

In philately, the Maltese cross is the first postmark used to extinguish postage from 1840 to 1844.

Patriarchal cross

Patriarchal cross

The Patriarchal Cross is used by archbishops and cardinals. It is also called the Catholic Cardinal's Cross and the Double-Barred Cross. The upper crossbar is the titulus (name board), introduced by order of Pontius Pilate. Under the name of the archbishop's cross, it is often found on the arms of archbishops.

This cross is widespread in Greece and is sometimes called the Angevin or Lorraine. It is sometimes mistakenly referred to as the Lorran Cross.

Papal cross

Papal cross

The papal cross with three horizontal bars is also known as the triple cross. Used in processions in which the Pope participates. The three cross lines represent power and the Tree of Life.

Russian cross

Russian cross (cross of St. Lazarus)

This eight-pointed cross is the cross of the Russian Orthodox Church. It is also called the eastern cross or the cross of St. Lazarus. Symbol of the Orthodox Church in the Eastern Mediterranean, Eastern Europe and Russia.

The upper of the three crossbeams is the titulus, where the name was written, as in the patriarchal cross, the lower crossbar is beveled.

Cross of Constantine (sign "Chi-Ro")

Cross of Constantine

Magic seal with the symbol "Chi-Ro" (Agrippa, 1533)

The Cross of Constantine is a monogram known as “Chi-Ro” (“chi” and “ro” are the first two letters of the Greek name for Christ). Legend has it that Emperor Constantine saw this cross in the sky on the way to Rome, together with the cross he saw the inscription "Conquer by this". According to another legend, he saw a cross in a dream on the night before the battle and heard a voice: “With this sign you will win”). It is said that it was this prediction that converted Constantine to Christianity. And the monogram became the first generally accepted symbol of Christianity - as a sign of victory and salvation.

Rosicrucian cross

Cross with a rose (Rosicrucian)

Another name is the cross of the rose (five-petal). Emblem of the Rosicrucian Order. The symbol of harmony, center, heart. The rose and the cross also symbolize the Resurrection and Atonement of Christ. This sign is understood as the divine light of the Universe (rose) and the earthly world of suffering (cross), as the feminine principle and masculine, material and spiritual, spiritual and sensual love. The cross with a rose is a symbol of the initiate, who, thanks to work on himself, was able to develop in himself love, life-giving and transforming matter.

Masonic cross

Masonic cross (cross in a circle)

The Masonic cross is a cross inscribed in a circle. It means a holy place and a cosmic center. The four dimensions of space in the heavenly circle symbolize the totality that includes the Great Spirit. This cross personifies the Cosmic Tree, spreading horizontally over the Earth and touching Heaven through the vertical central axis. Such a cross was either executed in stone, or depicted on the walls of Roman Gothic temples, symbolizing their consecration.

Pacifist cross

Pacifist Cross (Peace Cross)

This symbol was developed by Gerald Holt in 1958 for the then emerging nuclear disarmament movement. To design the symbol, he used the semaphore alphabet: he made a cross from its symbols - for "N" (nuclear, nuclear) and "D" (disarmament, disarmament) - and placed them in a circle, which symbolized a global agreement. Soon this cross became one of the most common signs of the 60s of the twentieth century, symbolizing both peace and anarchy.

Time images

The wise turn years into months, months into weeks, weeks into days.

Everything is perishable in this world.

The image of unforgiving time is a road. The symbol of time is sand flowing through your fingers. Measured time attributes - clock, burning candle; it is a symbol of the elusiveness of the present moment.

In the pantheon of gods of almost all ancient cultures, there is necessarily the god of Time.

Abraxas

Abraxas - a symbol of time (gnostic gem)

Abraxas is the personification of the divine cycles of the solar year. This is the mystical image of the Supreme Being, the highest of the seven. It consists of five emanations (radiations): Nus (Mind), Logos (Word), Fronesis (Mind), Sophia (Wisdom), Dynamis (Power). The human body in the image represents God. The two support-snakes emerging from it are Nus and Logos (intuition and quick understanding). The head of a rooster means foresight and vigilance (intelligence). Two hands hold the symbols of Sophia and Dynamis: the armor of wisdom and the lash of power.

Kalachakra

Namchu-vanden - the emblem of the Kalachakra

Kalachakra is literally "wheel of time", "passage of time". Secret doctrine in Vajrayana Buddhism. Astrological and astronomical system that penetrated Tibet from India. Kalachakra introduces the concept of cyclical time with periods of 12 and 60 years (Tibetan calendar). According to legend, the Kalachakra teachings were given by Buddha Shakyamuni. According to other sources, this teaching was brought to Tibet by Pitop, or the Great Kalachakrapada, which, having miraculously got to Shambhala, was initiated there by the king of Kalki into the Kalachakra teachings.

Kronos

Kronos (Roman Saturn), XV century

The ancient Greek symbol of time - the titan Kronos - in Russian became the ancestor of many words (the particle "chrono" is part of complex words indicating their relationship to time): chronic, chronology, chronometer, etc.

Kronos (Roman Saturn) is the god of Time, in the form of a withering autumn or the outgoing Sun, sometimes, along with his sickle, he also has a hood, which symbolizes invisibility, death and retreat. Since the hood covers the head, it also signifies thought and spirit.

Ourobor (tail-biting serpent)

Ourobor as an emblem of death (from George Witere's Collection of Emblems, Ancient and Modern, 1635)

The most obvious meaning of the symbol is associated with the concept of time: the passage of time is accompanied by destruction, since the past seems to be irretrievably lost. This is reflected in the fact that the serpent "devours" its own tail, like time, which apparently consumes itself. We can say that time has a cyclical nature (day follows night, seasons repeat, etc.), and this is expressed in the form of a serpent, in the fact that it coiled into a circle. The symbol of the emblem can be expressed by the phrase: "In my beginning is my end" or "The end is at the beginning."

Tempus

Image of Time - Tempus (Rome)

The Romans depicted time in the form of a male winged figure with goat legs, with a scythe in his hands ("the inexorable scythe of time") - this is Tempus (from Latin tempus - time).

The figure of Tempus personifies the frailty and transience of all living things, and therefore is associated with the symbol of Death.

