41. Background For An Allegory Of Grammar is a result of La Hyre s friendship with girard desargues, The GeometricalWork of girard desargues, Springer Verlag, 1987, passim). http://ateg.org/whitfield.htm

Background for An Allegory of Grammar This document, based closely on materials from Whitfield Fine Art , describes a companion painting to An Allegory of Grammar , called An Allegory of Geometry . It therefore provides useful background information on our painting. LAURENT DE LA HYRE (1601-1666), Allegory of Geometry The painting, signed and dated 1649, is the missing centrepiece of the series of Allegories of the Liberal Arts commissioned by Gédeon Tallemant (1613-68) to decorate the gallery of his Hotel in the Marais quarter of Paris. As the Allegory of Geometry, it is visually and intellectually the most significant of the whole series, which includes Music in the Metropolitan Museum, New York, Grammar in the National Gallery, London, Mathematics in Heino, Holland, Astronomy in the Musée d'Orléans, France, and Dialectics and Rhetoric in a private collection, Switzerland. Along with his contemporary Nicolas Poussin Laurent de la Hyre was one of France's premier seventeenth-century painters. From humble beginnings in the studio of his father at Fontainebleau before training with the painter Georges Lallement, La Hyre, unlike Poussin, forged a formidable career in his native country, where he was named as one of the founding members of the Académie Royale in 1648. The Allegory of Geometry, executed just before the onset of the final decade of his life, exhibits all the formal grandeur and intellectual rigour epitomised by the "atticisme parisien" that is the hallmark of La Hyre's mature style. The commission is described by Mariette: 'il y a aussi, dans la Marais au Temple, dans une maison qui appartenait autrefois à M. Tallemant, maître des requêtes, sept tableaux représentant les sept arts libéraux qui fond l'ornement d'une chambre ... elles sont grandes comme nature et ces tableaux sont ornés d'architecture et accompagnés d'enfants'.(P-J. Mariette, Abecedario de Mariette et autres notes inédites 6 vols., 1851-1860, III, 1856, p48f.).

42. List Of Scientists By Field Translate this page desargues, girard. Descartes, René du Perron. Descartes, René du Perron. Descartes,René du Perron. Descartes, René du Perron. Descartes, René du Perron http://www.indiana.edu/~newdsb/d.html

Dahlberg, Gunnar Dainelli, Giotto Dainelli, Giotto Dakin, Henry Drysdale Dakin, Henry Drysdale Dal Piaz, Giorgio Dal Piaz, Giorgio Dale, Henry Hallett Dale, Henry Hallett Dale, Henry Hallett Dall, William Healey Dalton, John Dalton, John Dalton, John Dalton, John Call Dalton, John Call Daly, Reginald Aldworth Daly, Reginald Aldworth Dam, Henrik Dam, Henrik Dana, James Dwight Dandelin, Germinal Pierre Dandelin, Germinal Pierre Danforth, Charles Haskell Danforth, Charles Haskell Daniell, John Frederic Daniell, John Frederic Daniell, John Frederic Daniels, Farrington Danti, Egnatio Danti, Egnatio Dantzig, David van Dantzig, David van Dantzig, David van Darboux, Jean-Gaston D'Arcet, Jean D'Arcy, Patrick D'Arcy, Patrick Darlington, Cyril Dean Darlington, William Darwin, Charles Galton Darwin, Charles Galton Darwin, Charles Robert Darwin, Charles Robert Darwin, Charles Robert Darwin, Erasmus Darwin, Erasmus Darwin, Erasmus Darwin, Erasmus Darwin, Francis Darwin, George Howard Darwin, George Howard Dasypodius, Cunradus Dasypodius, Cunradus Daubenton, Louis-Jean-Marie Daubenton, Louis-Jean-Marie

43. New Dictionary Of Scientific Biography Translate this page desargues, girard Descartes, René du Perron Dickson, Leonard Eugene Dickstein,Samuel Digges, Leonard Digges, Thomas Dini, Ulisse Dinostratus Diocles http://www.indiana.edu/~newdsb/math.html

