All mathematical terms and concepts. "etymological dictionary of mathematical terms"

Mathematical dictionary

Mathematical terms

A

Abscissa (Latin word abscissa - “cut off”). Borrowed from French V early XIX century French. abscisse - from latermin This is one of the Cartesian coordinates of a point, usually the first, denoted by the letter x. In the modern sense, the term was first used by the German scientist Gottfried Leibniz (in 1675).

Autocovariation(random process X(t)). X(t) and X(th)

Additivity(Latin word additivus - “added”). The property of quantities, consisting in the fact that the value of the quantity corresponding to the whole object is equal to the sum of the values ​​of quantities corresponding to its parts for any division of the object into parts.

Adjunct(Latin word adjunctus - “attached”). This is the same as algebraic complement.

Axiom(Greek word axios - valuable; axioma - “acceptance of position”, “honor”, ​​“respect”, “authority”). In Russian - since Peter's times. This is a basic proposition, a self-evident principle. The term first appears in Aristotle. Used in Euclid's Elements. An important role was played by the work of the ancient Greek scientist Archimedes, who formulated axioms related to the measurement of quantities. Contributions to axiomatics were made by Lobachevsky, Pash, Peano. A logically impeccable list of geometry axioms was indicated by the German mathematician Hilbert at the turn of the 19th and 20th centuries.

Axonometry(from the Greek words akon - “axis” and metrio - “I measure”). This is one of the ways to depict spatial figures on a plane.

Algebra(Arabic word “al-jabr”. Borrowed in the 17th century from Polish). This is a part of mathematics that develops in connection with the problem of solving algebraic equations. The term first appears in the work of the outstanding Central Asian mathematician and astronomer of the 11th century Muhammed ben-Musa al-Khwarizmi.

Analysis(Greek word analozis - “decision”, “resolution”). The term “analytic” goes back to Viethe, who rejected the word “algebra” as barbaric, replacing it with the word “analysis”.

Analogy(Greek word analogia - “correspondence”, “similarity”). This is an inference based on the similarity of particular properties of two mathematical concepts.

Antilogarithmlatermin the word nummerus - “number”). This number, which has a given table value of the logarithm, is denoted by the letter N.

Antje(French word entiere - “whole”). This is the same as the integer part of a real number.

Apothem(Greek word apothema, apo - “from”, “from”; thema - “attached”, “delivered”).

1. In a regular polygon, an apothem is a segment of a perpendicular descended from its center to any of its sides, as well as its length.

2.B correct pyramid apothem - the height of any of its side faces.

3. In a regular truncated pyramid, the apothem is the height of any of its side faces.

applicata(Latin word applicata - “attached”). This is one of the Cartesian coordinates of a point in space, usually the third, denoted by the letter Z.

Approximation(Latin word approximo - “approaching”). Replacement of some mathematical objects with others, in one sense or another close to the original ones.

Function argument(Latin word argumentum - “object”, “sign”). This is an independent variable whose values ​​determine the values ​​of the function.

Arithmetic(Greek word arithmos - “number”). This is the science that studies operations with numbers. Arithmetic originated in the countries of the Ancient East, Babylon, China, India, and Egypt. Special contributions were made by: Anaxagoras and Zeno, Euclid, Eratosthenes, Diophantus, Pythagoras, Leonardo of Pisa (Fibonacci), etc.

arctangent, Arcsine (prefix “arc” - the Latin word arcus - “bow”, “arc”). Arcsin and arctg appear in 1772 in the works of the Viennese mathematician Schaeffer and the famous French scientist J.L. Lagrange, although they had already been considered somewhat earlier by D. Bernoulli, but who used different symbolism.

Asymmetry(Greek word asymmetria - “disproportion”). This is the absence or violation of symmetry.

Asymptote(Greek word asymptotes - “mismatched”). This is a straight line to which the points of a certain curve approach indefinitely as these points move away to infinity.

Astroid(Greek word astron - “star”). Algebraic curve.

Associativity(Latin word associatio - “connection”). Combination law of numbers. The term was coined by William Hamilton (in 1843).

B

Billion(French word billion, or billion - milliard). This is a thousand million, a number represented by one followed by 9 zeros, the term. number 10 9. In some countries, a billion is a number equal to 10 12.

binomial latermin the words bi - “double”, nomen - “name”. It is the sum or difference of two numbers or algebraic expressions called binomial terms.

Bisector(latermin of the words bis - “twice” and sectrix - “secant”). Borrowed in the 19th century from the French language where bissectrice - goes back to the Latin phrase. This is a straight line passing through the vertex of the angle and dividing it in half.

IN

Vector(Latin word vector - “carrying”, “carrier”). This is a directed segment of a straight line, one end of which is called the beginning of the vector, the other end is called the end of the vector. This term was introduced by the Irish scientist W. Hamilton (in 1845).

Vertical angles(the later term of the word verticalis is “vertex”). These are pairs of angles with a common vertex, formed by the intersection of two straight lines so that the sides of one angle are a continuation of the sides of the other.

G

Hexahedron(Greek words geks - “six” and edra - “edge”). This is a hexagon. This term is attributed to the ancient Greek scientist Pappus of Alexandria (3rd century).

Geometry(Greek words geo - “Earth” and metreo - “I measure”). Old Russian Borrowed from Greek. The part of mathematics that studies spatial relationships and shapes. The term appeared in the 5th century BC in Egypt, Babylon.

Hyperbola(Greek word hyperballo - “passing through something”). Borrowed in the 17th century from Latin It is an open curve of two unlimitedly extending branches. The term was introduced by the ancient Greek scientist Apollonius of Perm.

Hypotenuse(Greek word gyipotenusa - “contracting”). Borrowed from Latin in the 17th century, in which hypotenusa is from Greek. side of a right triangle opposite right angle. The ancient Greek scientist Euclid (3rd century BC) wrote instead of this term, “the side that subtends a right angle.”

Hypocycloid(Greek word gipo - “under”, “below”). The curve that a point on a circle describes.

Goniometry(Latin word gonio - “angle”). This is the study of "trigonometric" functions. However, this name did not catch on.

Homothety(Greek word homos - “equal”, “same”, thetos - “located”). This is an arrangement of figures that are similar to each other, in which the straight lines connecting the corresponding points of the figures intersect at the same point, called the center of homothety.

Degree(Latin word gradus - “step”, “step”). A unit of measurement for a plane angle equal to 1/90 of a right angle. The measurement of angles in degrees appeared more than 3 years ago in Babylon. Designations reminiscent of modern ones were used by the ancient Greek scientist Ptolemy.

Schedule(Greek word graphikos - “inscribed”). This is a graph of a function - a curve on a plane depicting the dependence of the function on the argument.

D

Deduction(Latin word deductio - “deduction”). This is a form of thinking through which a statement is derived purely logically (according to the rules of logic) from certain given statements - premises.

Defenders(Latin word defero - “carry”, “move”). This is the circle around which the epicycloids of each planet rotate. For Ptolemy, the planets rotate in circles - epicycles, and the centers of the epicycles of each planet rotate around the Earth in large circles - deferents.

Diagonal(Greek dia - “through” and gonium - “angle”). This is a straight line connecting two vertices of a polygon that do not lie on the same side. The term is found in the ancient Greek scientist Euclid (3rd century BC).

Diameter(Greek word diametros - “diameter”, “through”, “measuring” and the word dia - “between”, “through”). The term “division” in Russian was first found by Leonty Fillipovich Magnitsky.

Headmistress(Latin word directrix - “director”).

Discreteness(Latin word discretus - “divided”, “discontinuous”). This is discontinuity; opposed to continuity.

Discriminant(Latin word discriminans - “discriminating”, “separating”). This is an expression made up of quantities defined by a given function, the reversal of which to zero characterizes one or another deviation of the function from the norm.

Distributivity(Latin word distributivus - “distributive”). Distributive law connecting addition and multiplication of numbers. The term was introduced by the French. scientist F. Servois (in 1815).

Differential(Latin word differento - “difference”). This is one of the main concepts mathematical analysis. This term was found by the German scientist G. Leibniz in 1675 (published in 1684).

Dichotomy(Greek word dichotomia - “division in two”). Method of classification.

Dodecahedron(Greek words dodeka - "twelve" and edra - "foundation"). This is one of the five regular polyhedra. The term was first found by the ancient Greek scientist Theaetetus (4th century BC).

Z

Denominator- a number showing the size of the fractions of a unit from which the fraction is composed. It was first found by the Byzantine scientist Maximus Planud (late 13th century).

AND

Isomorphism(Greek words isos - “equal” and morfe - “kind”, “form”). This is a concept of modern mathematics, clarifying the widespread concept of analogy, model. The term was introduced in the middle of the 17th century.

Icosahedron(Greek words eicosi - "twenty" and edra - base). One of the five regular polyhedra; has 20 triangular faces, 30 edges and 12 vertices. The term was given by Theaetetus, who discovered it (4th century BC).

