1. Alexis Claude Clairaut (1713-1768) Analytic Geometry, XVIII c Pierre Louis Moreau de Maupertuis (1698-1759)

2. Leonard Euler  rectangular and oblique-angled coordinates and their transformations  classification algebraic curves, including curves of the 3rd and 4th orders  properties of diameters of curves and questions of symmetry  systematization of data on similarity and affine properties of curves

3. Maria Gaëtana Agnesi (1718 – 1799) «Analytical Institutions for the Use of Italian Youth» (1748) «Witch of Agnesi» Starting with a fixed circle, a point O on the circle is chosen. For any other point A on the circle, the secant line OA is drawn. The point M is diametrically opposite to O. The line OA intersects the tangent of M at the point N. The line parallel to OM through N, and the line perpendicular to OM through A intersect at P. As the point A is varied, the path of P is the Witch of Agnesi.

4. Gaspard Monge 1746 - 1818 Смирнов В.И. Гаспар Монж 1746-1946 1947. 86 с

5. 1780 - Member of the Paris Academy of Sciences 1783 - Moving to Paris 1791 - dispute with Marat 1792 - Minister of the Navy post 1794 - organization of courses for workers, the Central School of Public Works - The future of the Ecole Polytechnique 1796 - the beginning of cooperation with Napoleon (acquaintance - 1792) 1798-1801 - the Egyptian campaign of Napoleon 1806 - President of the Senate 1809 - Monge stop teaching (paralyzed arm) 1815 – Mong was with Napoleon during the 100 days, then - the emigration Gaspard Monge 1746 - 1818

7. Analytic Geometry 1795  Planar geometry is considered as a special case of spatial  He found conditions perpendicular to the plane passing through a given point  He determine the length of a straight line dropped in the space perpendicular  He use the "Plucker" coordinates for 60 years before Plucker Monge’s Theorem. If the two surfaces of 2nd order described about a third surface or entered into it, the line of intersection splits into two plane curves of order 2. Plane of the curve passes through the straight line joining the points of contact lines.

8. Differential Geometry Differetial Geometry, branch of mathematics that studies the geometry of curves, surfaces, and manifolds (manifold) (the higher- dimensional analogs of surfaces). The discipline owes its name to its use of ideas and techniques from differential calculus, though the modern subject often uses algebraic and purely geometric techniques instead. Although basic definitions, notations, and analytic descriptions vary widely, the following geometric questions prevail: How does one measure the curvature of a curve within a surface (intrinsic) versus within the encompassing space (extrinsic)? How can the curvature of a surface be measured? What is the shortest path within a surface between two points on the surface? How is the shortest path on a surface related to the concept of a straight line?

9. Descriptive and proective geometry Descriptive geometry is the branch of geometry which allows the representation of three-dimensional objects in two dimensions, by using a specific set of procedures. The resulting techniques are important for engineering, architecture, design and in art. The theoretical basis for descriptive geometry is provided by planar geometric projections. Projective geometry is the study of geometric properties that are invariant under projective transformations. This means that, compared to elementary geometry, projective geometry has a different setting, projective space, and a selective set of basic geometric concepts. The basic intuitions are that projective space has more points than Euclidean space, in a given dimension, and that geometric transformations are permitted that move the extra points (called "points at infinity") to traditional points, B.Pascal, A.Durer, L.Carnot Girard Desargues 1591 - 1661  Desarguesian plane  Non-Desarguesian plane  Desargues' theorem  Desargues graph  Desargues configuration

10. THE PROBLEMS SOLVED BY MONGE IN DESCRIPTIVE GEOMETRY:  reliable and unambiguously to represent a spatial figure on the plane  to have an opportunity according to the flat image to judge a form, the sizes, geometrical properties of figures and their relative positioning RESULTS:  Statement of a method of projections, orthogonal design  Studying of laws of creation of the tangent planes and normals to curves of the 2nd order  Theory of crossing of curve surfaces and its annex to development of creation of cars  Questions of curvature of spatial curves and surfaces, annex to problems of profiling of cams and teeths of cogwheels PROECTIVE GEOMETRY, MAIN IDEAS OF G.MONGE: Bases of linear prospect Laws of air prospect Theorems of tangents and surfaces

11. Jean-Victor Poncelet 1788-1867 Гузевич Д.Ю., Гузевич И.Д. Понселе и русские счеты http://science.mir-x.ru/article_read.asp?id=696http://science.mir-x.ru/article_read.asp?id=696 J L Coolidge, The Rise and Fall of Projective Geometry, Amer. Math. Monthly 41 (4) (1934), 217-228. Jean-Victor Poncelet, Obituary Notices of Fellows Deceased, Proc. Royal Soc. London 18 (1869 - 1870), i-xl.