The "clock" of our body

The "clock" of our body (the numbers in the inner circle are the time of day)

The Chinese consider it useful to influence the organs of the body in a strictly defined period of the day (stimulate - during activity, and vice versa).

Twelve main organs, according to medical practice, have two hours of activity (see figure). Designations: GB - gallbladder: (from 23 to 1 o'clock); Liv - liver; Lu - lungs; Li - large intestine; St - stomach; Sp, spleen; H - heart; Si - small intestine; UB - bladder; K - kidneys; P - brain; TW is the spinal cord.

Symbols of the plant kingdom

The beauty of plants is a common property of the world, that is, it is always macrocosmic, not microcosmic.

The symbol of the plant kingdom is a tree. Its branches, personifying diversity, branch off from a common trunk, which is a symbol of unity. A green, flowering tree is a symbol of life; dead, withered - a symbol of death. An old, gnarled tree can mean wisdom and strength.

The flower is the emblem of the cycle of birth, life, death and rebirth. Flowers represent beauty (especially feminine), innocence, divine blessing, spring, youth, but also the brevity of being. Everything in a flower can carry a certain symbolism: its shape, and the number of petals, and color, and smell ...

Vine

Ornament - motif of the vine

Grapes are one of the oldest symbols of fertility, abundance and vitality. The vine is one of the symbols of Christ. The importance of wine in many religious rituals is based on the symbolic link between grapes and divine blessings. The vine was the first plant planted by Noah after the flood.

Grape juice resembles human blood. In some mysteries, grapes are a symbol of lust and debauchery, greed and drunkenness. The bunch of grapes is sometimes presented as a phallic symbol. But grapes are also seen as a symbol of the solar spirit.

Cherry

Sakura (19th century Japanese engraving, Utagawa Kunisada)

In Christian iconography, a cherry is sometimes depicted instead of an apple as a fruit from the Tree of Knowledge of Good and Evil; sometimes Christ is depicted with cherries in his hand. In China, the cherry tree is a symbol of good luck, spring (due to early flowering) and virginity; the vulva is called the "spring cherry". Blooming cherry (sakura) - the symbol of Japan; it is cultivated as an ornamental tree; its fruits are inedible. The Japanese identify the cherry blossoms with the rising sun. Cherries are also the emblem of the samurai.

Garnet

Expanding grenade

The opening pomegranate (fruit) symbolizes the Easter Resurrection of Christ, gives Christians confidence in forgiveness, faith in the future life and resurrection. Due to the abundance of seeds, pomegranates are a symbol of fertility. It is also the ancient eastern emblem of the sun god and the emblem of life, a divine symbol called the "forbidden secret."

The remains of a flower (thorn) on the top of the fruit serve as a crown in heraldry. The pomegranate is always depicted in gold. And there are always twelve pomegranate seeds - a number that has symbolized perfection since ancient times.

Oak and acorn

Acorn

Oak is a symbol of power, endurance, longevity and nobility, as well as glory. In ancient Rome, a wreath of oak leaves was the highest award for a victorious commander.

As an emblem of valor and courage, oak (oak leaf, oak branch, oak wreath, oak garland) is used in military insignia in many countries.

An oak with acorns is an emblem of maturity, full of strength. An oak without acorns is the emblem of youthful valor. The acorn is a symbol of fertility, prosperity, spiritual energy that grows from the seed of truth.

Kabbalistic tree

Kabbalistic Tree (drawing from the book of R. Floodd, 1574-1637)

This is an inverted Cosmic Tree. Its crown touches the ground, and its roots are strengthened in the spirit world and feed on the spiritual energy of the sky, spreading it to the outside world and down. This is a favorite image in Kabbalism and other mystical and magical teachings. It testifies to the fact that human life is the descent of the spirit into the body and back. It is also a symbol of philosophical growth, growth inward.

In the Bhagavatgita, an inverted tree means the origin of everything from a single root, in Islam it is a symbol of happiness and good luck.

Cypress

Seven cypresses and twelve branches - the personification of the universe and its eternal truths (Istanbul, Turkey)

In the West, cypress is a mystical symbol of death and mourning, the personification of sorrow and grief, since it was used in embalming the body and for making coffins. In Asia, it is a symbol of longevity and immortality. The Arabs call cypress the Tree of Life. In Greece, cypress has always had a dual reputation: it was a symbol of the dark god of the underworld of Hades, but at the same time, more cheerful gods - Zeus, Apollo, Aphrodite and Hermes. Therefore, he became a symbol of rebirth and life after death. In China, the smoke of cypress branches is a symbol of light forces, a talisman against misfortune.

Clover

Four petal clover

The three-leafed clover (shamrock) is a symbol of the Christian Trinity. The rare quatrefoil is a symbol of good luck; there is a belief that Eve took one four-leafed leaf as a memory of a lost paradise. But the five-petaled clover brings bad luck.

In China, clover is the emblem of spring. The Irish use clover leaves as their national emblem, which probably dates back to the Celtic veneration of the plant for its vigorous growth in spring.

Roots

Seed and roots

A symbol of connection with the earth, with the family.

"A man with roots" - they say about a man who stands firmly on his feet.

"To look at the root" - to pay attention to the most essential, to delve into the essence.

The "root of evil" is the source, the core of evil.

"Uprooting" means taking life, cutting off access to food, radically solving the problem.

Laurel

Laurel wreath

The laurel symbolizes immortality, but also triumph, victory and success. He personifies peace, purification, protection, divinity, secret knowledge. According to ancient Greek myth, the god of the sun, dawn and poetry Apollo pursued the nymph Daphne, who, fleeing from him, turned into a laurel bush (in Greek, "laurel" - "daphne"). In the arms of Apollo there was a tree, with branches of which he adorned his head and lyre. That is why in ancient Greece, musicians, poets, dancers, whose patron was Apollo, were awarded with laurel wreaths. The Romans extended this tradition to military conquerors.

Lily

Fleur-de-lys, coat of arms of the French kings

One of the most versatile and even contradictory symbols. The triple lily is a symbol of the Trinity and the three virtues: Faith, Hope and Mercy. Lily is an attribute of many saints, including the Archangel Gabriel. White lilies can sometimes symbolize death. Lily is also associated with fertility and erotic love due to its arrow-shaped or spear-shaped (phallus-like) pistil and specific strong scent. Lily - a sign of prosperity and royal power in Byzantium, later - the emblem of the French kings.