Invariance(the later term of the word in is “negation” and varians is “changing”). This is the invariance of any quantity in relation to transformations of the coordinate, a term introduced by the English J. Sylvester (in 1851).

Induction(Latin word inductio - “guidance”). One of the methods of proving mathematical statements. This method first appears in Pascal.

Index(Latin word index - “index”. Borrowed at the beginning of the 18th century from Latin). A numeric or alphabetic indicator that is provided with mathematical expressions to distinguish them from each other.

Integral(Latin word integro - “to restore” or integer - “whole”). Borrowed in the second half of the 18th century. from the French language based on the latermin integralis - “whole”, “complete”. One of the basic concepts of mathematical analysis, which arose in connection with the need to measure areas, volumes, and find functions from their derivatives. These integral concepts are usually associated with Newton and Leibniz. This word was first used in print by the Swiss Scientist Jacob Bernoulli (in 1690). The sign ∫ is a stylized letter S from the latermin word summa - “sum”. First appeared in Gottfried Wilhelm Leibniz.

Interval(Latin word intervallum - “interval”, “distance”). The set of real numbers satisfying the inequality a< x

Irrational number(the term is irrationalis - “unreasonable”). A number that is not rational. The term was introduced by the German. scientist Michael Stiefel (in 1544). A rigorous theory of irrational numbers was built in the 2nd half of the 19th century.

Iteration(the term is iteratio - “repetition”). The result of repeatedly applying a mathematical operation.

TO

Calculator- the German word kalkulator goes back to the latermin word calculator - “to count”. Borrowed at the end of the 18th century. from German language Portable computing device.

Canonical expansion- Greek word canon - “rule”, “norm”.

Tangent- Latin word tangens - “touching”. Semantic tracing paper of the late 18th century.

Leg- Latin word katetos - “plumb line”. The side of a right triangle adjacent to a right angle. The term first appears in the form “cathetus” in Magnitsky’s “Arithmetic” of 1703, but already in the second decade of the 18th century the modern form became widespread.

Square- Latin word quadratus - “quadrangular” (from guattuor - “four”). A rectangle in which all sides are equal, or, equivalently, a rhombus in which all angles are equal.

Quaternions- Latin word quaterni - “in fours”. A system of numbers that arose in attempts to find a generalization of complex numbers. The term was proposed by the English Hamilton (in 1843).

Quintillion- French quintillion. A number represented by a one followed by 18 zeros. Borrowed at the end of the 19th century.

Covariance(correlation moment, covariance moment) - in probability theory and mathematical statistics, a measure of the linear dependence of two random variables. wikipedia. ENG: Covariance

Collinearity- the Latin word con, com - “together” and linea - “line”. Location on one line (straight). The term was introduced by America. scientist J. Gibbs; however, this concept was encountered earlier by W. Hamilton (in 1843).

Combinatorics- The Latin word combinare means “to connect.” A branch of mathematics that studies the various connections and arrangements involved in counting combinations of elements of a given finite set.

Coplanarity- laterminwords con, com - “together” and planum - “flatness”. Location in one plane. The term first appears in J. Bernoulli; however, this concept was encountered earlier in W. Hamilton (in 1843).

Commutativity- Late Latin word commutativus - “changing”. The property of adding and multiplying numbers, expressed by the identities: ab=ba, ab=ba.

Congruence- Latin word congruens - “proportionate”. A term used to denote the equality of segments, angles, triangles, etc.

Constant- Latin word constans - “constant”, “unchangeable”. A constant value when considering mathematical and other processes.

Cone- Greek word konos - “pin”, “bump”, “top of a helmet”. A body bounded by one cavity of a conical surface and a plane intersecting this cavity and perpendicular to its axis. The term received its modern meaning from Aristarchus, Euclid, and Archimedes.

Configuration- the Latin word co - “together” and figura - “view”. Location of figures.

Conchoid- Greek word conchoides - “like a mussel shell.” Algebraic curve. Introduced by Nicomedes of Alexandria (2nd century BC).

Coordinates- the Latin word co - “together” and ordinates - “determined”. Numbers taken in a certain order, determining the position of a point on a line, plane, space. The term was introduced by G. Leibniz (in 1692).

Cosecant- Latin word cosecans. One of the trigonometric functions.

Cosine- the Latin word complementi sinus, complementus - “supplement”, sinus - “hollow”. Borrowed at the end of the 18th century. from the language of learned Latin. One of the trigonometric functions, denoted cos. Introduced by Leonhard Euler in 1748.

Cotangent- the Latin word complementi tangens: complementus - “supplement” or from the latermin of the word cotangere - “to touch”. In the second half of the 18th century. from the language of scientific Latin. One of the trigonometric functions, denoted ctg.

Coefficient- the Latin word co - “together” and efficiens - “producing”. A multiplier, usually expressed in numbers. The term was introduced by Vietermin

Cube - The Greek word kubos is "dice". Borrowed at the end of the 18th century. from learned Latin. One of the regular polyhedra; has 6 square faces, 12 edges, 8 vertices. The name was introduced by the Pythagoreans, then found by Euclid (3rd century BC).

L

Lemma- The Greek word lemma means “assumption”. This is an auxiliary sentence used in proving other statements. The term was introduced by ancient Greek geometers; is especially common in Archimedes.

Lemniscate- Greek word lemniscatus - “decorated with ribbons.” Algebraic curve. Invented by Bernoulli.

Line- Latin word linea - “linen”, “thread”, “cord”, “rope”. One of the main geometric images. The idea of ​​it can be a thread or an image described by the movement of a point in a plane or space.

Logarithm- The Greek word logos - “relation” and arithmos - “number”. Borrowed in the 17th century from French, where logarithme is English. logarithmus - formed by adding the Greek. words The exponent m to which a must be raised to obtain the N term was proposed by J. Napier.

M

Maximum- Latin word maximum - “greatest”. Borrowed in the second half of the 19th century from Latin The greatest value of a function on the set of definition of a function.

Mantissa- The Latin word mantissa means “increase”. This is the fractional part of the decimal logarithm. The term was proposed by the Russian mathematician Leonhard Euler (in 1748).

Scale- German the word mas - “measure” and stab - stick.” This is the ratio of the length of a line in a drawing to the length of the corresponding line in reality.

Mathematics- Greek word matematike from the Greek words matema - “knowledge”, “science”. Borrowed at the beginning of the 18th century. from Latin, where mathematica is the Greek Science of quantitative relations and spatial forms of the real world.

Matrix- Latin word matrix - “uterus”, “source”, “beginning”. This is a rectangular table formed from a certain set and consisting of rows and columns. The term first appeared by William Hamilton and scientists A. Cayley and J. Sylvester in mid. XIX century. The modern designation is two verticals. dashes - introduced by A. Cayley (in 1841).

Median(triug-ka) - the Latin word medianus - “middle”. This is a segment connecting the vertex of a triangle to the middle of the opposite side.

Meter- the French word metre - “stick for measuring” or the Greek word metron - “measure”. Borrowed in the 17th century from French, where metre is Greek. This is the basic unit of length. She was born 2 centuries ago. The meter was “born” by the French Revolution in 1791.

Metrics- Greek word metric< metron - «мера», «размер». Это правило определения расстояния между любыми двумя точками данного пространства.

Million- Italian word millione - “thousand”. Borrowed in the Petrine era from the French language, where million is an Italian Number written with six zeros. The term was coined by Marco Polo.

Billion- The French word mille means “thousand”. Borrowed in the 19th century from the French language, where milliard is a suffix. Derived from mille - "thousand".

Minimum- Latin word minimum - “smallest”. The smallest value of a function on the function's definition set.

Minus- Latin word minus - “less”. This is a mathematical symbol in the form of a horizontal line, used to indicate negative numbers and the action of subtraction. Introduced into science by Widmann in 1489.

Minute- Latin word minutus - “small”, “reduced”. Borrowed at the beginning of the 18th century. from French, where minute is latermin This is a unit of plane angles equal to 1/60 of a degree.

Module- Latin word modulus - “measure”, “magnitude”. This is the absolute value of a real number. The term was coined by Roger Cotes, a student of Isaac Newton. The modulus sign was introduced in the 19th century by Karl Weierstrass.

Multiplicativity- Latin word multiplicatio - “multiplying”. This is a property of the Euler function.

N

Norm- Latin word norma - “rule”, “model”. Generalization of the concept of absolute value of a number. The “norm” sign was introduced by the German scientist Erhard Schmidt (in 1908).

Zero- Latin word nullum - “nothing”, “nothing”. Originally the term meant the absence of a number. The designation zero appeared around the middle of the first millennium BC

Numbering- Latin word numero - “I count.” This is notation or a set of techniques for naming and designating numbers.

ABOUT

Oval- the Latin word ovaum - “egg”. Borrowed in the 17th century from French, where ovale is latermin This is a closed convex flat figure.

Circle The Greek word periferia is “periphery”, “circle”. This is the set of points on a plane located at a given distance from a given point lying in the same plane and called its center.