Make Suggestions Mathematics Abel, Niels Henrik Abraham Bar ?iyya Ha-Nasi Abu Kamil Shuja? Ibn Aslam Ibn Mu?ammad Ibn Shuja? Abu'l-Wafa? al-Buzjani, Mu?ammad Ibn Mu?ammad Ibn Ya?ya Ibn Isma?il Ibn al- ?Abbas Adams, John Couch Adelard of Bath Adrain, Robert Aepinus, Franz Ulrich Theodosius Agnesi, Maria Gaetana Aguilon, François d' A?mad Ibn Yusuf Aida Yasuaki Ajima Naonobu Akhiezer, Naum Il'ich Albert, Abraham Adrian Albert of Saxony Alberti, Leone Battista Aleksandrov, Pavel Sergeevich Alembert, Jean Le Rond d' Alzate y Ramírez, José Antonio Ampère, André-Marie Amsler, Jakob Anatolius of Alexandria Anderson, Oskar Johann Viktor Andoyer, Henri Angeli, Stefano Degli Anthemius of Tralles Antiphon Apollonius of Perga Appell, Paul Arbogast, Louis François Antoine Arbuthnot, John Archimedes Archytas of Tarentum Argand, Jean Robert Aristaeus Aristarchus of Samos Arnauld, Antoine Aronhold, Siegfried Heinrich Artin, Emil Atwood, George Autolycus of Pitane Auzout, Adrien

44. Perspective In Mathematics And Art Born to one of the richest men in France, girard desargues (1591 – 1661) iscredited with unifying the theory of conics. A highly competent and original http://www.math.nus.edu.sg/aslaksen/projects/perspective/desargues.htm

Girard Desargues and Projective Geometry Born to one of the richest men in France, Girard Desargues (1591 – 1661) is credited with unifying the theory of conics. A highly competent and original mathematician, he conceived problems in three-dimensional terms, just like Benedetti did fifty years earlier. The difference was that unlike Benedetti, Desargues fully appreciated the power of this method, and used it to give a projective treatment of conics. Desargues wrote his most important work, the treatise on projective geometry, when he was 48. It was entitled “Rough draft for an essay on the results of taking plane sections of a cone” ( Brouillon proiect d’une atteinte aux evenemens des rencontres du cone avec un plan ). In the course of his work, he became recognized as the first mathematician to get the idea of infinity properly under control, in a precise, mathematical way. For example, Desargues defined a line as one to be produced to infinity in both directions, while a plane was similarly taken to extend to infinity in all directions. A set of parallel lines were defined as a set of concurrent lines whose meeting point lied at an infinite distance. One of the most important parts of his treatise can be viewed as a generalization of a theorem proved by Piero della Francesca (Fig. 20). Desargues’ theorem allowed a way of defining the pattern of division even when the second line was not parallel to the first. In a sense, Desargues was generalizing perspective into becoming a technique of use to mathematicians.

45. Girard - Definition Of Girard By The Free Online Dictionary, Thesaurus And Encyc girard College Alumni Association girard desargues girard High School (USA) girard Township girard Township, Clearfield County, PA http://www.thefreedictionary.com/Girard

Domain='thefreedictionary.com' word='Girard' join mailing list webmaster tools Word (phrase): Word Starts with Ends with Definition subscription: Dictionary/ thesaurus Computing dictionary Medical dictionary Legal dictionary Financial dictionary Acronyms Columbia encyclopedia Wikipedia encyclopedia ... encyclopedia Girard Also found in: Columbia Wikipedia Hutchinson 0.03 sec. Page tools Printer friendly Cite / link Email Feedback Thesaurus Legend: Synonyms Related Words Antonyms Noun Girard - United States financier (born in France) who helped finance the War of 1812 (1750-1831) Stephen Girard financier moneyman - a person skilled in large scale financial transactions Mentioned in References in classic literature No references found Untermann, a revolutionist, in July, 1903, published a pamphlet at Girard , Kansas, on the "Militia Bill. The Iron Heel by London, Jack View in context Near the city, is a most splendid unfinished marble structure for the Girard College, founded by a deceased gentleman of that name and of enormous wealth, which, if completed according to the original design, will be perhaps the richest edifice of modern times. American Notes for General Circulation by Dickens, Charles

46. Les Pensées De Blaise Pascal René, L’œuvre mathématique de girard desargues, PUF, Paris, http://odalix.univ-bpclermont.fr/Cibp/Pensees/Sel55.htm