Palm branch

Palm branch

This is the main symbol of victory and triumph (“palm tree”).

In ancient Greece, the palm branch was presented with a wreath to the winner of the Olympic Games as a personal wish of health and longevity. In ancient Rome, they were also awarded to victorious soldiers and gladiators. On Palm Sunday in Jerusalem, priests distribute consecrated palm leaves in the form of a cross. In Russia, they are replaced by pussy willows. The palm branch is a symbol of longevity and one of the emblems of peace, and unlike a dove, it is a secular emblem.

the Rose

Ten petalled rose

The rose has polar symbolism: it is heavenly perfection and earthly passion, time and eternity, life and death, fertility and virginity. It is also a symbol of the heart, the center of the universe, the cosmic wheel, divine, romantic and sensual love. Rose - completeness, the mystery of life, its focus, the unknown, beauty, grace, happiness, but also voluptuousness, passion, and in combination with wine - sensuality and seduction. A rosebud is a symbol of virginity; withered rose - the transience of life, death, sorrow; her thorns are pain, blood and martyrdom.

Heraldic roses

Heraldic roses: 1 - Lancaster; 2 - Yorks; 3 - Tudors; 4 - England (badge); 5 - German rose Rosenov; 6 - Russian stamp

The heraldic medieval rose has five or ten petals, which associates it with the Pythagorean pentad and decade. The rose with red petals and white stamens is the emblem of England, the most famous badge of the English kings. After the "War of the Scarlet and White Roses", named after the badges of the surnames that fought for the English crown, the scarlet rose of Lancaster and the white Yorkie were combined in the form of the "Rose of the Tudors". The bright crimson rose is the unofficial emblem of Bulgaria. The famous tea rose is the emblem of Beijing. Nine white roses are in the coat of arms of Finland.

Sprouts

Fern sprouts (four-part scheme)

Sprouts (heart-shaped pattern)

The sprout is a symbol of the awakening of life. The simplest type is a seed "hatching from its shell", a sprout that resembles a folded fern leaf. These images are accompanied by a rounded or cordate stripe. The heart-shaped pattern (point upwards) is a stable expression of the agrarian ornament. A four-part composition with sprouts of a fern (a sacred plant among many peoples), the leaves of which are directed in all directions, is widely used.

Pumpkin

Painted gourd-gourd, vessel and talisman (China, XIX century)

A gourd pumpkin in Chinese culture is a symbol of health, wisdom and even the entire universe.

In America, the pumpkin is the main attribute of the traditional holiday of evil spirits - Halloween. For this holiday, faces are cut out on pumpkins, and candles are inserted inside the pumpkin and with such "lamps" they go home.

In a belittled symbolism, a pumpkin is called a head.

Thistle

Thistle

Scotland emblem

Thistle means challenge, asceticism, vindictiveness, misanthropy. Donkey food. It also symbolizes sin, sorrow, the curse of God during the expulsion from paradise; according to the Book of Genesis, Adam was punished with a thistle. In Christian art, the thistle is the emblem of martyrdom.

But there is another side to the symbolism of the thistle. Like some other thorny plants, it is considered a talisman and is endowed with the ability to heal wounds. This is a plant with strong magical properties.

Apple tree, apple

The sovereign apple is one of the symbols of monarchical power

The apple tree is a symbol of fertility, one of the symbols of Mother Earth. A blossoming apple tree is eternal youth, and in China - peace and beauty. An apple is a symbol of bliss, especially sexual, a symbol of restoration of potential, integrity, health and vitality. The apple personifies love, marriage, spring, youth, longevity or immortality, in Christianity it is associated with temptation, the fall of man and his salvation. A bitten apple is a symbol of sin, anarchy, but also knowledge and hope. In art, an apple in the mouth of a monkey or a snake is a symbol of original sin.

Symbols of the animal kingdom

The animal kingdom in its different breeds embodies the different impulses of the human psyche.

N.P. Rudnikova

In the human mind, animals (animals, birds, fish, insects, etc.) act as symbols on the basis of which figurative pictures of certain aspects of life are made. The symbolism of animals extends to the higher foundations of man himself (for example, ideas about the soul find expression in the form of a bird).

The ancient Egyptians believed that certain animals could embody cosmic and divine energies. The twelve animals of the zodiac are archetypal symbols and represent a closed cycle of energies.

Stork

"He who has gained immortality flies into the sky on a stork" (stork and crane are symbols of immortality)

The stork symbolizes new life, the arrival of spring, good luck, daughter or son affection. In Christianity, the stork personifies purity, chastity, piety, vigilance. In the East, the stork is a symbol of immortality. For the Slavs, the stork is an ancient totem bird, a symbol of the homeland, family well-being, home comfort, love for one's home. The punishment for ruining a nest or killing a stork is a fire that incinerates the killer's house or himself. There is a belief that a stork brings newborn babies. A stork carrying a baby is a symbol of christening.

Butterfly

Butterfly image

Currently, the symbolism of the butterfly is dominated by the meaning of the anemone, a carefree creature, but also pure joy. In ancient times, it was represented as a symbol of transformation and immortality due to its life cycle: life (bright caterpillar) - death (dark doll) - rebirth (free flight of the soul). The butterfly is a symbol of the soul in many regions of the world. In China, it is a symbol of easy entertainment and a sign of lovers. In Japan, the butterfly is a symbol of a fickle and windy lover, as well as female fussiness and the craft of a geisha; two butterflies - conjugal happiness.

Ram (Aries)

Ram head

One of the most important symbols and one of the most widespread emblems in the world (in variants: lamb, golden fleece, head of a ram, horns of a ram). The ram symbolizes fire, solar energy, ardent passion, courage, impulsiveness, stubbornness. In many cultures, since ancient times, it means masculine strength and sexual potency. The symbol of the elements - both creative and destructive, requiring sacrifice.

In the modern everyday sense, the word "ram" is often synonymous with stupidity or stupid stubbornness.

Bull

Sacred bull Apis (Egypt)

The symbol of the fertility of the earth. The most common symbol of sexual power, as well as violence and rage. This is the embodied power, power, male fertility. A symbol of divinity, royalty, elemental forces of nature, which changed meanings in different eras and in different cultures. The bull's horns are a sign of the full moon, his huge body is the support of the world in Islamic and Vedic traditions; its abundant seed is nourished by the Moon in Iranian mythology; its hum, hoof stomping and horn shaking are commonly associated with thunder and earthquakes.