Octahedron- Greek words okto - “eight” and edra - “base”. It is one of the five regular polyhedra; has 8 triangular faces, 12 edges and 6 vertices. This term was given by the ancient Greek scientist Theaetetus (4th century BC), who first built the octahedron.

Ordinate- Latin word ordinatum - “in order”. One of the Cartesian coordinates of a point, usually the second, denoted by the letter y. As one of the Cartesian coordinates of a point, this term was used by the German scientist Gottfried Leibniz (in 1694).

Ort- Greek word orthos - “straight”. The same as a unit vector, the length of which is assumed to be equal to one. The term was introduced by the English scientist Oliver Heaviside (in 1892).

Orthogonality- Greek word ortogonios - “rectangular”. Generalization of the concept of perpendicularity. Found in the ancient Greek scientist Euclid (3rd century BC).

P

Parabola- the Greek word parabole - “application”. This is a non-central line of the second order, consisting of one infinite branch, symmetrical about the axis. The term was introduced by the ancient Greek scientist Apollonius of Perga, who considered a parabola as one of the conic sections.

Parallelepiped- Greek word parallelos - “parallel” and epipedos - “surface”. This is a hexagon, all of whose faces are parallelograms. The term was found among the ancient Greek scientists Euclid and Heron.

Parallelogram- Greek words parallelos - “parallel” and gramma - “line”, “line”. This is a quadrilateral whose opposite sides are parallel in pairs. Euclid began to use the term.

Parallelism- parallelos - “walking nearby.” Before Euclid, the term was used in the school of Pythagoras.

Parameter- Greek word parametros - “measuring”. This is an auxiliary variable included in formulas and expressions.

Perimeter- the Greek word peri - “around”, “about” and metreo - “measure”. The term is found among the ancient Greek scientists Archimedes (3rd century BC), Heron (1st century BC), Pappus (3rd century BC).

Perpendicular- Latin word perpendicularis - “steep”. This is a straight line intersecting a given straight line (plane) at a right angle. The term was formed in the Middle Ages.

Pyramid- the Greek word pyramis, the cotermin comes from the Egyptian word permeous - “side edge of a structure” or from pyros - “wheat”, or from pyra - “fire”. Borrowed from terminology. language This is a polyhedron, one of whose faces is a flat polygon, and the remaining faces are triangles with a common vertex that does not lie in the plane of the base.

Square- Greek word plateia - “wide”. Origin unclear. Some scientists believe Borrowed from terminology. Others interpret it as originally Russian.

Planimetry- the Latin word planum - “plane” and metreo - “I measure”. This is a part of elementary geometry in which the properties of figures lying in a plane are studied. The term is found in ancient Greek. scientist Euclid (4th century BC).

Plus- Latin word plus - “more”. This is a sign to indicate the action of addition, as well as to indicate the positivity of numbers. The sign was introduced by the Czech (German) scientist Jan (Johann) Widmann (in 1489).

Polynomial- the Greek word polis - “numerous”, “extensive” and the Latin word nomen - “name”. This is the same term as a polynomial. the sum of a certain number of monomials.

Potentiation- the German word potenzieren - “to raise to a power.” The action of finding a number using a given logarithm.

Limit- Latin word limes - “border”. This is one of the basic concepts of mathematics, meaning that a certain variable value in the process of its change under consideration indefinitely approaches a certain constant value. The term was introduced by Newton, and the currently used symbol lim (the first 3 letters of limes) was introduced by the French scientist Simon Lhuillier (in 1786). The expression lim was first written down by the Irish mathematician William Hamilton (in 1853).

Prism- The Greek word prisma means “sawed off piece.” This is a polyhedron, two of whose faces are equal n-gons, called the bases of the prism, and the remaining faces are lateral. The term is found already in the 3rd century BC in ancient Greek. scientists Euclid and Archimedes.

Example- Greek word primus - “first”. Number problem. The term was invented by Greek mathematicians.

Derivative- French derivee. Introduced by Joseph Lagrange in 1797.

Projection- The Latin word projectio means “throwing forward.” This is a way of depicting a flat or spatial figure.

Proportion- Latin word proportio - “ratio”. This is an equality between two ratios of four quantities.

Percent- the Latin word pro centum - “from a hundred.” The idea of ​​interest originated in Babylon.

Postulate- Latin word postulatum - “demand”. A name sometimes used for the axioms of a mathematical theory

R

Radian- Latin word radius - “spoke”, “ray”. This is a unit of measurement for angles. The first publication containing this term appeared in 1873 in England.

Radical- Latin word radix - “root”, radicalis - “radical”. The modern sign √ first appeared in Rene Descartes's book Geometry, published in 1637. This sign consists of two parts: a modified letter r and a bar that previously replaced parentheses. The Indians called it “mula,” the Arabs called it “jizr,” and the Europeans called it “radix.”

Radius- Latin word radius - “spoke in a wheel”. Borrowed from Latin in the Petrine era. This is a segment connecting the center of a circle with any point on it, as well as the length of this segment. The term did not exist in ancient times; it was first found in 1569 by the French scientist Pierre Ramet, then by François Vieta, and became generally accepted at the end of the 17th century.

Recurrent- the Latin word recurrere - “to go back.” This is a backward movement in mathematics.

Rhombus- Greek word rombos - “tambourine”. This is a quadrilateral with all sides equal. The term was used by the ancient Greek scientists Heron (1st century BC), Pappus (2nd half of the 3rd century).

Rolls- French roulette - “wheel”, “compare”, “roulette”, “steering wheel”. These are curves. The term was coined by the French. mathematicians who studied the properties of curves.

C

Segment- Latin word segmentum - “segment”, “strip”. This is a part of a circle limited by the arc of the boundary circle and the chord connecting the ends of this arc.

Secant- the Latin word secans - “secant”. This is one of the trigonometric functions. Denoted by sec.

Sextillion- French sextillion. A number represented with 21 zeros, term. number 1021.

Sector- the Latin word seco - “cut”. This is a part of a circle limited by the arc of its boundary circle and its two radii connecting the ends of the arc with the center of the circle.

Second- Latin word secunda - “second”. This is a unit of plane angles equal to 1/3600 of a degree or 1/60 of a minute.

Signum- Latin word signum - “sign”. This is a function of the real argument.

Symmetry- Greek word simmetria - “proportionality”. The property of the shape or arrangement of figures being symmetrical.

Sinus- latermin sinus - “bend”, “curvature”, “sinus”. This is one of the trigonometric functions. In the 4th-5th centuries. called “ardhajiva” (ardha - half, jiva - bowstring). Arab mathematicians in the 9th century. the word "jibe" is a convexity. When translating Arabic mathematical texts in the 12th century. The term has been replaced by "sine". The modern designation sin was introduced by the Russian scientist Euler (in 1748).

Scalar- Latin word scalaris - “stepped”. This is a quantity, each value of which is expressed by one number. This term was introduced by the Irish scientist W. Hamilton (in 1843).

Spiral- The Greek word speria means “coil”. This is a flat curve that usually circles around one (or more) points, approaching or moving away from it.

Stereometry- Greek words stereos - “volumetric” and metreo - “measure”. This is a part of elementary geometry in which spatial figures are studied.

Sum- Latin word summa - “total”, “total quantity”. The result of the addition. Sign? (Greek letter “sigma”) was introduced by the Russian scientist Leonhard Euler (in 1755).

Sphere- Greek word sfaira - “ball”, “ball”. This is a closed surface obtained by rotating a semicircle around a straight line containing its subtending diameter. The term is found among the ancient Greek scientists Plato and Aristotle.

T

Tangent- Latin word tanger - “to touch”. One of the trigonometers. functions. The term was introduced in the 10th century by the Arab mathematician Abu-l-Wafa, who compiled the first tables for finding tangents and cotangents. The designation tg was introduced by the Russian scientist Leonhard Euler.

Theorem- Greek word tereo - “I explore.” This is a mathematical statement whose truth is established through proof. The term was also used by Archimedes.

Tetrahedron- Greek words tetra - “four” and edra - “base”. One of the five regular polyhedra; has 4 triangular faces, 6 edges and 4 vertices. Apparently, the term was first used by the ancient Greek scientist Euclid (3rd century BC).

Topology- Greek word topos - “place”. A branch of geometry that studies the properties of geometric figures related to their relative positions. Euler, Gauss, and Riemann believed that the term Leibniz refers specifically to this branch of geometry. In the second half of the last century, a new field of mathematics was introduced, it was called topology.

Dot- Russian the word “poke” is as if the result of an instant touch, a prick. N.I. Lobachevsky, however, believed that the term comes from the verb “to sharpen” - as a result of the touch of the tip of a sharpened pen. One of the basic concepts of geometry.

Tractor- Latin word tractus - “extended”. Plane transcendental curve.

Transposition- Latin word transpositio - “rearrangement”. In combinatorics, a permutation of elements of a given set in which 2 elements are swapped.

Protractor- the Latin word transortare - “to transfer”, “to shift”. A device for constructing and measuring angles in a drawing.

