The proposed book is compiled on the basis of the available historical and mathematical literature and thirty years of personal experience of the author in secondary and higher school. The purpose of this manual is to provide specific assistance to the teacher in the use of historical materials in mathematics when studying with schoolchildren on a certain topic of the program. In compiling the book, the author sought to ensure that it was accessible to a certain extent to the students themselves. This book is intended for an eight-year school (grades V - VIII). Preface Introduction Chapter I. Arithmetic History of Arithmetic in Class V Classes Natural Numbers 1. Origin of Arithmetic . Invoice and decimal system 2. On the Origin and Development of Written Numbering. Numbers of different times 3. About metering devices. Russian Accounts . Computers 4. About natural series. 'Calculating grains of sand? Archimedes. Modern recording of large numbers 5. About the prime numbers. Euclid and Eratosthenes . Chebyshev 6. About Goldbach's Task. Unsolved Problems of Number Theory 7. Emergence and improvement of length measures. On the metric system of measures Common fractions 8. On the Origin of Fractions. Fractions in ancient Rome 9. Fractions in Ancient Egypt 10. Babylonian Numbering . Hexadecimal fractions 11. Numbering and fractions in ancient Greece 12. Ancient Chinese Problems with Fractions 13. Ancient Indian problem with flowers and bees 14. Tasks with fractions in ancient Armenians 15. Numbering and fractions in Russia 16. Al-Khwarizmi and his Arithmetic? 17. Abacysts and Algorithms in Medieval Europe 18. 'Arithmetic? Magnitsky. Tasks with fractions Decimal fractions 19. The origin of decimals 20. From hexadecimal to decimal fractions. Al Kashi 21. 'Tenth? Simone Stevin 22. Distribution of decimal fractions, their importance in the life of modern society 23. Figures 24. Triangular numbers 25. Square Numbers. Formula Diophantus 26. Magic Squares 27. Magic square A. Drer . Engraving'Melancholy? 28. Development of the concept of number. From natural to fractional numbers Joint actions on ordinary and decimal fractions. Ratio of magnitude. Measurement of magnitude 29. On Periodic Fractions 30. Ancient Egyptian problem with fractions 31. From a history of zero 32. On the Measurement of the Earth's Meridian by Eratosthenes 33. From Empirical to Theoretical Arithmetic Class VI Approximate Computing 34. On the Origin of Approximate Numbers 35. 'Rule A. N. Wings? Interest 36. Percentages past and present 37. Arithmetic signs and symbols. Sign of interest 38. On arithmetic tables Proportions 39. Number and ratio 40. Proportions in Ancient Greece 41. As recorded proportions in the past 42. On the triple rule 43. Is the problem proportional to the division of Arithmetic? L. F. Magnitsky 44. About how people got to real arithmetic History of arithmetic in extracurricular classes Finger account . Various Multiplication Techniques Verification of Actions with the Nine Pythagoras and His School. The friendly and perfect numbers. Problems waiting to be solved From the history of fractions Old Russian, metric and other measures. Modern science and the creation of an international system of measures . Oral and written numbering Accounts. Computing Machines How Humans Learned to Measure Time . (From calendar history). A New Definition of the Second On the Origin of Some Numerical Superstitions Historical Problems Chapter II. ALGEBRA History of Algebra in Class VI Classes Algebraic Expressions 1. From Arithmetic to Algebra 2. Letters and signs. Algebraic Expressions Rational Numbers. Equations 3. The occurrence of negative numbers 4. 'People don't approve of negative numbers... ? From Diophantus to Bhaskara 5. The path to recognition 6. The task of drawing up equations from the Moscow papyrus? Actions on algebraic expressions. From the History of Algebraic Symbolism 7. The beginning of the letter symbols. Building to Grade 8. On the coefficient of 9. From Rhetorical Algebra to Symbolic Algebra 10. Multiplication formulas. Geometric Algebra in Antiquity 11. Algebraic information in Arithmetic? L. F. Magnitsky 12. 'Universal Arithmetic? And. Newton's Class VII Equation with one unknown 13. From the history of equations. The False Position Method in Egypt 14. Solving Equations in Ancient Greece and India 15. On the origin of the word'algebra? 16. and . Newton on algebraic language Decomposition of polynomials by factors 17. From the history of brackets 18. On the Basic Laws of Action. Euclid's law of distribution 19. On one formula Diophantus 20. On record and signs of multiplication and division 21. 'Universal Arithmetic? L. Euler Algebraic fractions 22. and . Newton on the algebraic fraction 23. Marking 1/anan 24. Algebraic fractions in Diophantus 25. One Eulerian Identity 26. About letter coefficients. Ariabhatta Task Coordinates and graphs 27. About coordinates 28. On the coordinate method and on the graphs A system of first-degree equations with two unknowns 29. Undefined Equations 30. A system of first-degree equations with two unknowns and its solution in antiquity 31. Two Al-Khwarizmi Tasks 32. From the Greek Anthology? 