Wolf

A she-wolf feeding Romulus and Remus, the founders of Rome (bronze figure, 6th-5th century BC)

The symbolism of the wolf is twofold.

Negative symbolism: ferocity, deceit, greed, cruelty, evil, gluttony and sexuality. The stories of witches turned wolves and men turned werewolves epitomize the fear of demonic possession and male violence.

Positive symbolism: courage, victory, concern for the food of the family. The wolf is a common symbol of knowledge through experience, the emblem of warriors.

V heraldry wolf is a symbol of anger, gluttony, greed.

Raven, crow

Raven on the shield - a symbol of purification

“Daughters of Jerusalem! I am black, but beautiful "(alchemical symbol)

The raven and the crow have similar symbolism. On the one hand, crows are associated with war, death, desolation, evil and misfortune. Because of their blackness, they are considered symbols of chaos and darkness that preceded the light of creation. On the other hand, the raven is a symbol of wisdom and justice. The raven has a connection with the world of the dead, he is able to get living and dead water. It is believed that the raven is a travel assistant and fortuneteller. There is a belief that when the ravens begin to leave their nests, it portends hunger or other misfortunes.

Pigeon

Dove as a symbol of peace

Peace, purity, love, serenity, hope. Traditional Christian symbol of the Holy Spirit and baptism. There is a legend that the devil and witches can transform into any creature except a dove and a sheep. Pigeon cooing has been linked to both sex and childbirth. A pair of doves is a symbol of sexual harmony; so the dove became the personification of a tender wife. A dove with a laurel branch is a symbol of peace, a dove with a cornucopia is a fluke. In the East, the dove is one of the many symbols of longevity.

Dolphin

"Boy with a Dolphin" (Andrea del Verrocchio, 1475. Sculpture for the fountain)

Dolphin symbolizes love, power of the sea, speed, salvation, transformation. This is a friend of man in the sea element and its symbol. The dolphin is also a symbol of boundless joy, playfulness, unpredictability and even spiritual enlightenment. In ancient Greece, the ruler of the waters, Poseidon, (the Roman analogue is Neptune), was often depicted in a cart pulled by dolphins. As a symbol of Christ's sacrifice, the dolphin is often depicted with a pierced trident or an anchor (the secret symbol of the cross). Intertwined with an anchor, the dolphin is a symbol of caution, speed limit: "Hurry slowly."

Toad, frog

Stylized image of a frog

The toad is one of the attributes of witchcraft. According to European superstitions, this is a witches' companion, reminiscent of the death and torment of sinners. At the same time, the toad, personifying darkness and evil, greed and lust in the Middle Ages, is associated with birth and rebirth. A symbol of ugliness behind which a beautiful soul can lurk. It also symbolizes longevity and wealth: it is believed that the toad, like a snake, carries a gem in its forehead that attracts good luck.

The frog is a widespread symbol of fertility, a harbinger of spring rains and the awakening of nature.

Crane

Dances of cranes (bracelet from Kiev)

In China and Japan, the crane symbolizes vigilance, longevity, wisdom, devotion, honor. The image of a crane flying to the Sun is a symbol of social aspirations, its snow-white body is a symbol of purity, and its red head is the fire of life. In India and in some Celtic regions, the crane is a symbol of betrayal, a harbinger of misfortune. In Russia, cranes, along with storks and nightingales, are considered "birds of God", their symbolism is associated with the Sun.

Throughout the world, the crane is a symbol of communication with the gods.

Snake: general symbolism

Python (Greece)

The snake is the universal and most complex of all the symbols embodied in animals, as well as the most common and, perhaps, the most ancient of them. The serpent means death and destruction, but also life and resurrection. This is the solar principle and the moon, light and darkness, good and evil, wisdom and blind passion, healing and poison, a keeper and destroyer. This duality of symbolism makes one balance between fear and worship, the snake appears either as a hero or as a monster.

Snake: positive symbolism

"Serpentine Power"

An example of a positive symbolism of a snake is the concept of kundalini: a symbol of inner strength, psychic energy, a snake-like tangle of vital energy dormant at the base of the spine. Kundalini energy is called "serpentine power". She is sometimes depicted as a coiled snake with heads at both ends. In India and other regions, snakes are often considered the guardians of shrines, water sources, and treasures. This tradition is associated with the symbolism of fertility inherent in the snake, and with the belief that precious stones are the frozen saliva of a snake.

Snake: negative symbolism

Illustration for the "Poem of Gilgamesh" (seal of the Sumerian-Akkadian kingdom)

If we consider the frightening part of the symbolism of the snake, then it is a clear prototype of dragons and sea snakes or snake-like hybrids, symbolizing the many dangers that await a person in life. The snake is one of the most evil omens, a symbol of darkness, evil, hatred, sin, temptation, deception. The snake is accused of having lost God's gift of eternal life because of it.

Snakes were an indispensable attribute of witches, witch's potions included some parts of snakes.

Snake: cosmogonic symbolism

Snake and egg (image of a snake that keeps the world)

The snake is primarily a magical symbol of the forces that gave birth to life. A snake biting its own tail is a symbol not only of eternity, but also of divine self-sufficiency. The image of a snake guarding the eggs laid by it is associated with a huge snake that has entwined the whole world and supports it or helps the earth's disk float in the Ocean around it. The snake is in constant contact with the forces of earth, waters, darkness and the afterlife - lonely, cold-blooded, secretive, able to rejuvenate, shedding its skin.

Snake as a symbol of wisdom

A snake coiled around a wand

Totemic symbolism, combined with the belief that snakes know the secrets of the earth and are able to see in the dark, endows the snakes with wisdom or the gift of divination. “Be wise as serpents and simple as doves,” Christ said to his disciples (Gospel of Matthew 10:16). The Greek word "dragon" (which not only refers to a monster, but which also means "a serpent with a piercing gaze") is etymologically related to sight. In art, the snake is an attribute of the goddess of wisdom Athena (Minerva) and the allegorical figure of Prudence, meaning the gift of foresight.

