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Introducing Logarithms to Italy

CAVALIERI, Bonaventura. Directorium generale uranometricum in quo trigonometriae logarithmicae fundamenta... [Including:] Tabvla trigonom. Logarithmica. Bologna, Nicolai Tebaldini, 1632.

4to. [23 x 16 cm], (8) ff., 330 pp., (3) ff.; (110), (50) ff., 2 tables printed recto and verso on one very large sheet. Bound in contemporary flexible vellum, title written in a neat hand on spine. Endpapers tastefully replaced; title reinforced at gutter; some quires evenly toned or browned, but generally a fresh copy. Excellent.


Very attractive copy of the rare first edition of the first work on logarithms printed in Italy, the first published work of a great mathematician of whom Galileo wrote, “few, if any, since Archimedes, have delved as far and as deep into the science of geometry.” Cavalieri introduced and popularized logarithms throughout his country within a generation of Napier’s invention of them. The Directorium covers the construction, uses, and applications of logarithms, “together with noteworthy developments in trigonometry and applications to astronomy” (DSB). It also contains the author’s discovery of the expression for the area of a spherical triangle in terms of spherical excess. Two extensive appendices offer logarithmic-trigonometric tables derived from those of Napier and Henry Briggs, with logs of sines, versines (sinus versus) tangents and cotangents (but no cosines). Cavalieri included logarithms of trigonometric functions for the benefit of astronomers. A second edition of the Directorium was issued posthumously in 1653.

Cavalieri (1598-1647), who wrote on mathematics, optics and astronomy, invented the reflecting telescope. After studying with Benedetto Castelli he became a self-declared disciple of Galileo, to whom he wrote at least 112 letters. Today he is remembered for his work on the principle of indivisibles, which played a crucial role in the development of integral calculus.

OCLC lists NYPL, CalTech, Berkeley, Burndy, U. Michigan, Linda Hall, Cincinnati and Texas Tech.

* Riccardi I.322; Macclesfield Part II London June 10, 2004 #499; E. Carruccio in DSB III, 149-53.

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