Séminaire sur les Pensées de Pascal Fragment Sel. 55 (Liasse Vanité) " Si on est trop jeune on ne juge pas bien, trop vieil de même. Si on n'y songe pas assez, si on y songe trop, on s'entête et on s'en coiffe. Si on considère son ouvrage incontinent après l'avoir fait on en est encore tout prévenu, si trop longtemps après on (n') y entre plus. Ainsi les tableaux vus de trop loin et de trop près. Et il n'y a qu'un point indivisible qui soit le véritable lieu. Les autres sont trop près, trop loin, trop haut ou trop bas. La perspective l'assigne dans l'art de la peinture, mais dans la vérité et dans la morale qui l'assignera ? " Les barres de séparation ne figurent pas dans toutes les éditions. L'édition Lafuma dissocie deux paragraphes dans le dernier, quoique le manuscrit n'en comporte qu'un : Ainsi les tableaux vus de trop loin et de trop près. Et il n'y a qu'un point indivisible qui soit le véritable lieu. Les autres sont trop près, trop loin, trop haut ou trop bas. La perspective l'assigne dans l'art de la peinture, mais dans la vérité et dans la morale qui l'assignera? Dans on n'y entre plus , le n' est une addition de l'éditeur. Certaines éditions donnent

47. Pronunciation desargues, girard (15911661) (day ZÄRG) Descartes, Rene (1596-1650) (day CÄRT)Dirichlet, Peter Lejune (1805-1859) (dee ree KLAY). Euclid (YOU klid) http://www.math.ucla.edu/~bnewdelm/Pronunciation.htm

This list is for my math-hommies Stop teasing me !!!!!!! Agnesi, Maria Gaetana (1718-1799) (an YAY zee) Bernoulli, Jakob/Jacques/James (1654-1705)(ber NOO lee) Bernoulli, Johann/Jean/John (1667-1748) (ber NOO lee) Cauchy, Augustin-Louis (1789-1857) (ko SHE) Clairaut, Alexis-Claude (1713-1765) (kla ROW, as in row your boat) Dedekind, Richard (1831-1916) (DA de kint) Dirichlet, Peter Lejune (1805-1859) (dee ree KLAY) Euclid (YOU klid) Eudoxus (408-355 B. C.) (you DOK sis) Euler, Leonhard (1707-1783) (OI ler) Fourier, Jean Baptiste Joseph (1768-1830) (foo RYAY) Heine, Eduard (1821-1881) (HI na, not a long a) Hermite, Charles (1822-1901) (er MEET) Kronecker, Leopold (1823-1891) (KROW nek er) Kummer, Ernst (1810-1893) (KUM er) Laplace, Pierre-Simon de (1749-1827) (la PLAS) Lebesgue, Henri (1875-1941) (la BEG) in some elite cultures (la BAHJE) Leibniz, Gottfried Wilhelm (1646-1716) (LIP nits, long i) Napier, John1550-1617) (NAY pee air) Noether, Emmy (1882-1935) (NOI ter)

48. Pascal's Mystic Hexagram girard desargues (15931662) originated the idea of projective geometry, andPascal wrote that he (Pascal) owed everything he had found on the subject to http://www.mathpages.com/home/kmath543/kmath543.htm

Pascal's Mystic Hexagram One of the first applications of modern mathematics to emerge during the Renaissance was the study of perspective for the purposes of painting and architecture.  This led naturally to a consideration of projection, i.e., the mapping of images from one plane surface S to another plane surface S' by projection from a point O.  The point p on S maps to a point p' on S' such that O, p and p' are colinear.  Obviously the distances between points and the angles between lines are not preserved under a projective mapping, but certain properties of figures are preserved.  For example, straight lines map to straight lines, and conics map to conics.  In addition to these qualitative invariants, there are also quantitative invariants.  Consider four points A,B,C,D on a line in S, projected from the point O to the points A', B', C', D' on a line in S' as shown below. Applying the law of sines to the triangles OBA and OBD, we have The ratio of these two is Likewise if we apply the law of sines to the triangles OCD and OCA we get Thus if we multiply AB/BD by DC/CA the sines of m and n cancel out, and are left with

49. Odd Mathematical Lists Camille Jordan, Cantor, Hadamard, Hardy, Littlewood, Newton, girard desargues,Pascal, Weierstrass, Gentzen, Tschebycheff, Markov, Kolmogorov, Fredholm, http://sprott.physics.wisc.edu/pickover/mathq.htm