Snake: Alchemy and Healing

Rod of Mercury (caduceus)

Staff of Asclepius (Aesculapius)

The snake coiled around the wand is the alchemical symbol of Philosophical Mercury in its primary state.

According to mythology, Hermes (Mercury), the messenger of the gods, received a caduceus - a winged staff with the power to reconcile opponents. When he placed it between two wrestling serpents, they peacefully wrapped the staff around and calmed down. The snakes entwined with the caduceus symbolize the interaction of opposing forces. A snake coiling around a gnarled staff is the emblem of the Greek god of healing Asclepius (Aesculapius), who, it is believed, could even raise the dead.

Ibis

Ibis (Egyptian papyrus of the 19th dynasty, 1295-1186 BC)

The ibis is a sacred bird of the Egyptians. The symbol of wisdom. In ancient Egypt, the ibis was considered the embodiment of the lunar deity Thoth, the greatest god of Egypt, the patron saint of occult knowledge, who gave mankind a written language. He is portrayed as a man with the head of an Ibis. This bird is also called the guardian of the harvest. To kill an ibis, even by accident, was considered a terrible crime.

It is believed that the ibis can live only in Egypt and, transported to other countries, dies there of melancholy.

Goat

Goat

The goat is a symbol of potency, vitality, masculinity, but also cunning, lust and stupidity; he personifies destructive tendencies in a man. In Western tradition, a lustful old man is often called a goat. In China and India, the goat is a positive male symbol. In Christianity, the goat is the personification of impurity and base lust.

The goat is often used for sacrifice ("the scapegoat"). The Goat is closely related to Dionysus (Bacchus).

Cow

Holy cow

For many peoples, this animal symbolizes fertility, prosperity, as well as patience and passive endurance. The cow is an ancient symbol of mother's milk and (like the bull) the cosmic forces that created the world. In many cults, from Ancient Egypt to China, the cow personifies Mother Earth. She also symbolizes the moon and sky, as her horns resemble a crescent moon, her milk is associated with the Milky Way. The heads of the moon goddesses in various cultures are adorned with cow horns. Cows are held in high esteem in India.

a lion

Leo - the symbol of the Sun

The lion, commonly referred to as the king of beasts, has been one of the most common symbols of strength and greatness for thousands of years. General symbolism: divine, solar energy (symbol of fire and the Sun), royal power, strength, courage, wisdom, justice, protection, protection, but also cruelty, all-devouring ferocity and death. Leo is the image of all the great and terrifying forces of nature. He is considered both a destroyer and a savior, he is able to represent both evil and the struggle with evil. Leo is one of the hypostases of the Sphinx.

Heraldic lions

Heraldic lions

In heraldry - the most common and favorite image of an animal. Attributes of a heraldic lion: bow and arrows, saber, sword, ax, ax, halberds, etc. The main heraldic form is a lion on its hind legs and in profile. In this case, one eye and one ear are indicated on the head. Bloody tongue sticking out of the mouth. This lion is a symbol of strength, courage, generosity. There are other options for the image. In state emblems, a crowned lion is the emblem of power over subjects.

Bear

Heraldic bear

The bear is a symbol of good nature and rage, heroic strength and awkwardness, laziness and tender maternal feelings, gluttony and asceticism (albeit involuntary: he sleeps all winter without any food, “sucks his paw”). The bear personifies unpredictability, bad temper, evil, rudeness, greed, sinfulness, the devil, as well as cruel primitive force. The badge of the warriors in Northern Europe and Asia.

In addition, the bear is a symbol of the moon and the resurrection. K. Jung believes that the bear symbolizes the dark sides of the subconscious.

Mouse, rat

Mouse wedding

In Russia, the mouse is often called the "gray thief". The mouse is also a symbol of timidity, stealth. The mouse helps to find the loss in the house: "Mouse, mouse, play and give it back." The mouse gives a boost. In China, the mouse is one of the popular deities of wealth.

The general symbolism of the rat is destruction, aggressiveness, greed; the rat is associated with disasters (pestilence) and death, but it is also the embodiment of perseverance, dexterity, cunning and fertility, and also has the gift of foresight (the legendary ability to foresee the death of ships).

Monkey

Hanuman, the monkey god playing with the peaches of immortality (from a Chinese dish)

Monkey symbolism is controversial. Most often, the monkey personifies sin, in particular physical. She is also a symbol of cunning, deceit, striving for luxury, malice, laziness (because of her angular movements), drunkenness, sometimes a symbol of learning. The monkey (along with the white elephant and cow) is the third sacred animal in India. Even now, insulting a monkey with an action causes strong discontent among religious people. In Japan, the monkey's cry is a symbol of deep longing. In the East, carvings of three monkeys are considered a talisman protecting from slander.

Deer

Deer (badge of Richard II, late 14th century)

A universal symbol associated with the East, sunrise, light, purity, renewal, creation and spirituality, but also with loneliness. The characteristic qualities of a deer are swiftness, grace and beauty. Deer are wonderful messengers and guides. They are credited with healing powers, especially the ability to seek out medicinal herbs. The deer, in addition, is a symbol of caution and keen hearing. In China, deer is associated with wealth (abundance) and good luck. The deer is a strong magical protector, one of the patron spirits of the Siberian peoples.

Eagle

The eagle as a symbol of the supreme power and solar nature of the lord of the heavens and the head of all the gods of Zeus (painting on a Greek bowl, VI century BC)

The eagle is the lord of the air, the embodiment of power, speed. Solar symbol of the sun gods, rulers, warriors. Associated with greatness, power, domination, courage, inspiration. It personifies the midday Sun, liberation from bonds, victory, pride, contemplation, regal origin, height. It is believed that the eagle is able to fly to the Sun, therefore it is called the messenger of heaven. Double-headed eagles can mean omniscience and double power. An eagle with a snake in its claws symbolizes the victory of the spirit. In this battle, the eagle is the personification of the force of good, and the snake is the force of evil.

Heraldic eagles

Double-headed eagle (Russian embroidery)

Eagle - emblem of the USA

In heraldry, the eagle is a symbol of power, domination, generosity and sagacity. On the coats of arms, the eagle is most often depicted flying chest first, with wings raised upward or soaring. It can be one- or two-headed. Ever since the days of the founders of Rome Romulus and Remus, he was portrayed on the standards as "the bird of Jupiter." After the Christian conquest of Palestine, the double-headed eagle became the coat of arms of the Holy Roman Empire, and later the Austrian (Austro-Hungarian) and Russian empires. The American bald eagle with outstretched wings has become the emblem of the United States.