33. The doctrine of equations and the extension of the concept of the number VIII class Counting line 34. On the Counting Line Square Root and Square Equations 35. Extracting the square root from positive numbers 36. About Root Sign 37. Square Equations in Ancient Babylon 38. As composed and solved Diophantus square equations 39. Square Equations in India 40. Square equations in al-Khwarizmi 41. Square equations in Europe XIII?XVII c 42. About Wiet's theorem 43. On the Signs of Equality and Inequality 44. From the history of the solution of the system of equations containing one equation of the second degree and one linear Functions and graphs 45. Descartes' variable magnitude' turning point in the development of mathematics 46. Function concept 47. Further development of the concept of function 48. About cubic root 49. On Approximate and Graphical Solution of Equations 50. A brief overview of the historical development of algebra History of algebra in extracurricular classes Ancient mathematical entertainments and actions on algebraic expressions of Algebra in ancient India and China About Diophantine and diophantine equations , 'The Last Theorem of Fermat? Women Mathematicians On Term and Concept'algorithm? Geometric Algebra and the Solution of Square Equations Omar Khayyam' mathematician and poet Arithmetic and Algebra in Europe in XII?XV century From the History of the Development of Algebra in XVI in René Descartes' great mathematician and thinker XVII in On the Greatest Mathematics XVIII in . ' Leonard Euler On Two Outstanding Russian Mathematicians of the 19th Century. Ostrohrad and Chebyshev Historical Tasks Chapter III. GEOMETRY History of Geometry in Class VI Basic Concepts 1. On the Origin of Geometry 2. Geometrical Figures . Calculation of segments 3. On the origin of some terms and concepts Triangles 4. About triangles 5. On Symmetry 6. About the equilateral triangle. Thales Miletsky 7. On the signs of equality of triangles 8. On a Rectangular Triangle Parallelity 9. On parallel lines 10. And a straight line running through that point and parallel to that line. Axiom of parallelism 11. On the sum of the angles of the triangle 12. Geometric tools 13. About one ancient way of determining inaccessible distances Class VII Quadrilaterals 14. About Parallelogram 15. About trapezoid 16. On the challenges of building a polygonal area. Surface and volume prism 17. Calculation of the area in antiquity 18. The Pythagorean Theorem . Geometry in ancient India 19. Measurement of areas in ancient Greece. Heron of Alexandria 20. On the prism and parallelepiped 21. Volume Measurement Circumference 22. On the circle and its radius 23. About tangents to the circle . Archite of Tarenta 24. On the inscribed corners. Hippocrates of Chios 25. On the length of the circle and the area of the circle. Archimedes 26. About number'pi? 27. About the cylinder, its surface and volume 28. About one mistake of the ancient Egyptians VIII class Proportional segments. Similar to Figure 29. Ratio and proportionality of segments 30. On the division of the segment in this respect 31. About Similarity 32. 'Division in this respect? Apollonia 33. The construction of such figures . Proportional Circular . Galileo Trigonometric functions of acute angle 34. On the origin of trigonometry 35. About trigonometric tables 36. On Trigonometric Functions and on the Development of Trigonometry Written and Described Polygons 37. 'Wonderful? triangle points. Geometry of triangle 38. On regular polygons Calculation of areas and volumes of geometric bodies 39. About the pyramid and its volume 40. About Cone 41. About Ball 42. Brief overview of the development of geometry History of geometry in extracurricular activities Practical geometry in different peoples On the development of geometry in ancient Greece before Euclid the Alexandrian era. Euclid Archimedes Three Famous Tasks of Antiquity One Hundred Proofs . (From the History of the Pythagorean Theorem.) Ptolemy's theorem and the compilation of trigonometric tables Division of areas and transformations of equal figures Instruments and instruments in measurements and geometric constructions. Meridian measurement On the development of geometry. The geometry of Lobachevsky Historical problems Answers, instructions and solutions Literature Name index More materials on the topic "history of mathematics" Anosov D. In. A look at mathematics and something of it Arnold B. and . Huygens and Barrow, Newton and Hooke's first steps in mathematical analysis and catastrophe theory, from evolvent to quasicrystals Archimedes. Works by Bell E. T. Creators of mathematics Bogoljubov A . N. Mathematics . Mechanics. Viletner G.'s Biographical Handbook History of mathematics from Descartes to the mid-19th century Galanin D. D. Leonty Filippovich Magnitsky and his Arithmetic, vol. 1, , vol. 2, 3 Gindikin S. G. Tales of Physicists and Mathematicians, 4th Edition . ( 3rd Edition . ) Euclid . Started Wonderful Scientists / Under ed. C. P. Capitsa . Library'Quant', vp. 9 History of Mathematics, in 3 volumes. Edited by . A. P. Yushkevich Koire A . Essays on the history of philosophical thought Magnitsky L. F. Arithmetic (old publication) Mandryka A. P. Ballistic studies by Leonard Euler Pythagoras . Golden Canon . Esoteric Figures Ribenboim P. Fermat's Last Theorem for Fishermen K. A. History of mathematics in 2 volumes . Volume 1 ; Volume 2 Stillwell D. Mathematics and its history of the Tikhomirov V. M. Tales of Highs and Lows by Figier L. Lights of science from antiquity to the present day . Scientists of the XVII and XVIII centuries Chistyakov V. D. Collection of ancient problems in elementary mathematics with historical excursions and detailed solutions Euler L Works: Introduction to the analysis of infinite. (in 2 volumes) . Differential calculation . Integral calculus (in 3 volumes) . Euler L. Letters to scientists Yakovlev V. and . Prehistory of Analytical Mechanics Newton I. Philosophiae Naturalis Principia Mathematica