Odd Mathematical Lists Clifford A. Pickover I look forward to hearing from you. Please e-mail me your answers and I will post information here. (E-mail address is on main page.) 1. What are the five most famous or important unsolved mathematical problems today? 2. What is the most difficult-to-understand areas of mathematics today? 3. Who are the five most influential mathematicians that ever lived? 4. Who are the five most influential mathematicians alive today? 5. Who was the strangest mathematician that ever lived? 6. What are the five most interesting numbers? (And 5 most interesting integers?) 7. What one question would you like seen added to this list? Note: these questions and many more are now answered in my book Wonders of Numbers Some Sample Answers From Carl Speare: 1 + sqrt(5) 1 - sqrt(5) - and - 2 2 lim e^n * n! n->inf. - = sqrt(2 * pi) n^n * sqrt(n)

50. Francesca Fiorani C.V. Thesis Title The Treatises on Perspective by girard desargues and Abraham BosseScientific Culture and Painting in France around 1650 http://www.virginia.edu/art/homepage/faculty/ff-cv.html

AREAS OF RESEARCH INTEREST Relationships between art, science, and technology; scientific illustrations; maps; collecting; and religious art. EDUCATION Ph.D. History of Art, University of Rome "La Sapienza," June 1994 Dissertation Title: The Gallery of Maps in the Vatican Palace: Art and Cartography in the Late Renaissance M.A. History of Art, University of Rome "La Sapienza," November 1990 Thesis Title: The Treatises on Perspective by Girard Desargues and Abraham Bosse: Scientific Culture and Painting in France around 1650 B.A. History of Art, University of Rome "La Sapienza," June 1986 Thesis title: The Art Exhibitions in Weimar, 1799-1805 RECENT COURSES TAUGHT ARTH 230: XV Century Art ARTH 331: Gender and Art in Renaissance Italy ARTH 491: Renaissance Venice ARTH 491: Renaissance Florence ARTH 491: Baroque Rome ARTH 538: Renaissance Art Criticism SELECTED PUBLICATIONS "Cosmos the World of Cosimo," in Acts of the Norwegian Institute in Rome , forthcoming.

51. Workshop On Combinatorial Hopf Algebras Institut girard desargues (Lyon 1) A. Garsia, University of California, SanDiego I. Gessel, Brandies University R. Grossman, University of Illinois, http://www.math.tamu.edu/~sottile/conferences/Banff04/04w5011.html

Banff International Research Station Workshop on Combinatorial Hopf Algebras August 28 - September 2 2004 Schedule Abstracts Organizers: Nantel Bergeron , York University, Toronto. Louis Billera , Cornell University. Frank Sottile Stephanie van Willigenburg , University of British Columbia. Participants: M. Bayer, University of Kansas P. Cartier, IHES F. Chapoton, Institut Girard Desargues (Lyon 1) Kurusch Ebrahimi-Fard, IHES R. Ehrenborg, University of Kentucky Alessandra Frabetti, Institut Girard Desargues (Lyon 1) A. Garsia, University of California, San Diego I. Gessel, Brandies University R. Grossman, University of Illinois, Chicago Li Guo, Rutgers University, Newark M. Hazewinkel, CWI Amsterdam. G. Hetyei, University of North Carolina at Charlotte F. Hivert, Independent University of Moscow C. Hohlweg, IRMA Strasbourg, France S. Hsiao, University of Michigan Selma Kapetanovic, York University, Toronto Aaron Lauve, Rutgers University

52. Mathematics Of Computation Marc Deléglise Affiliation Institut girard desargues, UPRESA 5028 Mathematiques,Université Lyon I, 69622 Villeurbanne Cedex, France http://www.ams.org/mcom/1998-67-224/S0025-5718-98-00977-6/home.html

Journals Home Search Author Info Subscribe ... Help ISSN 1088-6842(e) ISSN 0025-5718(p) Previous issue Table of contents Next issue Articles in press ... All issues Computing Author(s): Journal: Math. Comp. MSC (1991): Primary 11Y70, 11N56 Retrieve article in: PDF DVI TeX PostScript This article is available free of charge Abstract References Similar articles Additional information Abstract: Let denote the Von Mangoldt function and . We describe an elementary method for computing isolated values of . The complexity of the algorithm is time and space. A table of values of for up to is included, and some times of computation are given. References: M. DELGLISE AND J. RIVAT, , Experimental Mathematics, 5 (1996), pp. 291-295. CMP height 2pt depth -1.6pt width 23pt, Computing : The Meissel, Lehmer, Lagarias, Miller, Odlyzko method , Mathematics of Computation, 65 (1996), pp. 235-245. MR D. R. HEATH-BROWN, Prime numbers in short intervals and a generalized Vaughan identity , Can.J.Math., 34 (1982), pp. 1365-1377.