Peacock

Peacock (medieval Persian drawing)

This is shining glory, immortality, greatness, incorruptibility. The peacock's magnificent tail is a symbol of the all-seeing Sun and eternal cosmic cycles, as well as the stellar firmament and, as a result, all-unity and interconnectedness. In ancient Rome, the peacock was considered the emblem of the empress and her daughters, while the eagle was the emperor's bird. In Islamic decorative art, the unity of opposites (the Sun at its zenith next to the full Moon) is depicted as two peacocks under the World Tree. In Christianity, a peacock, on the one hand, is a symbol of eternal life, and on the other, a symbol of pride, luxury and vanity.

Spider

The spider depicted on the amulet of the American Indian

Feminine principle. The Great Mother in the terrible guise of the weaver of fate is sometimes depicted as a spider. All moon goddesses are the spinners and weavers of fate. The web, which the spider weaves, weaves from the center in a spiral, is a symbol of the creative forces of the Universe, a symbol of the universe. The spider in the center of the web symbolizes the center of the world; The sun is surrounded by rays; The moon, personifying the cycles of life and death, spinning the web of time. The spider is often associated with luck, wealth, or rain. Killing a spider is a bad omen.

Pelican

Red stone plate depicting a pelican feeding its chicks with its blood (Staffordshire, circa 1660)

The pelican symbolizes self-sacrifice and parental love, as well as mercy. In heraldry, this bird is usually depicted like an eagle or a crane, standing in a nest and trying to feed the chicks with its blood. Early Christian writers compared a pelican feeding offspring with its flesh to Jesus Christ, who donated his blood for the salvation of mankind. The pelican is also a symbol of European occultism (primarily alchemists and Rosicrucians), expressing the feat of self-sacrifice and the eternal rebirth of life.

Rooster

Rooster - a sun bird (image-amulet, China, XX century)

The rooster is vigilance, courage, courage, foresight, reliability. Herald of the dawn, a symbol of the Sun and spiritual rebirth. These qualities prevail over pride, arrogance, lust, which are also inherent in him. The Romans mean "third watchman of time": between midnight and dawn. The rooster is a protector from all kinds of evil. It is believed that night ghosts and evil spirits disappear with the first crow of a rooster. The red rooster wards the fire away from the house, and the white rooster wards the ghosts. Before moving into a new house, the Eastern Slavs launched a rooster there. If he spent the night safely, then it was possible to move in.

Bee

Young Woman Collecting Bee Honey (15th century herbalist)

The bee personifies diligence, diligence, organizational and creative abilities, cleanliness, sociability, modesty, spirituality, courage, wisdom, selflessness, eloquence ("honey speech"). In Greek, Middle Eastern, Islamic traditions, the bee is an allegory of the soul. The Chinese associate the bee with the fickleness of "choosy brides." Among the ancient Slavs, the bee was a symbol of love, as it combined the "sweetness of honey and the bitterness of the sting." Queen bee, mother goddess, symbol of supreme power, fertility.

Scorpion

Scorpio (gnostic gem)

Scorpio is a symbol of evil, self-destruction, death, punishment, retribution, revenge, betrayal, but also a deep understanding of the world. Sometimes the scorpion serves as a talisman and amulet - Paracelsus advised people suffering from diseases of the reproductive system to wear it. In Africa, it was believed that the scorpion itself allocates funds against its poison, so it was a symbol not only of killing, but also of healing. The red star Antares on the "back" of the celestial constellation Scorpio was considered the worst fire in the sky in Europe.

Elephant

White elephant

At present, the huge mass and sluggishness of the elephant have become metaphorical. However, the elephant, first of all, is a symbol of strength: both gentle, loving, and furious, destructive. Elephants are considered vindictive because they never forget the grievances and ill-treatment inflicted on them. The thick skin of an elephant symbolizes mental invulnerability. The elephant is also a symbol of power, insight, prosperity, happiness, personifies the element of the Earth, memory, wisdom, longevity, loyalty, patience, compassion. The elephant is often depicted on good luck charms.

Dog

Noether Anubis (dog-god)

In some countries, a dog is a sacred animal, in others it is considered an unclean, greedy, even vile creature and personifies evil. According to Islamic beliefs, angels will never visit a house where a dog lives. But most often the dog is a symbol of protection and self-sacrifice. And also hunting (sometimes this symbol carries a negative connotation - persecution).

In ancient Egyptian mythology, dogs, as good guides and guards in the afterlife, were considered companions of Anubis, depicted with the head of a jackal or dog.

Owl

Wise owl - attribute of Athena (Greece)

The owl is a traditional symbol of wisdom, an allegorical figure of Night and Sleep. In some ancient cultures, especially in China, the owl has an ominous symbolism, symbolizing darkness, personifies the principle of yang with a negative, destructive connotation. Due to the noiselessness of the night flight, glowing eyes and eerie screams, the owl is associated with death and occult forces. She is also credited with the gift of prophecy. Nowadays, the owl is mainly a symbol of discernment and book erudition. "Learned owls" are called people of mental labor.

Falcon

Falcon - the image of the rising sun

The falcon, like the eagle, is a solar symbol of victory. The personification of superiority, strong spirit, light, freedom. In ancient Egypt, the falcon was a sacred symbol of the Sun, temples were dedicated to it, killing a falcon was considered a grave sin. In Western tradition, the falcon is a symbol of the hunt. A falcon with a cap worn on its head is a symbol of hope for light and freedom. Falcon as a symbol of aggression is rare. For the Slavs, this bird is a symbol of strength, courage, a good fellow. The falcon is opposed to the crow (as the embodiment of evil forces): "Where the falcons fly, the crow is not allowed there."

Ostrich

Australian coat of arms

In ancient Egypt, the ostrich feather is an attribute of the goddess of truth and justice, Maat. This feather, according to legend, was placed on the scales when weighing the souls of the dead in order to determine the severity of their sins. Since ostrich feathers are the same length, they were used as a symbol of justice. The belief that the ostrich hides its head in the sand when danger appears (a symbol of avoiding problems) probably originated from the threatening pose of the ostrich when it bends its head to the ground itself.