Transcendental- the Latin word transcendens - “going beyond”, “transcending”. It was first used by the German scientist Gottfried Leibniz (in 1686).

Trapezoid- Greek word trapezion - “table”. Borrowed in the 17th century from Latin, where trapezion is Greek. It is a quadrilateral whose two opposite sides are parallel. The term was first found by the ancient Greek scientist Posidonius (2nd century BC).

Triangulated- Latin word triangulum - “triangle”.

Trigonometry- Greek words trigonon - “triangle” and metreo - “measure”. Borrowed in the 17th century from learned Latin. A branch of geometry that studies trigonometric functions and their applications to geometry. The term first appears in the title of a book by the German scientist B. Titis (in 1595).

Trillion- French word trillion. Borrowed in the 17th century from the French language Number with 12 zeros, term. 1012.

Trisection- angles of the laterminword tri - “three” and section - “cutting”, “dissection”. The problem of dividing an angle into three equal parts.

Trochoid- Greek word trochoeides - “wheel-shaped”, “round”. Plane transcendental curve.

Mathematics (ancient Greek μᾰθημᾰτικά< др.-греч. μάθημα - изучение, наука) - the science of structures, order and relationships, historically developed on the basis of the operations of counting, measuring and describing the shape of objects. Mathematical objects are created by idealizing the properties of real or other mathematical objects and writing these properties in a formal language. Mathematics does not belong to the natural sciences, but is widely used in them both for the precise formulation of their content and for obtaining new results. Mathematics is a fundamental science that provides (general) language tools to other sciences; Thus, it reveals their structural relationship and contributes to the discovery of the most general laws of nature.

We present to your attention a dictionary of mathematical terms.

Abscissa- (Latin word abscissa - “cut off”). Borrowing from French language at the beginning of the 19th century Franz. abscisse - from lat. This is one of the Cartesian coordinates of a point, usually the first, denoted by x. In the modern sense, T. was first used by the German scientist G. Leibniz (1675).

Additivity- (Latin word additivus - “added”). The property of quantities, consisting in the fact that the value of the quantity corresponding to the whole object is equal to the sum of the values ​​of quantities corresponding to its parts for any division of the object into parts.

Adjunct- (Latin word adjunctus - “attached”). This is the same as algebraic complement.

Axiom- (Greek word axios - valuable; axioma - “acceptance of position”, “honor”, ​​“respect”, “authority”). In Russian - since Peter's times. This is a basic proposition, a self-evident principle. T. is first found in Aristotle. Used in Euclid's Elements. An important role was played by the work of the ancient Greek scientist Archimedes, who formulated axioms related to the measurement of quantities. Contributions to axiomatics were made by Lobachevsky, Pash, Peano. A logically impeccable list of geometry axioms was indicated by the German mathematician Hilbert at the turn of the 19th and 20th centuries.

Axonometry- (from the Greek words akon - “axis” and metrio - “I measure”). This is one of the ways to depict spatial figures on a plane.

Algebra- (Arabic word “al-jabr”). This is a part of mathematics that develops in connection with the problem of solving algebraic equations. T. first appears in the work of the outstanding mathematician and astronomer of the 11th century, Muhammad ben Musa al-Khwarizmi.

Analysis- (Greek word analozis - “decision”, “resolution”). T. "analytic" goes back to Vieta, who rejected the word "algebra" as barbaric, replacing it with the word "analysis".

Analogy -(Greek word analogia - “correspondence”, “similarity”). This is an inference based on the similarity of particular properties of two mathematical concepts.

Antilog - (Latin word nummerus - “number”). This number, which has a given table value of the logarithm, is denoted by the letter N.

Antje - (French word entiere - “whole”). This is the same as the integer part of a real number.

Apothem -(Greek word apothema, apo - “from”, “from”; thema - “attached”, “delivered”).
1. In a regular polygon, an apothem is a perpendicular segment dropped from its center to any of its sides, as well as its length.
2. In a regular pyramid, the apothem is the height of any of its side faces.
3. In a regular truncated pyramid, the apothem is the height of any of its side faces.

Applicate -(Latin word applicata - “attached”). This is one of the Cartesian coordinates of a point in space, usually the third, denoted by the letter Z.

Approximation- (Latin word approximo - “approaching”). Replacement of some mathematical objects with others, in one sense or another close to the original ones.

Function argument(Latin word argumentum – “object”, “sign”). This is an independent variable whose values ​​determine the values ​​of the function.

Arithmetic(Greek word arithmos - “number”). This is the science that studies operations with numbers. Arithmetic originated in the countries of Dr. East, Babylon, China, India, Egypt. Special contributions were made by: Anaxagoras and Zeno, Euclid, Eratosthenes, Diophantus, Pythagoras, L. Pisansky and others.

Arctangent, Arcsine(the prefix “arc” is the Latin word arcus – “bow”, “arc”). Arcsin and arctg appear in 1772 in the works of the Viennese mathematician Schaeffer and the famous French scientist J.L. Lagrange, although they had already been considered somewhat earlier by D. Bernoulli, but who used different symbolism.

Asymmetry(Greek word asymmetria - “disproportion”). This is the absence or violation of symmetry.

Asymptote(Greek word asymptotes - “non-matching”). This is a straight line to which the points of a certain curve approach indefinitely as these points move away to infinity.

Astroid(Greek word astron - “star”). Algebraic curve.

Associativity(Latin word associatio - “connection”). Combination law of numbers. T. was introduced by W. Hamilton (1843).

Billion(French word billion, or billion - milliard). This is a thousand million, a number represented by one followed by 9 zeros, i.e. number 10 9. In some countries, a billion is a number equal to 10 12.

Binomial(Latin words bi - “double”, nomen - “name) the sum or difference of two numbers or algebraic expressions, called members of a binomial.

Bisector(Latin words bis - “twice” and sectrix - “secant”). Borrowing In the 19th century from French language where bissecrice – goes back to lat. phrase. This is a straight line passing through the vertex of the angle and dividing it in half.

Vector(Latin word vector – “carrying”, “carrier”). This is a directed segment of a straight line, one end of which is called the beginning of the vector, the other end is called the end of the vector. This term was introduced by the Irish scientist W. Hamilton (1845).

Vertical angles(Latin word verticalis – “peak”). These are pairs of angles with a common vertex, formed by the intersection of two straight lines so that the sides of one angle are a continuation of the sides of the other.

Hexahedron(Greek words geks - “six” and edra - “edge”). This is a hexagon. This T. is attributed to the ancient Greek scientist Pappus of Alexandria (3rd century).

Geometry(Greek words geo – “Earth” and metreo – “I measure”). Old Russian borrowed from Greek The part of mathematics that studies spatial relationships and shapes. T. appeared in the 5th century BC. in Egypt, Babylon.

Hyperbola(Greek word hyperballo - “passing through something”). Borrowing in the 18th century from lat. language This is an open curve of two unlimitedly extending branches. T. was introduced by the ancient Greek scientist Apollonius of Perm.

Hypotenuse(Greek word gyipotenusa - “contracting”). Deputy from lat. language in the 18th century, in which hypotenusa – from the Greek. the side of a right triangle that lies opposite the right angle. The ancient Greek scientist Euclid (3rd century BC) wrote instead of this term, “the side that subtends a right angle.”

Hypocycloid(Greek word gipo – “under”, “below”). The curve that a point on a circle describes.

Goniometry(Latin word gonio - “angle”). This is the study of "trigonometric" functions. However, this name did not catch on.

Homothety(Greek word homos - “equal”, “identical”, thetos - “located”). This is an arrangement of figures that are similar to each other, in which the straight lines connecting the corresponding points of the figures intersect at the same point, called the center of homothety.

Degree(Latin word gradus - “step”, “step”). A unit of measurement for a plane angle equal to 1/90 of a right angle. The measurement of angles in degrees appeared more than 3 years ago in Babylon. Designations reminiscent of modern ones were used by the ancient Greek scientist Ptolemy.

Schedule(Greek word graphikos - “inscribed”). This is a graph of a function - a curve on a plane depicting the dependence of the function on the argument.

Deduction(Latin word deductio - “removal”). This is a form of thinking through which a statement is derived purely logically (according to the rules of logic) from certain given statements - premises.

Defenders(Latin word defero - “carry”, “move”). This is the circle around which the epicycloids of each planet rotate. For Ptolemy, the planets rotate in circles - epicycles, and the centers of the epicycles of each planet rotate around the Earth in large circles - deferents.

Diagonal(Greek word dia – “through” and gonium – “angle”). This is a straight line connecting two vertices of a polygon that do not lie on the same side. T. is found in the ancient Greek scientist Euclid (3rd century BC).

Diameter(Greek word diametros - “diameter”, “through”, “measuring” and the word dia - “between”, “through”). T. “division” in Russian is first found in L.F. Magnitsky.

Headmistress(Latin word directrix - “director”).

Discreteness(Latin word discretus – “divided”, “discontinuous”). This is discontinuity; opposed to continuity.