12. Development of projective geometry Arthur Cayley (1821 - 1895 ) August Ferdinand Möbius (1790 - 1868) Julius Plücker (1801 - 1868 )

13. Karl Mikhailovich Peterson (1828 – 1881) Osip Ivanovich Somov (1815 – 1876) Karl Georg Christian von Staudt (1798 - 1867 ) Jean Gaston Darboux(1842 - 1917) Michel Chasles (1793 - 1880 ) Jakob Steiner (1796 - 1863 )

14. Évariste Galois 1811-1832 Niels Henrik Abel 1802-1828

15. Niels Henrik Abel 1802-1828 O.Ore, Niels Henrik Abel, Mathematician Extraordinary (U. of Minnesota Press, 1957) Stubhaug, Arild (2000). Niels Henrik Abel and his Times. Trans. by Richard R. Daly. Springer

16. "Abel has left mathematicians enough to keep them busy for five hundred years.“ (Ch.Hermit)

17. Carl Gustav Jacob Jacobi 1804-1851 August Leopold Crelle (1780 – 1855) «Memoir on algebraic equations, in which the impossibility of solving the general equation of the fifth degree is proven» «Through these works you two will be placed in the class of the foremost analysts of our times.» (Legendre)

18. Lost article «A general representation of the possibility to integrate all differential formulas» «The French are much more reserved with strangers than the Germans. It is extremely difficult to gain their intimacy, and I do not dare to urge my pretensions as far as that; finally every beginner had a great deal of difficulty getting noticed here. I have just finished an extensive treatise on a certain class of transcendental functions to present it to the Institute which will be done next Monday. I showed it to Mr Cauchy, but he scarcely deigned to glance at it.» (N.Abel)

19. * Abel's binomial theorem * Abelian category * Abelian variety * Abelian variety of CM-type * Abel equation, a functional equation * Abel equation of the first kind, an ordinary differential equation * Abel function * Abelian group * Abel's identity * Abel's inequality * Abel's irreducibility theorem * Abel–Jacobi map * Abel Prize * Abel–Plana formula * Abel–Ruffini theorem * Abelian means * Abel's summation formula * Abel's test * Abel's theorem * Abel transform * Abel transformation * Dual abelian variety

20. Évariste Galois 1811-1832 Ротман Т. Короткая жизнь Эвариста Галуа //В мире науки, 1983. № 1. С.84-93 http://ega-math.narod.ru/Singh/Galois.htmhttp://ega-math.narod.ru/Singh/Galois.htm

22. Évariste Galois

23. Прежде всего, когда речь идёт о науке, общественные воззрения учёного не должны играть никакой роли: научные должности не могут быть наградой за те или иные политические или религиозные взгляды. Меня интересует, хорош преподаватель или плох, и мне нет дела до его мнений ни по каким вопросам, кроме научных… … Откуда взялась эта злосчастная манера нагромождать в вопросах искусственные трудности? Неужели кто-нибудь думает, что наука слишком проста? А что из этого получается? Ученик заботится не о том, чтобы получить образование, а о том, чтобы выдержать экзамены. Ему приходится готовить четыре ответа по каждой теореме, имея в виду четырёх разных экзаменаторов; он должен изучить их излюбленные методы и выучить заранее не только; что отвечать на каждый вопрос каждого экзаменатора, но и как себя при этом держать. Таким образом, можно с полным правом сказать, что несколько лет тому назад появилась новая наука; приобретающая с каждым днём всё большее и большее значение. Она состоит в изучении пристрастий господ экзаменаторов, их настроений, того, что они предпочитают в науке и к чему питают отвращение… В “Ла газетт дез эколь”, номер от 2 января 1831 года

24. Joseph Liouville (1809-1882) «Galois's theory came out of the frames which were planned by her creator». (Н.Чеботарев) Marie Ennemond Camille Jordan (1838 - 1922 ) In 1842 Liouville began to read Galois's unpublished papers. In September of 1843 he announced to the Paris Academy that he had found deep results in Galois's work and promised to publish Galois's papers together with his own commentary. Liouville was therefore a major influence in bringing Galois's work to general notice when he published this work in 1846 in his Journal. However he had waited three years before publishing the papers and, rather strangely, he never published his commentary although he certainly wrote a commentary which filled in the gaps in Galois's proofs. Liouville also lectured on Galois's work

25. Paolo Ruffini 1765 - 1822 Arthur Cayley 1821 - 1895 Marius Sophus Lie 1842-1899