In the Australian coat of arms, the emu is a supporter along with a kangaroo.

Tigers

“The tiger spring contains a tiger. Having mastered the contents of the tiger cave, a perfect man who subdued yin and yang "

The tiger is a symbol of energy, strength, speed and talent. This image is both lunar and solar at the same time. He is both a creator and a destroyer. The tiger fighting the snake is a symbol of solar power. In a battle with a lion or dragon, he becomes a symbol of the moon, cruel and fierce. In Europe, the tiger is a symbol of power and bloodlust. In the Far East, it is a symbol of nobility and happiness. In the cultures of Asia and India, it can be a symbol of aggression and protection, life and death, evil and good.

Turtle

Turtle entwined with a snake

The turtle symbolizes strength, patience, endurance, constancy, slowness, fertility, longevity, old age, wisdom. In many cultures, the tortoise is the oldest, most venerated symbol of cosmic order. According to ancient ideas, a turtle entwined with a snake is a symbol of the creation of the world. In India, the symbolism of stability is expressed in the idea that the earth rests on four elephants, which stand on a huge tortoise, slowly making its way through the chaos. The turtle is also a symbol of protection from fire and water.

Lizard

Gourd with a picture of a lizard

This nimble, fast animal is a symbol of agility, elusiveness, and also rebirth (the latter) is associated with the ability of a lizard to leave its tail to the one who caught it, which then grows back. Lizards, because they hide in the shade during the heat of the day, are considered guardians of shadows as well as keepers of sleep and dreams. The lizard, in addition, can symbolize the subconscious and the shadows of our inner world.

The lizard was considered a good sign in Egypt and in the ancient world, where it was sometimes associated with wisdom. She became an attribute of allegorical images of Logic. The symbol of Mercury, the messenger of the gods.

Mythical creatures

Imaginary animals are found all over the world in myths and folklore ... They enable us to clearly characterize phenomena that would be difficult to designate in any other way.

J. Tresidder

Mythical creatures are, as a rule, a combination of several animals, which allows the human imagination to endow them with unusual capabilities, including freedom from the usual principles of our world. Monsters, combining the appearance of several different animals, are a symbol of the initial chaos or the terrifying forces of nature, they also personify the evil forces in the nature of man himself. Fairy animals are often depicted as guarding treasures or hidden, secret knowledge.

Ba (bird)

Bird of the soul Ba, bent over the mummy before flying off to another world (Egypt)

Bird Ba is an Egyptian symbol of a human soul that flies off after his death to another world. This bird has a falcon body (according to some sources, a hawk) and a human head.

Basilisk (cockatrice)

Cock-headed basilisk

Basilisk is one of the deadliest creatures of medieval symbolism. According to some sources, the basilisk looks like a simplicissimus, but with the head and legs of a rooster. In occult and magical symbolism, the basilisk is depicted as a crowned serpent. Since, as is commonly believed, the basilisk destroys with a gaze everything it looks at, it was adopted as a magical symbol of wisdom, devouring a person by it symbolizes the process of initiation. It is believed that the only way to defeat a basilisk is to put a mirror in front of him.

Harpies

Harpy (XVI century)

These are half-women, half-birds (female head and chest, and the claws of a vulture) of a disgusting look. Associated with sudden death, whirlpools and storms. The feminine principle in its destructive aspect.

Garuda

Garuda (coat of arms of Thailand)

Bird of Life, Heaven, Sun, victory. Sometimes identified with Phoenix. She is also the vehicle of the god Vishnu, the creator and destroyer of everything ("Vishnu's horse"). She emerges from the egg as an adult and nests in the Tree of Life, which fulfills all desires. The head, chest (female), torso, legs up to the knees of the garuda are human, the beak, wings, tail, hind legs (below the knees) are eagle.

Garuda is often depicted fighting nagas (snakes) who personify evil.

Hydra

Hydra (Greece, XVI century)

In Greek mythology, Hydra is a dragon-serpent with seven heads. She symbolizes difficulties in the fight against evil: as soon as one of her heads is cut off, a new one immediately grows up. Blind, animal life force.

Griffin

Griffin protector (XVI century)

A solar hybrid creature that combines the head, wings and claws of an eagle with the body of a lion - these animals personify the power over air and earth (the king of birds and the king of beasts), therefore the griffin is a symbol of strength and vigilance. In Greece, the griffin was dedicated to Apollo, whose chariot he was carrying across the sky, for Athena he personified wisdom, for Nemesis - retribution. Legends say that griffins guarded the gold of India and the Scythians. There is also a legend that griffins living in the Far North guard the gold of Zeus, located in the country of the Hyperboreans.

The Dragon

Chinese dragon Chiao, symbol of a lucky break

The dragon - a "winged serpent", but only with paws like an eagle, unites in itself a snake and a bird, spirit and matter. This is one of the most versatile and complex symbols. The dragon can be sunny and lunar, good and evil. This is the keeper of treasures and secret knowledge. Longevity symbol. In the East, the dragon, as a rule, is the Heavenly Power that brings good, in the West it is a destructive and evil force. In Russia, the dragon is a sign of Satan, the devil. Victory over the dragon means the victory of light over darkness, over our own nature.

Unicorn

Heraldic unicorn

A unicorn is a mystical creature, an animal with the body of a horse or deer, which has a long sharp horn. In general, it symbolizes the feminine, lunar principle, purity, purity, chastity. In China, it represents abundance and longevity. According to legends, only a chaste maiden sitting alone in the forest can be caught: sensing her purity, the unicorn can approach her, put his head on her lap and fall asleep. Based on these legends, he became a symbol of purity, in particular for women.

Centaur

Centaur, lore hunter

According to Greek myths, a centaur is a creature with the body of a horse and a human torso. This is a symbol of the lower nature of man (lust, violence, drunkenness), his bestial nature, combined with a higher nature by human dignity and the ability to judge. It is a symbol of the conflict between the fierce and the good aspects of human nature.

There is a version about morally impeccable centaurs (among them - Chiron), descending from Kronos. They symbolize the superiority of reason over instinct.