Discriminant(Latin word discriminans - “discriminating”, “separating”). This is an expression made up of quantities defined by a given function, the reversal of which to zero characterizes one or another deviation of the function from the norm.

Distributivity(Latin word distributivus – “distributive”). Distributive law connecting addition and multiplication of numbers. T. was introduced by the French. scientist F. Servois (1815).

Differential(Latin word differento- “difference”). This is one of the basic concepts of mathematical analysis. This T. is found by the German scientist G. Leibniz in 1675 (published in 1684).

Dichotomy(Greek word dichotomia - “division in two”). Method of classification.

Dodecahedron(Greek words dodeka - “twelve” and edra - “foundation”). This is one of the five regular polyhedra. T. is first encountered by the ancient Greek scientist Theaetetus (4th century BC).

Unfortunately, the ability to read the site in the Tatar language is under development (this requires financial investments and reworking of technical parts). Therefore, most mathematical terms do not have a translation into the Tatar language. But you can read the meaning of these terms (explanations, their meaning or other data) in the Tatar language using online translators (there are many such translators on the Internet). Below are some translator links. Copy the text and paste it into the translation field.

ELECTRONIC DICTIONARY OF THE TATAR LANGUAGE /open website with translator/

RUSSIAN-TATAR, TATAR-RUSSIAN DICTIONARY /open website with dictionary/

MATHEMATICAL TERMS AND INTERPRETATIONS

Abscissa(Latin word abscissa - “cut off”). Borrowing from French language at the beginning of the 19th century Franz. abscisse - from lat. This is one of the Cartesian coordinates of a point, usually the first, denoted by x. In the modern sense, T. was first used by the German scientist G. Leibniz (1675).

Additivity(Latin word additivus - “added”). The property of quantities, consisting in the fact that the value of the quantity corresponding to the whole object is equal to the sum of the values ​​of quantities corresponding to its parts for any division of the object into parts.

Adjunct(Latin word adjunctus - “attached”). This is the same as algebraic complement.

Axiom(Greek word axios - valuable; axioma - “acceptance of position”, “honor”, ​​“respect”, “authority”). In Russian - since Peter's times. This is a basic proposition, a self-evident principle. T. is first found in Aristotle. Used in Euclid's Elements. An important role was played by the work of the ancient Greek scientist Archimedes, who formulated axioms related to the measurement of quantities. Contributions to axiomatics were made by Lobachevsky, Pash, Peano. A logically impeccable list of geometry axioms was indicated by the German mathematician Hilbert at the turn of the 19th and 20th centuries.

Axonometry(from the Greek words akon - “axis” and metrio - “I measure”). This is one of the ways to depict spatial figures on a plane.

Algebra(Arabic word “al-jabr”. Borrowed in the 18th century from Polish). This is a part of mathematics that develops in connection with the problem of solving algebraic equations. T. first appears in the work of the outstanding Central Asian mathematician and astronomer of the 11th century Muhammed ben-Musa al-Khorezmi.

Analysis(Greek word analozis - “decision”, “resolution”). T. "analytic" goes back to Vieta, who rejected the word "algebra" as barbaric, replacing it with the word "analysis".

Analogy(Greek word analogia - “correspondence”, “similarity”). This is an inference based on the similarity of particular properties of two mathematical concepts.

Antilogarithmlat. the word nummerus - “number”). This number, which has a given table value of the logarithm, is denoted by the letter N.

Antje(French word entiere - “whole”). This is the same as the integer part of a real number.

Apothem(Greek word apothema, apo - “from”, “from”; thema - “attached”, “delivered”).

1. In a regular polygon, an apothem is a segment of a perpendicular descended from its center to any of its sides, as well as its length.

2. In a regular pyramid, the apothem is the height of any of its side faces.

3. In a regular truncated pyramid, the apothem is the height of any of its side faces.

applicata(Latin word applicata - “attached”). This is one of the Cartesian coordinates of a point in space, usually the third, denoted by the letter Z.

Approximation(Latin word approximo - “approaching”). Replacement of some mathematical objects with others, in one sense or another close to the original ones.

Function argument(Latin word argumentum - “object”, “sign”). This is an independent variable whose values ​​determine the values ​​of the function.

Arithmetic(Greek word arithmos - “number”). This is the science that studies operations with numbers. Arithmetic originated in the countries of Dr. East, Babylon, China, India, Egypt. Special contributions were made by: Anaxagoras and Zeno, Euclid, Eratosthenes, Diophantus, Pythagoras, L. Pisansky and others.

arctangent, Arcsine (prefix “arc” - the Latin word arcus - “bow”, “arc”). Arcsin and arctg appear in 1772 in the works of the Viennese mathematician Schaeffer and the famous French scientist J.L. Lagrange, although they had already been considered somewhat earlier by D. Bernoulli, but who used different symbolism.

Asymmetry(Greek word asymmetria - “disproportion”). This is the absence or violation of symmetry.

Asymptote(Greek word asymptotes - “mismatched”). This is a straight line to which the points of a certain curve approach indefinitely as these points move away to infinity.

Astroid(Greek word astron - “star”). Algebraic curve.

Associativity(Latin word associatio - “connection”). Combination law of numbers. T. was introduced by W. Hamilton (1843).

Billion(French word billion, or billion - milliard). This is a thousand million, a number represented by one followed by 9 zeros, i.e. number 10 9. In some countries, a billion is a number equal to 10 12.

Binom lat. the words bi - “double”, nomen - “name”. It is the sum or difference of two numbers or algebraic expressions called binomial terms.

Bisector(Latin words bis - “twice” and sectrix - “secant”). Borrowing In the 19th century from French language where bissectrice - goes back to lat. phrase. This is a straight line passing through the vertex of the angle and dividing it in half.

Vector(Latin word vector - “carrying”, “carrier”). This is a directed segment of a straight line, one end of which is called the beginning of the vector, the other end is called the end of the vector. This term was introduced by the Irish scientist W. Hamilton (1845).

Vertical angles(Latin word verticalis - “peak”). These are pairs of angles with a common vertex, formed by the intersection of two straight lines so that the sides of one angle are a continuation of the sides of the other.

Hexahedron(Greek words geks - “six” and edra - “edge”). This is a hexagon. This T. is attributed to the ancient Greek scientist Pappus of Alexandria (3rd century).

Geometry(Greek words geo - “Earth” and metreo - “I measure”). Old Russian borrowed from Greek The part of mathematics that studies spatial relationships and shapes. T. appeared in the 5th century BC. in Egypt, Babylon.

Hyperbola(Greek word hyperballo - “passing through something”). Borrowing in the 18th century from lat. language This is an open curve of two unlimitedly extending branches. T. was introduced by the ancient Greek scientist Apollonius of Perm.

Hypotenuse(Greek word gyipotenusa - “contracting”). Deputy from lat. language in the 18th century, in which hypotenusa - from the Greek. the side of a right triangle that lies opposite the right angle. The ancient Greek scientist Euclid (3rd century BC) wrote instead of this term, “the side that subtends a right angle.”

Hypocycloid(Greek word gipo - “under”, “below”). The curve that a point on a circle describes.

Goniometry(Latin word gonio - “angle”). This is the study of "trigonometric" functions. However, this name did not catch on.

Homothety(Greek word homos - “equal”, “same”, thetos - “located”). This is an arrangement of figures that are similar to each other, in which the straight lines connecting the corresponding points of the figures intersect at the same point, called the center of homothety.

Degree(Latin word gradus - “step”, “step”). A unit of measurement for a plane angle equal to 1/90 of a right angle. The measurement of angles in degrees appeared more than 3 years ago in Babylon. Designations reminiscent of modern ones were used by the ancient Greek scientist Ptolemy.

Schedule(Greek word graphikos - “inscribed”). This is a graph of a function - a curve on a plane depicting the dependence of the function on the argument.

Deduction(Latin word deductio - “removal”). This is a form of thinking through which a statement is derived purely logically (according to the rules of logic) from certain given statements - premises.

Defenders(Latin word defero - “carry”, “move”). This is the circle around which the epicycloids of each planet rotate. For Ptolemy, the planets rotate in circles - epicycles, and the centers of the epicycles of each planet rotate around the Earth in large circles - deferents.

Diagonal(Greek word dia - “through” and gonium - “angle”). This is a straight line connecting two vertices of a polygon that do not lie on the same side. T. is found in the ancient Greek scientist Euclid (3rd century BC).

Diameter(Greek word diametros - “diameter”, “through”, “measuring” and the word dia - “between”, “through”). T. “division” in Russian is first found in L.F. Magnitsky.

Headmistress(Latin word directrix - “director”).

Discreteness(Latin word discretus - “divided”, “discontinuous”). This is discontinuity; opposed to continuity.

Discriminant(Latin word discriminans - “discriminating”, “separating”). This is an expression made up of quantities defined by a given function, the reversal of which to zero characterizes one or another deviation of the function from the norm.

