Philippe de la Hire: Was He Desargues’ Schüler?

Abstract

Philippe de la Hire (1640–1718) was the third of the seventeenth century pioneers of projective geometry, after Girard Desargues (1591–1661) and Blaise Pascal (1623–1662). We know very little about La Hire beyond what he tells us in his various published works and what Bernard de Fontenelle reported in his Eloge, issued soon after La Hire’s death. That vacuum of information has been filled with misinformation and speculation. Beyond the annoying falsehoods, there is the very real issue of the degree of influence of Desargues in La Hire’s geometry, especially his Nouvelle méthode en Géométrie pour les Sections des Superficies coniques et Cylindriques of 1673. La Hire’s originality has been questioned, beginning, apparently, soon after the 1673 publication, reviving in the late nineteenth century after publication of Desargues’ long lost work of 1639 and, again, in the writing of eminent scholar René Taton around 1950. Much of the discussion of originality has centered on the availability of Desargues’ booklet to La Hire, rather than an examination of the work itself. The claim of this study is that comparison of the work of Desargues and La Hire shows that Desargues’ influence was minimal.