Paris: de l'imprimerie de M. & I. Henault, et se vendent, chez F. l'Anglois dit Chartres, 1644.
First edition, complete with its very rare supplement, of this polemic against Girard Desargues (1591-1661). Important for containing literal extracts from Desargues’ Brouillon Projet, the work also contains the first printed reference to ‘La Pasqualle’, the mystic hexagram, published in 1640 by the sixteen year-old Pascal in a broadside of which only one copy survives.
Desargues’ most important work, which constitutes the birth of modern projective geometry, was Brouillon projet d'une atteinte aux événemens des rencontres du Cone avec un Plan. “The Brouillon Projet on conics, of which he published fifty copies in 1639, is a daring projective presentation of the theory of conic sections; although considered at first in three-dimensional space, as plane sections of a cone of revolution, these curves are in fact studied as plane perspective figures by means of involution, a transformation that holds a place of distinction in the series of demonstrations” (DSB IV 47). Desargues intended his work to appeal not only to theoreticians but also practical men, and this perhaps explains his use of an original vocabulary which, however, made the pamphlet very difficult to read. It exerted little influence at the time, and disappeared from view (in fact, it was thought to be lost until a copy was found in 1951). Nevertheless, its methods formed the basis of the new techniques of projective geometry developed in the nineteenth century by Poncelet and his followers.
“In August 1640, Desargues published, again under the general title Brouillon Projet, an essay on techniques of stone-cutting and gnomonics. While refining certain points of his method of perspective presented in 1636 [in a pamphlet now lost], he gives an example of a new graphical method... In attempting thus to improve the graphical procedures employed by many technicians, Desargues was in fact attacking an area of activity governed by the laws of the trade guilds; he also drew the open hostility of those who were attached to the old methods and felt they were being injured by his preference for theory rather than practice” (ibid.)
One of these technicians was Curabelle, who published in the present work a violent attack on Desargues’ methods, “finding nothing in them but mediocrity, errors, plagiarism and information of no practical use” (ibid.). Desargues replied with a pamphlet defending his work, to which Curabelle responded with Foiblesse pitoyable. This experience so affected Desargues that he published virtually no scientific work after 1644, turning instead to a career in architecture.
In Oeuvres de Desargues (II, 389), Poudra notes that the Foiblesse pitoyable is bound at the end of the Examen and, because of its rarity, transcribes it in full.
For a detailed account of Desargues’ work, see J V Field and J J Gray, The geometrical work of Girard Desargues, 1987.
Macclesfield 581 (this copy); Arnaud de Vitry 165; Vagnetti EIIIb39.
4to (285 x 206 mm), pp [1-2] 3-81 [1:blank] with 16 engravings printed in the text (several full-page); pp 9  with an engraving printed on one page, 18th century vallum-backed blue paper boards (calf spine showing under the vellum which is cracking), lower inner corner of the first eight pages with some damage (but not affecting the printing area). Provenance: with the book plate and blind stamp of the Macclesfiled library.