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War of words on perspective, conic sections, cutting architectural stones and making sundials: the Jesuit versus the Cartesian

[DUBREUIL, Jean] and others.
Advis charitables sur les diverses oeuvres, et feuilles volantes du Sr. Girard Desargues Lyonois. Publiees sous les titres.
I. De Brouïllon Projet d'une atteinte aux evenements des rencontres du cone avec un plan: ...
II. De Brouïllon Projet d'exemple d'une maniere universelle, touchant la pratique du traict a preuves, pour la couppe des pierres en l'architecture.
III. D'une maniere de tracer tous quadrans d'heures égales au soleil, au moyen du style posé: ...
Mis au jour. ...
With: [DUBREUIL, Jean]. Diverses methodes universelles, et nouvelles, en tout ou en partie pour faire des perspectives. ... Tirees pour la plus-part du contenu du livre de La perspective pratique. Ce qui servira de plus de response aux deux affiches du Sieur Desargues, contre ladite Perspective pratique.
Paris, Melchior Tavernier, François l'Anglois, dit Chartres, 1642. 2 works (4 & 2 parts) in 1 volume. 4to (25.5 x 18 cm). The first work in 4 parts. It lacks two small engraved plates. The second work with 10 full-page engravings on integral leaves. Half white sheepskin parchment (ca. 1900?). Ad 1: [4], [4]; 10; 14, [2 blank]; 17, [3 blank] pp.; Ad 2: [15] pp., 10 double-page spreads, [1 blank] p.
€ 22,500
Very rare and important first editions forming the culmination of an on-going war of words on perspective, conic sections, cutting stones for architectural use and making sundials, with the Parisian Jesuit architect Jean Dubreuil (1602-1670) attacking the Lyonese mathematician and engineer Girard Desargues (1591-1661), who spent much time in Paris in the circles of Descartes, Fermat and Pascal (the young Blaise and his father) and pioneered the modern principles of perspective drawing. Ironically the publications on both sides of this war came from the same printing and publishing office. Desargues's rigorously mathematical Exemple de l'une des manieres universelles ... touchant la practique de la perspective ... (Paris, 1636), is now recognized as the pioneering work on the mathematics of projective geometry, the key to understanding the principles of perspective. Although Dubreil's two present works do not explicitly cite it, both respond to Desargues's criticisms and the title-page of the Advis charitables cites Desargues's later publications that reiterated parts of his 1636 treatise and added further material.
With a neat manuscript list of the contents and reference to the 1864 edition of Desargues's works on the front paste-down. Two parts of the first work each lacking one small engraved plate, as noted, but no complete copy with all parts has been located. Otherwise a good copy and including the two integral blank leaves. With traces of a blue, 19th-century blue paper wrapper stuck to the first title-page, covering two letters in the title, and some water stains and spotting in the second work. A very rare pair of works on perspective and related matter, part of a dispute concerning methods of using perspective.
Extensive description available on request. BAL 338 note (mentioning ad 1 & ad 2, without noting ad 1 part I); Taton, L'oeuvre ... de G. Desargues (1951), pp. 50 ff. (ad 1 & ad 2); WorldCat (7 copies of ad 1, none with all parts and plates; 7 copies of ad 2).
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