Distributivity(Latin word distributivus - “distributive”). Distributive law connecting addition and multiplication of numbers. T. was introduced by the French. scientist F. Servois (1815).

Differential(Latin word differento- “difference”). This is one of the basic concepts of mathematical analysis. This T. is found by the German scientist G. Leibniz in 1675 (published in 1684).

Dichotomy(Greek word dichotomia - “division in two”). Method of classification.

Dodecahedron(Greek words dodeka - “twelve” and edra - “foundation”). This is one of the five regular polyhedra. T. is first encountered by the ancient Greek scientist Theaetetus (4th century BC).

Denominator- a number showing the size of the fractions of a unit from which the fraction is composed. It was first found by the Byzantine scientist Maximus Planud (late 13th century).

Isomorphism(Greek words isos - “equal” and morfe - “view”, “form”). This is a concept of modern mathematics, clarifying the widespread concept of analogy, model. T. was introduced in the mid-17th century.

Icosahedron(Greek words eicosi - “twenty” and edra - base). One of the five regular polyhedra; has 20 triangular faces, 30 edges and 12 vertices. T. was given by Theaetetus, who discovered it (4th century BC).

Invariance(Latin words in - “negation” and varians - “changing”). This is the invariance of any quantity with respect to coordinate transformations. T. entered English. scientist J. Sylvester (1851).

Induction(Latin word inductio - “guidance”). One of the methods of proving mathematical statements. This method first appears in Pascal.

Index(Latin word index - “index”. Borrowed at the beginning of the 18th century from Latin). A numeric or alphabetic indicator that is provided with mathematical expressions to distinguish them from each other.

Integral(Latin word integro - “restore” or integer - “whole”). Borrowing in the second half of the 18th century. from French language based on lat. integralis - “whole”, “complete”. One of the basic concepts of mathematical analysis, which arose in connection with the need to measure areas, volumes, and find functions from their derivatives. These integral concepts are usually associated with Newton and Leibniz. This word was first used in print by a Swede. Scientist J. Bernoulli (1690). Sign? - stylized letter S from lat. words summa - “sum”. First appeared in G. W. Leibniz.

Interval(Latin word intervallum - “interval”, “distance”). The set of real numbers satisfying the inequality a< x

Irrational number(i.e. the word irrationalis - “unreasonable”). A number that is not rational. T. introduced German. scientist M. Stiefel (1544). A rigorous theory of irrational numbers was built in the 2nd half of the 19th century.

Iteration(at. word iteratio - “repetition”). The result of repeatedly applying a mathematical operation.

Calculator- German The word kalkulator goes back to Lat. to the word calculator - “to count”. Borrowing at the end of the 18th century. from German language Portable computing device.

Canonical expansion- Greek the word canon is “rule”, “norm”.

Tangent- Latin word tangens - “touching”. Semantic tracing paper of the late 18th century.

Leg- lat. the word katetos is “plumb line”. The side of a right triangle adjacent to a right angle. T. is first found in the form “cathetus” in Magnitsky’s “Arithmetic” of 1703, but already in the second decade of the 18th century the modern form became widespread.

Square- Latin word quadratus - “quadrangular” (from guattuor - “four”). A rectangle in which all sides are equal, or, equivalently, a rhombus in which all angles are equal.

Quaternions- lat. the word quaterni means “in fours.” A system of numbers that arose in attempts to find a generalization of complex numbers. T. suggested by English. scientist Hamilton (1843).

TOvintillion- French word quintillion. A number represented by a one followed by 18 zeros. Borrowed at the end of the 19th century.

Collinearity- the Latin word con, com - “together” and linea - “line”. Location on one line (straight). T. introduced America. scientist J. Gibbs; however, this concept was encountered earlier in W. Hamilton (1843).

Combinatorics- Latin word combinare - “to connect”. A branch of mathematics that studies the various connections and arrangements involved in counting combinations of elements of a given finite set.

Coplanarity- Latin words con, com - “together” and planum - “flatness”. Location in one plane. T. is first found in J. Bernoulli; however, this concept was encountered earlier in W. Hamilton (1843).

Commutativity- late lat. the word commutativus is “changing.” The property of addition and multiplication of numbers, expressed by identities: a+b=b+a, ab=ba.

Congruence- lat. the word congruens is “proportionate.” T., used to denote the equality of segments, angles, triangles, etc.

Constant- Latin word constans - “constant”, “unchangeable”. A constant value when considering mathematical and other processes.

Cone- Greek the word konos is “pin”, “bump”, “top of a helmet”. A body bounded by one cavity of a conical surface and a plane intersecting this cavity and perpendicular to its axis. T. received its modern meaning from Aristarchus, Euclid, and Archimedes.

Configuration- lat. the word co - “together” and figura - “view”. Location of figures.

Conchoid- Greek the word conchoides is “like a mussel shell.” Algebraic curve. Introduced by Nicomedes of Alexandria (2nd century BC).

Coordinates- Latin word co - “together” and ordinates - “determined”. Numbers taken in a certain order, determining the position of a point on a line, plane, space. T. was introduced by G. Leibniz (1692).

Cosecant- lat. the word cosecans. One of the trigonometric functions.

Cosine- Latin word complementi sinus, complementus - “supplement”, sinus - “hollow”. Borrowing at the end of the 18th century. from the language of learned Latin. One of the trigonometric functions, denoted cos. Introduced by L. Euler in 1748.

Cotangent- lat. the word complementi tangens: complementus - “supplement” or from lat. the words cotangere - “to touch”. In the second half of the 18th century. from the language of scientific Latin. One of the trigonometric functions, denoted ctg.

Coefficient- lat. the word co - “together” and efficiens - “producing”. A multiplier, usually expressed in numbers. T. introduced Viet.

Cube - Greek the word kubos is "dice". Borrowing at the end of the 18th century. from learned Latin. One of the regular polyhedra; has 6 square faces, 12 edges, 8 vertices. The name was introduced by the Pythagoreans, then found in Euclid (3rd century BC).

Lemma- Greek the word lemma is “assumption”. This is an auxiliary sentence used in proving other statements. T. was introduced by ancient Greek geometers; is especially common in Archimedes.

Lemniscate- Greek the word lemniscatus is “decorated with ribbons.” Algebraic curve. Invented by Bernoulli.

Line- lat. the word linea is “linen”, “thread”, “cord”, “rope”. One of the main geometric images. The idea of ​​it can be a thread or an image described by the movement of a point in a plane or space.

Logarithm- Greek the word logos - “relation” and arithmos - “number”. Borrowing in the 18th century from French language, where logarithme is English. logarithmus - formed by adding the Greek. words The exponent m to which a must be raised to obtain N.T. suggested by J. Napier.

Maximum- the Latin word maximum - “the greatest”. Borrowing in the second half of the 19th century. from lat. language The largest value of a function on the function's definition set.

Mantissa- lat. the word mantissa is “increase”. This is the fractional part of the decimal logarithm. T. was proposed by the Russian mathematician L. Euler (1748).

Scale- German the word mas - “measure” and stab - stick.” This is the ratio of the length of a line in a drawing to the length of the corresponding line in reality.

Mathematics- Greek the word matematike from the Greek word matema - “knowledge”, “science”. Borrowing at the beginning of the 18th century. from lat. lang., where mathematica is Greek. The science of quantitative relations and spatial forms of the real world.

Matrix- lat. the word matrix is ​​“uterus”, “source”, “beginning”. This is a rectangular table formed from a certain set and consisting of rows and columns. T. first appeared in W. Hamilton and scientists A. Cayley and J. Sylvester in the middle. 19th century. The modern designation is two verticals. dashes - introduced by A. Cayley (1841).

Median(triug-ka) - lat. the word medianus is “middle”. This is a segment connecting the vertex of a triangle to the middle of the opposite side.

Meter- French the word metre - “stick for measuring” or Greek. the word metron is “measure”. Borrowing in the 18th century from French language, where metre is Greek. This is the basic unit of length. She was born 2 centuries ago. The meter was “born” by the French Revolution in 1791.

Metrics- Greek word metric< metron - «мера», «размер». Это правило определения расстояния между любыми двумя точками данного пространства.

Million- Italian the word millione is “thousand”. Borrowing in the Peter the Great era from the French. language, where million is Italian. A number written with six zeros. T. was invented by Marco Polo.

Billion- French the word mille is “thousand”. Borrowing in the 19th century from French language, where milliard is suf. Derived from mille - "thousand".

Minimum- Latin word minimum - “smallest”. The smallest value of a function on the function's definition set.

Minus- Latin word minus - “less”. This is a mathematical symbol in the form of a horizontal line, used to indicate negative numbers and the action of subtraction. Introduced into science by Widmann in 1489.

Minute- lat. the word minutus is “small”, “reduced”. Borrowing at the beginning of the 18th century. from French lang., where minute - lat. This is a unit of measurement for plane angles, equal to 1/60 of a degree.

Module- lat. the word modulus is “measure”, “magnitude”. This is the absolute value of a real number. T. was introduced by R. Coats, a student of I. Newton. The modulus sign was introduced in the 19th century by K. Weierstrass.