53. Mathematics Of Computation Affiliation Institut girard desargues, Université Lyon I, 21, avenue ClaudeBernard, 69622 Villeurbanne Cedex, France Email Marc.Deleglise@igd.univlyon1. http://www.ams.org/mcom/2004-73-247/S0025-5718-04-01649-7/home.html

Journals Home Search Author Info Subscribe ... Help ISSN 1088-6842(e) ISSN 0025-5718(p) Previous issue Table of contents Next issue Articles in press ... All issues Counting primes in residue classes Author(s): Journal: Math. Comp. MSC (2000): Primary 11Y40; Secondary 11A41 Posted: February 25, 2004 Retrieve article in: PDF DVI TeX PostScript ... Additional information Abstract: We explain how the Meissel-Lehmer-Lagarias-Miller-Odlyzko method for computing can be used for computing efficiently , the number of primes congruent to modulo up to . As an application, we computed the number of prime numbers of the form less than for several values of up to and found a new region where is less than near References: C. Bays and R. H. Hudson, On the fluctuations of Littlewood for primes of the form , Math. Comp. MR C. Bays, K. Ford, R. H. Hudson and M. Rubinstein, Zeros of Dirichlet -functions near the real axis and Chebyshev's bias , J. Number Theory

54. 1600-luvun Puolivali desargues, girard 1591 – 1661. Lyonissa vaikuttanut ranskalainen arkkitehti jainsinööri, joka tutki perspektiivioppia ja geometriaa ja jonka kirjoitukset http://matta.hut.fi/matta/isom/tskhtml/matemaat6.html

Sisällön pääryhmät Matematiikka tieteenä Matemaatikot E S I T I E D O T K A T S O M Y S matematiikka Kansisivu Sisältö Hakemisto 1600-luvun puoliväli Desargues, Girard Descartes, René Discours de la méthode pour bien conduire sa raison et chercher la verité dans les sciences satasivuisessa liitteessä La géométrie . Descartes kuoli Tukholmassa, jonne oli kuningatar Kristiinan kutsusta saapunut 1649. Cavalieri, Bonaventura de Fermat, Pierre x n y n z n ei ole kokonaislukuratkaisua x y z , jos , mutta todistus ei mahdu marginaaliin. Tätä ns. Torricelli, Evangelista Pascal, Blaise Desargues (geometria) Desargues geometria (projektiivinen) Descartes (geometria) ... Pascal Kivelä, niinkuin matematiikka, versio 1.12

55. JCA 11026 Institut girard desargues, Universite Lyon I, 21 Av. Claude Bernard, 69622Villeurbanne, France, clarke@igd.univ.lyon1.fr C. Nour Institut girard desargues http://www.heldermann.de/JCA/JCA11/jca11026.htm

Journal Home Page Complete Contents of this Volume Previous Article ... Next Article Journal of Convex Analysis 11 (2004), No. 2, 413436 The Hamilton-Jacobi Equation of Minimal Time Control F. H. Clarke Institut Girard Desargues, Universite Lyon I, 21 Av. Claude Bernard, 69622 Villeurbanne, France, clarke@igd.univ.lyon1.fr C. Nour Institut Girard Desargues, Universite Lyon I, 21 Av. Claude Bernard, 69622 Villeurbanne, France, chadi@igd.univ.lyon1.fr We study the solutions of the Hamilton-Jacobi equation that arise in connection with minimal time control, in a new global framework. These solutions, for which we establish existence using the minimal time function as a function of two variables, turn out to be closely related to time-geodesic trajectories. Keywords: minimal time function, viscosity solutions, geodesic trajectories, proximal analysis, monotonicity of trajectories, nonsmooth analysis. FullText-pdf (616 KB) for subscribers only.

56. Les Maths Dans La Rue d ailleurs IGD Institut girard desargues Nemours Lycée Etienne Bezout http://www.espacemath.com/mathsrue.htm

Forum Math Guide Dimatu Accueil ... Revues Les Maths dans la rue Sommaire Accueil Collège Concours Dimaf ... Rédaction Quelque soit la partie du monde que vous habitez, signalez-nous les rues, restaurants, cités, magasins, lieux publics en général, portant des noms mathématiques ou des noms de mathématiciens. Tous seront ici classés par pays et par ville. France. Arcueil Rue Cauchy Rue Monge Avon Rue Bézout Blanc-Mesnil Avenue Descartes (René) Charbonnières Lycée Blaise Pascal Dijon Place Monge Fermat timbré Information sur Fermat donnée par Mireille Chaleyat-Maurel le 21/08/01 : I inform you that the French Post Office has issued yesterday a stamp for the 400th anniversary of the birthday of Pierre de Fermat (4,50FF). server. Lille Dans la vieille bourse de Lille (place du général de Gaulle) on peut voir une plaque commémorative sur Gaspard Monge. Le portrait y est gravé. information donnée par Géry Huvent. Lyon Plaque honorant la mémoire de Girard Desargues sur l'hôtel de ville dont il fut d'ailleurs dans les années 1630 l'un des deux architectes. La plaque est visible place de la comédie à Lyon en face de l'opéra.

