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Three important first editions on analytical geometry, differential calculus and infinitesimals

TORELLI, Guiseppe.
De nihilo geometrico, libri II.
Verona, Augostino Carattoni, 1758. With a woodcut vignette on the title-page (with a globe, book and instruments), and many fine-line diagrams in text.
With:
(2) SALADINI, Girolamo. Elementa geometriae infinitesimorum. Libri tres.
Bologna, Tommaso d'Aquino, 1760. Title-page with an engraved vignette of a putto with drafting instruments and an armillary sphere, and with numerous diagrams on 9 folding engraved plates.
(3) CARNOT, Lazare. Oeuvres mathématiques.
Basel, J. Decker, 1797. With a stipple-engraved (and aquatint) frontispiece portrait of Carnot by Jean Jacques de Mechel, and 6 diagrams on a folding engraved plate. 3 works in 1 volume. 8vo. Contemporary half tanned sheepskin, gold-tooled spine. 117, [3 blank]; XIV, [2], 139, [2], [1 blank]; XVI, 208 pp.
€ 9,000
Three important 18th-century mathematical first editions, together in one volume.
Ad 1: First (and only?) edition of a text book on infinitesimal geometry by Guiseppe Torelli (1721-1781), a wide-ranging Veronese scholar best known for his works on geometry. His De nihilo geometrico presents a new basis for infinitesimal analysis, which had been started but not exhaustively treated by Newton and Leibniz. His rejection of the concept of limits and his support of the ideas of Bernard Nieuwentijt against Leibniz caused his work to be largely ignored in modern times.
Ad 2: First and only edition of another work on infinitesimal geometry, the first major work of the Italian mathematician Girolamo Saladini (1731-1813), with full references to Newton and Leibniz. Saladini's work is divided into three parts, the first giving axioms and theorems, and the other two with 16 and 18 propositions respectively, the last part closing with three "scholia". Though little known today, Saladini together with Vicenzo Riccati published the first extensive treatise on integral calculus in their Institutiones analyticae (1765-1767), pre-dating Euler.
Ad 3: First edition of the mathematical works of Lazare Carnot (1753-1823), much better known than the treatises of Torelli and Saladini above. The book begins with his "Essai sur les machines en général", which contains his famous theorem on the loss of kinetic energy during inelastic collisions. Divided into two parts, the book contains all the elements of engineering mechanics: the first truly theoretical work on the subject. The last 80 pages present his "Réflexions sur la métaphysique du calcul infinitésimal", an interesting philosophical discussion of differential calculus.
With occasional minor foxing and a few slightly browned leaves, but still in very good condition and with generous margins. The binding is slightly scuffed around the extremities, with a small crack at the head of the back hinge, but otherwise also very good. A collection of 18th-century mathematical first editions, especially interesting for the discussion of infinitesimals. Ad 1: G.T. Bagni, "Unintuizione dellinfinitesimo attuale: De nihilo geometrico (1758) ...", in: Didattica delle scienze XXIII (1998): ICCU UFIE003084; Riccardi II, 538; ad 2: ICCU UFIE003018; for Saladini also DSB XI, pp. 401-402; ad 3: DSB III, p. 78.
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