Multiplicativity- lat. the word multiplicatio is “multiplication.” This is a property of the Euler function.

Norm- Latin word norma - “rule”, “model”. Generalization of the concept of absolute value of a number. The “norm” sign was introduced by the German scientist E. Schmidt (1908).

Zero- Lat word nullum - “nothing”, “nothing”. Initially, T. denoted the absence of a number. The designation zero appeared around the middle of the first millennium BC.

Numbering- lat. the word numero - “I count.” This is notation or a set of techniques for naming and designating numbers.

Oval- lat. the word ovaum - “egg”. Borrowing. in the 18th century from French, where ovale is lat. This is a closed convex flat figure

Circle Greek the word periferia is “periphery”, “circle”. This is the set of points on a plane located at a given distance from a given point lying in the same plane and called its center.

Octahedron- Greek the words okto - "eight" and edra - "base". It is one of the five regular polyhedra; has 8 triangular faces, 12 edges and 6 vertices. This T. was given by the ancient Greek scientist Theaetetus (4th century BC), who was the first to construct the octahedron.

Ordinate- Latin word ordinatum - “in order.” One of the Cartesian coordinates of a point, usually the second, denoted by the letter y. As one of the Cartesian coordinates of a point, this T. is used in German. scientist G. Leibniz (1694).

Ort- Greek the word orthos is “straight”. The same as a unit vector, the length of which is assumed to be equal to one. T. entered English. scientist O. Heaviside (1892).

Orthogonality- Greek the word ortogonios is "rectangular". Generalization of the concept of perpendicularity. Found in the ancient Greek scientist Euclid (3rd century BC).

Parabola- Greek the word parabole is “application”. This is a non-central line of the second order, consisting of one infinite branch, symmetrical about the axis. T. was introduced by the ancient Greek scientist Apollonius of Perga, who considered the parabola as one of the conic sections.

Parallelepiped- Greek word parallelos - “parallel” and epipedos - “surface”. This is a hexagon, all of whose faces are parallelograms. T. was found among the ancient Greek scientists Euclid and Heron.

Parallelogram- Greek words parallelos - “parallel” and gramma - “line”, “line”. This is a quadrilateral whose opposite sides are parallel in pairs. T. started using Euclid.

Parallelism- parallelos - “walking nearby.” Before Euclid, T. was used in the school of Pythagoras.

Parameter- Greek word parametros - “measuring”. This is an auxiliary variable included in formulas and expressions.

Perimeter- Greek word peri - “around”, “about” and metreo - “I measure”. T. is found among the ancient Greek scientists Archimedes (3rd century BC), Heron (1st century BC), and Pappus (3rd century).

Perpendicular- Latin word perpendicularis - “steep”. This is a straight line intersecting a given straight line (plane) at a right angle. T. was formed in the Middle Ages.

Pyramid- Greek word pyramis, cat. comes from the Egyptian word permeous - “side edge of a structure” or from pyros - “wheat”, or from pyra - “fire”. Borrowing from Art.-Sl. language This is a polyhedron, one of whose faces is a flat polygon, and the remaining faces are triangles with a common vertex that does not lie in the plane of the base.

Square- Greek the word plateia is “wide”. Origin unclear. Some scientists consider borrowing. from Art.-Sl. Others interpret it as originally Russian.

Planimetry- the Latin word planum - “plane” and metreo - “I measure”. This is a part of elementary geometry in which the properties of figures lying in a plane are studied. T. is found in ancient Greek. scientist Euclid (4th century BC).

Plus- Latin word plus - “more”. This is a sign to indicate the action of addition, as well as to indicate the positivity of numbers. The sign was introduced by the Czech scientist J. Widman (1489).

Polynomial- the Greek word polis - “numerous”, “extensive” and the Latin word nomen - “name”. This is the same as a polynomial, i.e. the sum of a certain number of monomials.

Potentiation- the German word potenzieren - “to raise to a power.” The action of finding a number using a given logarithm.

Limit- the Latin word limes - “border”. This is one of the basic concepts of mathematics, meaning that a certain variable value in the process of its change under consideration indefinitely approaches a certain constant value. T. was introduced by Newton, and the currently used symbol lim (the first 3 letters of limes) was introduced by the French scientist S. Lhuillier (1786). The expression lim was first written down by W. Hamilton (1853).

Prism- Greek the word prisma is “sawed off piece.” This is a polyhedron, two of whose faces are equal n-gons, called the bases of the prism, and the remaining faces are lateral. T. is found already in the 3rd century BC. in ancient Greek scientists Euclid and Archimedes.

Example- Greek word primus - “first”. Number problem. T. was invented by Greek mathematicians.

Derivative- French word derivee. Introduced by J. Lagrange in 1797.

Projection- Latin word projectio - “throwing forward.” This is a way of depicting a flat or spatial figure.

Proportion- Latin word proportio - “ratio”. This is an equality between two ratios of four quantities.

Percent- the Latin word pro centum - “from a hundred.” The idea of ​​interest originated in Babylon.

Postulate- Latin word postulatum - “demand”. A name sometimes used for the axioms of a mathematical theory

Radian- Latin word radius - “spoke”, “ray”. This is a unit of measurement for angles. The first publication containing this term appeared in 1873 in England.

Radical- lat. the word radix is ​​“root”, radicalis is “radical”. Modern sign? first appeared in R. Descartes's book “Geometry”, published in 1637. This sign consists of two parts: a modified letter r and a bar that replaced earlier brackets. The Indians called it “mula,” the Arabs called it “jizr,” and the Europeans called it “radix.”

Radius- Lat word radius - “spoke in a wheel”. Borrowing in the Petrine era from lat. language This is a segment connecting the center of the circle with any point on it, as well as the length of this segment. In ancient times, T. did not exist; it was found for the first time in 1569 among the French. scientist P. Rame, then F. Viet and became generally accepted at the end of the 17th century.

Recurrent- the Latin word recurrere - “to go back.” This is a backward movement in mathematics.

Rhombus- Greek word rombos - “tambourine”. This is a quadrilateral with all sides equal. T. is used by the ancient Greek scientists Heron (1st century BC), Pappus (2nd half of the 3rd century).

Rolls- French word roulette - “wheel”, “compare”, “roulette”, “steering wheel”. These are curves. T. was invented by the French. mathematicians who studied the properties of curves.

Segment- Latin word segmentum - “segment”, “strip”. This is a part of a circle limited by the arc of the boundary circle and the chord connecting the ends of this arc.

Secant- the Latin word secans - “secant”. This is one of the trigonometric functions. Denoted by sec.

Sextillion- French word sextillion. A number represented with 21 zeros, i.e. number 1021.

Sector- the Latin word seco - “cut”. This is a part of a circle limited by the arc of its boundary circle and its two radii connecting the ends of the arc with the center of the circle.

Second- Latin word secunda - “second”. This is a unit of plane angles equal to 1/3600 of a degree or 1/60 of a minute.

Signum- Latin word signum - “sign”. This is a function of the real argument.

Symmetry- Greek word simmetria - “proportionality”. The property of the shape or arrangement of figures being symmetrical.

Sinus- lat. sinus - “bend”, “curvature”, “sinus”. This is one of the trigonometric functions. In the 4th-5th centuries. called “ardhajiva” (ardha - half, jiva - bowstring). Arab mathematicians in the 9th century. the word "jibe" is a convexity. When translating Arabic mathematical texts in the 12th century. T. was replaced by “sine”. The modern notation sin was introduced by the Russian scientist Euler (1748).

Scalar- Latin word scalaris - “stepped”. This is a quantity, each value of which is expressed by one number. This T. was introduced by the Irish scientist W. Hamilton (1843).

Spiral- Greek word speria - “coil”. This is a flat curve that usually circles around one (or more) points, approaching or moving away from it.

Stereometry- Greek the words stereos - “volumetric” and metreo - “measure”. This is a part of elementary geometry in which spatial figures are studied.

Sum- Latin word summa - “total”, “total amount”. The result of the addition. Sign? (Greek letter “sigma”) was introduced by the Russian scientist L. Euler (1755).

Sphere- Greek the word sfaira is “ball”, “ball”. This is a closed surface obtained by rotating a semicircle around a straight line containing its subtending diameter. T. is found among the ancient Greek scientists Plato and Aristotle.

Tangent- Latin word tanger - “touch”. One of the trigonometers. functions. T. was introduced in the 10th century by the Arab mathematician Abu-l-Wafa, who compiled the first tables for finding tangents and cotangents. The designation tg was introduced by the Russian scientist L. Euler.

Theorem- Greek word tereo - “I explore.” This is a mathematical statement whose truth is established through proof. T. was also used by Archimedes.

Tetrahedron- Greek words tetra - “four” and edra - “base”. One of the five regular polyhedra; has 4 triangular faces, 6 edges and 4 vertices. Apparently, T. was first used by the ancient Greek scientist Euclid (3rd century BC).

