The Greek Legacy

When Desargues circulated fifty copies of his Brouillon project d’une atteinte aux evenmens des rencontres du Cone avec un Plan (Rough Draft of an Essay on the results of taking plane sections of a cone) in 1639, he was contributing to a lively contemporary study of geometry. Descartes’ novel algebraic methods had been published two years before, and in 1639 Mydorge published a more classical treatment of the conic sections. The classical authors themselves were increasingly well studied. Desargues had available Commandino’s Latin edition of Euclid’s Elements, published in 1572, as well as his Latin edition of the first four books of Apollonius’ Conics, published in 1566 with extensive commentaries by Eutocius, Pappus and Commandino himself. The last four books of the Conics were unknown in Desargues’ time. Two editions of Pappus’ Collection had also been published by Commandino (posthumously) in 1588 and 1602. In this chapter we sketch what in these ancient works forms the background to Desargues’ remarkable text. The mathematical details of his reformulation of those ideas is described in more detail in Chapter IV. Ironically, the modern (Greek-less) English reader is in some ways scarcely more able than Desargues was to approach the originals. There is, of course, Heath’s three-volume edition of Euclid’s Elements (see Bibliography for details). But only the first three books of Apollonius’ Conics exist in English, translated by R. C. Taliaferro in 1939; the first seven books exist in the French translation of Ver Eecke, 1923. Heath provided an extensive detailed commentary on the Conics in 1896. Finally, Book VII of Pappus’ Collection is only now translated into English, by A. Jones (see the Bibliography); happily Ver Eecke put all of it that survives into French in 1933.