Makara

Makara

In the western tradition, the Makara is a fantastic sea monster of enormous size (a fish with the head of a crocodile). A symbol of the power of the seas and oceans, rivers and lakes. In Hinduism, a makara has the appearance of a fish with the head and front legs of an antelope. This is one of the beings on which Vishnu travels. This is a positive symbol associated with rainbow and rain, with a lotus growing out of water, the return of the Sun after the winter solstice. In a number of legends, Makara is associated with deities acting as guardians of the world - lokapal (Varuna, Soma, Indra, Kubera ...).

Medusa Gorgon

Medusa Gorgon (Greece) - horror

Medusa the Gorgon is a female monster with snakes for hair, boar teeth, golden wings and bronze legs. This is the most outspoken personification of hostile evil, the Great Mother in her terrible aspect of the destroyer, the embodiment of horror. One glance at her turned people to stone, so her image later became a protective amulet. After Perseus cut off the head of Medusa Gorgon, the giant Chrysaor and the winged horse Pegasus were born from her blood.

Nagi

Buddha sitting on a coiled naga, symbolizing knowledge hidden in instinct (statue from the temple of Angkor)

In Hinduism, these are demigods, depicted with a snake body and one or more human heads (sometimes they are just multi-headed snakes). According to the legends, they own the underworld - patala, where they guard the untold treasures of the earth. According to legend, the nagas washed Gautam Buddha at his birth, and also protected his remains after death. Nagas are guardians of treasures and esoteric knowledge, serpent kings and queens, life forces of waters, passionate nature. These are the guardians of natural forces that can be controlled.

Pegasus

Pegasus (XVI century)

This is the winged horse of the Muses, which appeared from the neck of Medusa when Perseus cut off her head. Pegasus, on which Bellerophon defeated the Chimera, personifies a combination of lower and higher nature, striving for the higher, and symbolizes the superiority of the spiritual over the material. It is also a symbol of eloquence, poetic inspiration and contemplation. In European heraldry, Pegasus is depicted on the coats of arms of thinkers. It is often used today as an emblem for air transport.

Mermaid

Mermaid (15th century)

A fish woman capable of living in the human world and the supernatural world. Magic symbol of initiation. The Mermaid is a naval version of the Centaur. However, it also has more positive symbolism, according to the stories of the sailors. In Slavic mythology, mermaids (swimmers, watercaps, scraps, pitchforks, undines) are harmful creatures, especially dangerous during the Rusal week (following the Trinity). Mermaids are often confused with such creatures of ancient Greek mythology as nereids, naiads, water nymphs. But these eternally young maidens do not have, unlike mermaids, a fish tail.

Salamander

Salamander on fire

Salamander is a mythical creature in the form of an ordinary animal, but with supernatural powers. The salamander is usually depicted as a small lizard or wingless dragon, sometimes with a human or canine-like figure among flames. These creatures are considered the most venomous of creatures, their bite is deadly. Salamander is an element of fire and is able to live in fire as it has a very cold body. It is a symbol of the fight against sensual temptations. Since the salamander is considered a sexless creature, it also symbolizes chastity.

Simplicissimus

Harold's emblem

The simplicissimus is a fictional dragon-like beast with two eagle-like legs and a pike-shaped tail twisted in a loop. Symbolizes war, envy, stench, calamity, Satan, but also vigilance.

Simplicissimus was the personal emblem of King Harold (simplicissimus is depicted twice on French carpets from Bayeux, which tells of the Battle of Hastings and Harold's death in 1066).

Fo dog

Fo dog (China)

In translation from Chinese "Fo" means "great luck". It is a symbol of valor and energy, a talisman for the home. Fo dogs should be purchased in pairs and placed side by side. If you put them (or hang their images) in front of the front door, they meet everyone who comes in and protect every member of the family from troubles and failures. Housed in the wealth zone (southeast), the Fo dogs contribute to the well-being and prosperity of the home. Located in the central sector, they will quickly bring wealth to the house.

Sphinx

Egyptian coin with the image of the Sphinx

The Sphinx is a creature with the body of a lion and a human head (male or female) or with the head of a ram. The oldest and largest is the Great Sphinx at Giza (Egypt). This is an ancient image that personifies a mysterious, solar power, a symbol of dignity, royal power of wisdom, power, a symbol of the union of physical power with the highest intellect.

The Egyptian Sphinx has nothing to do with the later Greek legend of the "mystery of the Sphinx", which made him a symbol of mystery, the keeper of ancient wisdom, but Jung considered the Sphinx to be a symbol of female greed, as well as the "Terrible Mother".

Scylla and Charybdis

Scylla (Greece) - danger

In Greek mythology, these are two monsters of the Sicilian Sea that lived on both sides of the narrow strait and destroyed the sailors sailing between them. Ruthless incarnations of the powers of the sea. Once from beautiful nymphs, they were turned into monsters with six heads, with three rows of teeth in each head, with ugly long necks. These roaring, thundering monsters swallowed the sea and spat it back out (the image of the opening of the deep sea). Being between Scylla and Charybdis means being in danger at the same time from different sides.

Triton

Triton (Greece) - soothing waves

Depicted as an old man or a youth with a fish tail instead of legs. In Greek mythology, it is considered a sea deity - the son of Poseidon and the mistress of the seas Amphitrida. Triton blows a horn from a shell and rules the powers of the waters. Marine version of the mermaid, but male.

Phoenix

Phoenix (XVI century)

Phoenix is ​​the most famous of all resurrection symbols, the ancient symbol of immortality, the Sun. An animal that has a normal appearance, but with supernatural powers. This legendary bird is reborn from the ashes in the fire every 500 years. Phoenix became the emblem of the rebirth of the human spirit in the eternal struggle with the difficulties of the material world. From Ancient Egypt, this symbol passed completely intact into Slavic mythology (Firebird, Finist-Clear Falcon).

Chimera

Chimera (Vatican)

According to Homer's description, it is a monster with the head of a lion, the body of a goat, and the tail of a snake. It feeds on fire, was killed by Bellerophon, who ruled the winged pegasus.

In heraldry, the chimera is sometimes depicted with the head and chest of a woman and the tail of a dragon.

The Chimera causes winds and storms on land and at sea. Symbolizes danger, as well as delusion (can give rise to illusions). Moreover, it is a symbol of non-existence.

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