Topology- Greek word topos - “place”. A branch of geometry that studies the properties of geometric figures related to their relative positions. Euler, Gauss, and Riemann believed that T. Leibniz belongs precisely to this branch of geometry. In the second half of the last century, a new field of mathematics was introduced, it was called topology.

Dot- Russian the word “poke” is as if the result of an instant touch, a prick. N.I. Lobachevsky, however, believed that T. comes from the verb “to sharpen” - as a result of the touch of the tip of a sharpened pen. One of the basic concepts of geometry.

Tractor- Latin word tractus - “extended”. Plane transcendental curve.

Transposition- Latin word transpositio - “rearrangement”. In combinatorics, a permutation of elements of a given set in which 2 elements are swapped.

Protractor- lat. the word transortare - “transfer”, “shift”. A device for constructing and measuring angles in a drawing.

Transcendental- Latin word transcendens - “going beyond”, “transitioning”. It was first used by the German scientist G. Leibniz (1686).

Trapezoid- Greek word trapezion - “table”. Borrowing in the 18th century from lat. language, where trapezion is Greek. It is a quadrilateral whose two opposite sides are parallel. T. is found for the first time in the ancient Greek scientist Posidonius (2nd century BC).

Triangulated- Latin word triangulum - “triangle”.

Trigonometry- Greek words trigonon - “triangle” and metreo - “I measure”. Borrowing in the 18th century from learned Latin. A branch of geometry that studies trigonometric functions and their applications to geometry. T. first appears in the title of the book of the German scientist B. Titisk (1595).

Trillion- French word trillion. Borrowing in the 18th century from French language A number with 12 zeros, i.e. 1012.

Trisection- angle of the Latin word tri - “three” and section - “cutting”, “dissection”. The problem of dividing an angle into three equal parts.

Trochoid- Greek the word trochoeides - “wheel-shaped”, “round”. Plane transcendental curve.

Corner- Latin word angulus - “angle”. A geometric figure consisting of two rays with a common origin.

Unicursal- lat. the words unus - “one”, cursus - “way”. A route to traverse all the edges of the constructed graph, such that no edge passes twice.

Factorial (k)- Latin word factor - “multiplier”. First appeared by the French mathematician Louis Arbogast. The designation k was introduced by the German. mathematician Chretien Crump.

Figure- Latin word figura - “appearance”, “image”. T. applied to various sets of points.

Focus- Latin word focus - “fire”, “hearth”. Distance to this point. The Arabs called the parabola the “incendiary mirror”, and the point at which the sun’s rays are collected - the “place of ignition”. Kepler in “Optical Astronomy” translated this T. with the word “focus”.

Formula- lat. the word formula is “form”, “rule”. This is a combination of mathematical symbols that expresses a proposition.

Function- lat. the word functio is “fulfillment”, “completion”. One of the basic concepts of mathematics, expressing the dependence of some variables on others. T. first appears in 1692 in German. the scientist G. Leibniz, and not in the modern sense. T., close to the modern one, is found in the Swiss scientist I. Bernoulli (1718). The notation for the function f(x) was introduced by the Russian scientist L. Euler (1734).

Characteristic- Greek word character - “sign”, “feature”. The integer part of the decimal logarithm. T. was proposed by the Austrian scientist G. Briggs (1624).

Chord- Greek the word horde is “string”, “string”. A line segment connecting two points on a circle.

Center- lat. the word centrum is “the point of the leg of a compass,” “a piercing weapon.” Borrowing in the 18th century from lat. The middle of something, such as a circle.

Cycloid- Greek the word kykloeides is "circular". The curve that a marked point on a circle describes, rolling without slipping in a straight line.

Cylinder- Greek the word kilindros - “roller”, “skating rink”. Borrowing in the 18th century from it. lang., where zilinder is Latin, but going back to Greek. kylindros. This is a body bounded by a cylindrical surface and two parallel planes perpendicular to its axis. T. is found among the ancient Greek scientists Aristarchus and Euclid.

Compass- lat. the word circulus - “circle”, “rim”. Borrowing in the first third of the 19th century. from lat. language A device for drawing arcs, circles, linear measurements.

Cissoid- Greek the word kissoeides is “ivy-shaped.” Algebraic curve. Invented by the Greek mathematician Diogles (2nd century BC).

Numbers- Latin word cifra - “digit”, derived from the Arabic word “sifr”, meaning “zero”.

Numerator- a number showing how many parts a fraction is made up of. T. is first encountered by the Byzantine scientist Maximus Planud (late 13th century).

Number?- (from the beginning of the letter of the Greek word perimetron - “circle”, “periphery”). The ratio of the circumference of a circle to its diameter. First appeared in W. Jones (1706). Became generally accepted after 1736. ? = 3.141592653589793238462…

Scale- Latin word scalae - “step”. A sequence of numbers used to quantify any quantities.

Involute- the Latin word evolvens - “unfolding”. Unfolding a curve.

Exhibitor- Latin word exponentis - “showing”. Same as exponential function. T. was introduced by the German scientist G. Leibniz (1679, 1692).

Extrapolation- Latin words extra - “over” and polio - “smooth”, “straighten”. The extension of a function beyond its domain of definition, such that the extended function belongs to a given class.

Extremum- Latin word exstremum - “extreme”. This is the general name for the maximum and minimum of a function.

Eccentricity- Latin words ex - “from”, “from” and centrum - “center”. A number equal to the ratio of the distance from the point of the conic section to the focus to the distance from this point to the corresponding directrix.

Ellipse- Greek the words ellipsis - “disadvantage”. This is an oval curve. T. was introduced by the ancient Greek scientist Apollonius of Perga (260-190 centuries BC).

Entropy- Greek word entropia - “turn”, “transformation”.

Epicycloid- Greek words epi - “above”, “on” and kykloeides - “circular”. This is a plane curve described by a point on a circle.

To plunge to such depth is a feat! Now rise slowly and calmly - otherwise you will become dizzy from the information! And be sure to eat something sweet! Glucose normalizes brain function!

Title: Mathematical terms. Directory.

This reference book discusses issues related to the origin and history of mathematical terms. It contains the following information: who and when introduced this or that mathematical concept, definition, etc.; what it was called when it first appeared; who proposed the modern term; what does it mean translated into Russian; when and by whom the designation was introduced.
The book is of interest to students of physics and mathematics faculties, as well as to university teachers.

The idea for this book arose when it was discovered that information about the origin of mathematical terms and notations was not collected anywhere. They are scattered in a huge number of articles and books, in prefaces, notes and footnotes. The only thing that was able to be found that was written specifically on this topic was a few pages in the magazines “Mathematics at School” for 1941 (author - N.I. Shevchenko), a brochure by Nikishov V.V. “Glossary of the Adventures of Mathematical Terms” (1935) and the book Ch. Mugler. “Dictionnaire historique de la termi-nologie geometrique des grecs” (Paris, 1958). In the first two works, only the translation of some mathematical terms from Latin and Greek into Russian (Ukrainian) is given; the third provides a translation of Greek terms into the main European languages ​​and provides a summary of the senses in which each term was used. The situation is much better with notation, but Cajori's two-volume History of Mathematical Notation is difficult to obtain.
This handbook does not provide definitions of mathematical concepts. In cases where a term is used in different senses, the origin of the concept and use of the term in only one of the areas is often stated and the emergence of other word usage is left aside.
It should be said that in the case where there are different opinions about the history of a term or the origin of a designation, as a rule, one is given that is closest to the views of the author; however, references to the literature also indicate sources presenting other points of view.
In references, the book number in the list of cited literature is first given; if a publication has several volumes or issues, then the corresponding number is given in parentheses, then the pages are indicated.

CONTENT
Preface
Dictionary of mathematical terms
ABSOLUTE (4) - AFFINITY (12). BASIS (12) - BRACHISTOCHRON (14). VARIATION (14)-SUBTRACT (20). GAMMA FUNCTION (20) - GROUP (28). DECA (29) - FRACTION (36). e (37). LAW OF LARGE NUMBERS (37). i (40) - ITERATION (52). CARDIOID (53) - CUBE (68). LEMMA (68) - INTE-TRAL LOGARITHM (72). MAJORANT (73) - POWER OF SET (81). NABLA (82) -ZERO (85). IMAGE (86) - CONFORMAL DISPLAY (90). PANTOGRAPH (91) - PSEUDOSPHERE (115). EQUALITY (116)-FOURIER SERIES (123). COLLECTION (124)-SPHERE (135). TABLE (136)-TRICHOTOMY (143). ANGLE (143) - D'Alembert - EULER CONDITIONS (148). FACTORIAL (149) - FUNCTION ANIMID (158). CHARACTERISTIC (158) - CHORD (159). CENTER (159) - DIGIT (160). ALGEBRAIC NUMBERS (161)-MEMBER (165). BALL (165) - WHITE NOISE (165). EVOLUTE (165)-EPICYCLOID (167). GIBBS PHENOMENON (167) - WORKING CELL (168)
Literature
Name index

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