Trigonometria plana, et sphaerica, linearis, & logarithmica. Hoc est, tam per sinuum, tangentium, & secantium multiplicationem, ac divisionem iuxta veteres: quam per logarithmorum simplicem fere additionem iuxta recentiores; Ad triangulorum dimetiendos angulos, & latera procedens. Cum canone duplici trigonometrico, & chiliade numerorum absolutorum ab 1 usque ad 1000, eorumque logarithmis, ac differentijs. Opusculum universae mathesi utilissimum: omniumque; terrestium, ac caelestium dimensionum promptuarium.

Bologna: Victor Benatis, 1643.

First edition. “Cavalieri, a pupil of Galileo, introduced logarithms into Italy in his Trigonometria and several other works.” (Hook & Norman: Origins of Cyberspace, No. 3). “From the standpoint of mathematics alone the Italian writer who influenced the science most in the 17th century was probably Bonaventura Cavalieri, ... [he] was one of the first to recognize the great value of logarithms” (Smith: History of Mathematics, p.362).

“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. In this connection we might mention ‘Directorium generale uranometricum’ (1632), ..., ‘Nuova pratica astrologica’ (1639), and ‘Trigonometria plana, et sphaerica, linearis et logarithmica’ (1643). The ‘Directorium’, the ‘Pratica’, and the ‘Trigonometria’ contain, moreover, excellent logarithmictrig-onometric tables.” (DSB III, p.152).

The final 104 pages of the Trigonometria contain Cavalieri’s tables; “the main table in this work the logarithms of numbers up to 1000 are exhibited to seven decimals with characteristic and interscript first differences.” (Henderson: Bibliotheca Tabularum Mathematicarum, no. 37).

The Trigonometria also contains a preliminary defense by Cavalieri of his method of indivisibles; “Throughout the last three of the four volumes of his ‘Centrobaryca’ (1635-1641) [Paul] Guldin had commented upon Cavalieri’s use of indivisibles and had particularly criticized it very outspokenly in Chapter 5 of the fourth volume. Shortly before Guldin’s death [in 1643] Cavalieri published a defense of his method in the section ‘Admonitio circa auctorem centrobaryacae’ of his Trigonometria (1643, pp. 6-8)”. (Kirsti Andersen: Cavalieri’s Method of Indivisibles, Archive for History of Exact Sciences, vol. 31, p.295). Cavalieri’s full defense of his method appeared in his ‘Exercitationes Geometricae’ 1647.

The Erwin Tomasch Library C-52; Riccardi I/1 328; Cinti 111.

4to (225 x 168 mm), engraved frontispiece pp. 16, 71, (1); (104) and 1 engraved folding plate, contemporary limp vellum, inner hinges a little loose, front pastedown and free end paper with a little worming (hardly effecting the inner margin of the frontispiece), in all avery good and clean copy in its original state.

Item #3005

Price: $3,250.00