Directorium generale uranometricum in quo trigonometriae logarithmicae fundamenta, ac regulae demonstrantur, astronomicaeq; supputationes ad solam fere unigarem additionem reductuntur... [Including:] Tabvla trigonom. logarithmica in qua sinus totus 10000

Bologna: Nicolai Tebaldini, 1632. Rare first edition of the first work on logarithms printed in Italy and this great mathematician’s first published work. Professor of Mathematics at Bologna, the Milanese Cavalieri introduced and popularized logarithms throughout his country within a generation of Napier’s invention of these “valuable auxiliaries to numerical calculation.” The Directorium covers the construction, uses, and applications of logarithms, “together with noteworthy developments in trigonometry and applications to astronomy” (E. Carruccio in DSB III.152). It also contains the author’s discovery of the expression for the area of a spherical triangle in terms of spherical excess.The Directorium incorporates two extensive appendices of “excellent logarithmic-trigonometric tables,” derived from those of Napier and Henry Briggs. The tables include 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 was issued posthumously in 1653.Cavalieri (1598-1647) was one of the major mathematicians of his period. After studying with Benedetto Castelli, he became a self-declared disciple of Galileo to whom he wrote at least 112 recorded letters. In a letter that helped secure for Cavalieri the chair of mathematics at Bologna, Galileo wrote glowingly of him: “few, if any, since Archimedes, have delved as far and as deep into the science of geometry.”OCLC lists NYPL, CalTech, Berkeley, Burndy, U. Michigan, Linda Hall, Cincinnati and Texas Tech.. 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 renewed; title reinforced at gutter; some quires evenly toned or browned as often with Bologna imprints from the 1630/40s, but generally a fresh copy. Excellent. (Inventory #: 3715)