# History of Modern Geometry

### Timeline

## Fermat· 1636 Pierre de Fermat published “Ad Locos Planos et Solidos lsagoge” | ## Descartes · 1637 the manuscript “Discours de la method…” was published in an appendix “La Geometrie” by Rene Descartes | ## Desargues · 1639 “Rough draft for an essay on the results of taking plane sections of a cone” was a work that invented perspective geometry by Girard Desargues |

## Descartes

## Pascal · 1639 “Pascal’s mystic hexagon” was published by Blaise Pascal · 1640 “Essay on Conic Sections” was published by Pascal proving him to be a contributor to modern projective geometry. | ## Desargues · 1648 “Desargues’ Theorem” was published in and progressed into what is today projective geometry · 1648-1654 “The Generation of Conic Sections” published | ## Saccheri · 1733 Saccheri published “Euclides ab Omni Naevo Vindicatus” |

## Pascal

· 1640 “Essay on Conic Sections” was published by Pascal proving him to be a contributor to modern projective geometry.

## Desargues

· 1648-1654 “The Generation of Conic Sections” published

## Euler · 1766 Euler produced almost all of his work. | ## Legendre · 1794 Adrien-Marie Legendre contributed to geometry and published “Elements de Geometrie” | ## Monge · 1799 Gaspard Monge , the father of descriptive geometry and differential geometry, published “Geometri descriptive” · 1800 “Application de l’Analyse a la Geometrie” was published |

## Gauss · 1828 Carl Friedrich Gauss published “Disquisitiones generals circa superficies curva” which contained “Gaussian curvature” and “Theorema Egregrium” | ## Lobachevsky · 1829 Nikolai Lobachevsky published a paper on hyperbolic geometry which was the first paper to appear in print on non-Euclidean geometry | ## Bolyai· 1831 Janos Bolyai published his work on the replacement on Euclid’s parallel axiom as an appendix |

## Gauss

## Lobachevsky

## Reimann · 1851 Bernhard Riemann developed his thesis which investigated the geometry of “Riemann surfaces” | ## Klein · 1872 Felix Klein “Erlanger Programm synthesized geometry as the study of invariants under groups of transformations. | ## Hilbert· 1888 David Hilbert first worked on invariant theory and proved his famous “Basis Theorem” and in 1899 published “Grundlagen der Geometrie” which used 21 axioms · 1900 gave his famous Paris speech and it was a list of 23 open problems in geometry. |

## Reimann

## Klein

## Poncelet · 1822 Jean-Victor Poncelet published “Trite des properietes projetives des figures” which is where the term “projective geometry was created | ## Grassmann · 1840-1844 Hermann Grassmann the creator of vector analysis and the vector dot and cross product published his books | ## Cayley · Arthur Cayley unified Euclidean, non-Euclidean, projective, and metrical geometry |

## Poncelet

## Grassmann

## Veblen · 1903 Oswald Veblen developed “A System of Axioms for Geometry” · 1933 “The Foundations of Differential Geometry” was published and it gave the first definition of a differentiable manifold. | ## Coxeter · 1947-1989 Donald Coxeter contributed to polytopes, non-Euclidean geometry and published many books |

## Veblen

· 1933 “The Foundations of Differential Geometry” was published and it gave the first definition of a differentiable manifold.