57. Art Bulletin, The: The Invention Of Infinity: Mathematics And Art In The Renaiss geometry of Johannes Kepler and girard desargues as well as important articles on From this art historian s perspective, understanding desargues is http://www.findarticles.com/p/articles/mi_m0422/is_3_83/ai_84192652

@import url(/css/us/style1.css); @import url(/css/us/searchResult1.css); @import url(/css/us/articles.css); @import url(/css/us/artHome1.css); Advanced Search Home Help IN free articles only all articles this publication Automotive Sports 10,000,000 articles - not found on any other search engine. FindArticles Art Bulletin, The Sept 2001 Content provided in partnership with 10,000,000 articles Not found on any other search engine. Related Searches Books / Reviews The Invention of Infinity: Mathematics and Art in the Renaissance (Book) / Reviews Featured Titles for ALAN Review Afterimage American Drama American Music Teacher ... View all titles in this topic Hot New Articles by Topic Automotive Sports Top Articles Ever by Topic Automotive Sports The Invention of Infinity: Mathematics and Art in the Renaissance. - book review Art Bulletin, The Sept, 2001 by Lyle Massey Save a personal copy of this article and quickly find it again with Furl.net. It's free! Save it. J. V. FIELD The Invention of Infinity: Mathematics and Art in the Renaissance Oxford: Oxford University Press, 1997. 264 pp.; 100 b/w ills., 32 color, 200 line drawings. $35

58. Citations Saturation And Stability In The Theory Of Computation Technical Report 1997/3, Institut girard desargues, Universit e Claude BernardLyon I, 1997. To appear in Annals of Pure and Applied Logic. http://citeseer.ist.psu.edu/context/437785/187626

59. Knuf - Amsterdam 2005 Translate this page He was greatly influenced by girard desargues who was born in Lyon in 1591 andin Paris in 1626 lays down a proposition for the construction of fountains. http://www.amsterdambookfair.com/cat/knuf.htm

Back Table of Contents About the book shop Frits Knuf Antiquarian Books tel. +33 - 254-722 656, fax +33 - 254-722 682 e-mail: info@books-on-books.com site: www.books-on-books.com Bosse, Abraham. Gilbert, C. Collection of Drawings. 18mo. 19th century red half calf, marbled bds. Spine goldtooled. Back Table of Contents

60. CONIC SECTION - LoveToKnow Article On CONIC SECTION about the beginning of the I7th century by girard desargues and Blaise Pascal . desargues has a special claim to fame on account of his beautiful http://5.1911encyclopedia.org/C/CO/CONIC_SECTION.htm

CONIC SECTION CONIC SECTION The definitions given above reflect the intimate association of these curves, but it frequently happens that a particular conic is defined by some special property (as the ellipse, which is the locus of a point such that the sum of its distances from two~ fixed points is constant); such definitions and other special properties are treated in the articles ELLIPSE, HYPERBOLA and PARABOLA. In this article we shall consider the historical development of the geometry of conics, and refer the reader to the article GEOMETRY: Analytical and Projective, for the special methods of investigation. But the greatest Greek writer on the conic sections was Apollonius of Perga, and it is to his Conic Sections that we are indebted for a review of the early history of this subject. Of the eight books which made up his original treatise, only seven are certainly known, the first fouI in the original Greek, the next three are found in Arabic translations, and the eighth was restored by Edmund Halley in 1710 from certain introductory lemmas of Pappus. The first four books, of which the first three are dedicated to Eudemus, a pupil of Aristotle and author of the original Eudemian Summary, contain little that is original, and are principally based on the earlier works of Menaechmus, Aristaeus (probably a senior contemporary of Euclid, flourishing about a century later than Menaechmus),Euclid and Archimedes. The remaining books are strikingly original and are to~be regarded as embracing Apolloniuss own researches.

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