Cavalieri’s Early Work on Logarithms by a Pupil of Galileo

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CAVALIERI, Bonaventura.

Trigonometria plana, et sphærica, linearis, & logarithmica.

Bologna, Benati, 1643.

4to (22 x 15.5 cm), [1] engraved allegorical frontispiece, 16 pp., 71 pp., [1] t.p. to logarithm tables, 104 pp. of tables, [1] engraved plate riveted to final leaf. Bound in contemporary half-vellum and paper boards. Some worming to spine, foot weak, title-page toned, light toning or spotting to some leaves, faint waterstain to upper left margin of about 24 leaves of plates. Generally good.

First edition of a text providing new applications for logarithms, the new computational tool by Napier that Cavalieri had recently introduced in Italy.

Cavalieri opens by solving 16 problems in planar and 10 problems in spherical geometry, followed by a set of axioms and definitions. Having laid the groundwork, he then presents 104 full pages of tables, printing the logarithmic values of sine, tangent and secant. “The main table in this work is a trigonometrical one, but at the end of this table the logarithms of numbers up to 12000 are exhibited to seven decimals with characteristic and interscript first differences” (Henderson). The volume concludes with a single full-page plate, with engravings of some basic trigonometric figures.

Bonaventura Cavalieri (1598-1647), one of the last members of the Gesuati order, was professor of mathematics in Bologna; he also wrote on optics and astronomy. A friend and pupil of Galileo, he later taught Galileo’s thesis on “massimi sistemi” in Bologna between 1642-45. He is remembered today for his work on the principle of indivisibles, which played a crucial role in the development of integral calculus.

* Cinti III; Riccardi 328, no. 9; DSB III.152-3; Henderson 1926, no. 37.

Price: $2,250.00