By Carl B. Boyer

The earliest contributions --
The Alexandrian age --
The medieval interval --
The early sleek prelude --
Fermat and Descartes --
The age of commentaries --
From Newton to Euler --
The definitive formula --
The golden age.

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Neugebauer has made the interesting suggestion that the discovery of the conic sec­ tions may have resulted from a study of the shadows cast by sundials. See "The Astro­ nomical Origin of the Theory of Conic Sections," Proceedings of the A merican Philosophical Socidy, v. XCII ( 1948), p. 13fH38. �, CHAPTER II The Alexandrian Age A kmnder, IM king of IM Macedonians, began UM a wrdch to karn geometry that M might know how liltk IM earth was whereof M had possessed. fJerJ liUle. ---8BNE CA G REEK history customarily is divided into two periods, the Hellenic and the Hellenistic.

273, note I I . tla, v. 11 ( 1912), p. 1-47. 1 See TIN Worls of Arclitn«lu (edited by T. L. Heath, Cambridge ( 1897)), p. hi ff. , ,,. " This work, perhaps the first textbook on the conic sections, has been lost, probably irretrievably, along with the four books on conics by Euclid. Presumably, however, the first four books of the Conics of Apollonius8 include most of the material given by Aristaeus and Euclid. The author himself says that the first four books coordinate and complete previous knowledge, but he emphasized the originality of his mode of treatment ; the other four books, of which the last has been lost, are presumed to be substantially original in con­ tent.

Lack 11 J. H. Weaver, "On Foci of Conics," Bulletin, A merican Matliematical Society, ( 1916-1917), p. 357--365. 11 See T'he Works of A rchimedes (Heath ), p. lxvi i . v. XXIII THE ALEXANDRIAN AGE 37 To Pappus one owes also the clearest statement in antiquity on the nature of analysis. Greek geometry was divided into three parts : the elements (as found in Euclid) ; practical geometry or geodesy (rep­ resented by Heron) ; and higher geometry (illustrated by Apollonius and Archimedes) . The loss of many ancient works in the third cate­ gory makes the Mathematical Collection of Pappus (itself incompletely preserved) an indispensable work on the elements of higher geometry.

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