CAVALIERI, Bonaventura Trigonometria plana, et sferica, linearis, & logarithmica. Hoc est tam per sinuum, tangentium, & secantium multiplicationem, ac divisionem iuxta veteres: quam per logarithmorum simplicem fere additonem iuxta recentiores; ad triangulorum dimetiendos angulos, & latera prcedens. Cum canone duplici trigonometrico, & chiliade numerorum absolutorum ab 1 usque ad 1000, eorumque logarithmis, ac differentiis... Bologna, heirs of Vittorio Benacci, 1643 1643
4to (231 x 156 mm), pp 16; 71 [1]; [104], with engraved frontispiece and one engraved plate; final gatherings and plate very slightly browned, a fine copy in eighteenth-century Italian marbled half calf and patterned boards. £2250
First edition of Cavalieri's logarithmic-trigonometric tables, and containing Cavalieri's defence of his method of indivisibles against the criticisms of the Jesuit mathematician Paul Guldin. This appears in the preface, and is entitled 'Admonitio circa auctorum Centrobarycae' (Guldin's Centrobaryca was published in four volumes, Vienna 1635-1641). In the fourth volume of the Centrobaryca Guldin 'criticized Cavalieri's use of indivisibles in his Geometrica... asserting not only that the method had been taken from Kepler but also that since the number of indivisibles was infinite, they could not e compared with one another. Furthermore, he pointed out a number of fallacies to which the method if indivisibles appeared to lead.
'Cavalieri ... defended himself against the first charge by pointed out that his method differed from that of Kepler in that it made use only of indivisibles, and against the second by observing that the two infinities of elements to be compared are of the same kind' (DSB, wrongly attributing Cavalieri's defence to his Exercitationes of 1647, whereas in fact it appears in the present work). Cavalieri's Geometria indivisibibus (1635), was the most important precursor of the calculus.
'Logarithms were introduced into mathematics in the work of Napier in 1614. In Italy such valuable auxiliaries to numerical calculation were introduced by Cavalieri, together with noteworthy developments in trigonometry and applications to astronomy' (DSB). Cavalieri's tables and methods introduced in this work were invaluable to the astronomical researches of Gian Domenico Cassini.
The frontispiece shows the goddess Trigonometria opening a door on which mathematical and astronomical images are inscribed, revealing a landscape in which are depicted the various applications of the art.
Provenance: contemporary inscription of the Jesuit college of Bologna on title (Cavalieri was professor there); engraved armourial ex libris of the Counts Riccati; the family had several distinguished mathematicians, including Iacopo Francesco Riccati (1676-1754)
Cinti 111; Riccardi I 328
£2250
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