Opus novum de proportionibus numerorum, motuum, ponderum, sonorum, aliarumque rerum mensurandarum ... Praeterea artis magnae, sive de regulis algebraicis liber unus ... Item, de aliza regula liber by CARDANO, Girolamo - 1570

Basel: Henricus Petri, 1570. 1st Edition. Hardcover. Very Good. 1st Edition. Hardcover. Folio - over 12 - 15" tall. Three parts in one volume. Folio (311 x 191 mm). [16], 271 [1], 163 [1], [8], 111 [1] pp. Signatures: *6, A-R6 Q8 R2 S-Y6, Z4, Aa-Tt4, Vv6, *4, AA-OO4. Separate title-page and pagination for Artis magnae and Operis perfecti sui sive algebraicae, printer's device on general title and verso of final leaf, numerous woodcut diagrams in text, pp 177 to 184 of gathering P mispaginated 171-178. Bifolium Gg2-3 in second part differs in condition, printed on different paper stock, and is possibly supplied. Bound in contemporary blind-stamped vellum (stained and spotted). Text somewhat browned throughout, occasional minor spotting, waterstain in center creating hole in first five leaves of gathering *, these restored and missing letters of printed text redrawn by black ink, some light dampstaing to upper gutter throughout and to lower corner of third part, wormtracks at lower blank margin in first part, small holes at lower margin of leaf Ll1; title page with date in Roman numbers added by hand. Provenance: erased stamp on title. ----

Adams C689; Smith p.338-9; Riccardi I 256; DSB III, p.65-66. - FIRST EDITION. Comprising Cardano's three most important scientific works: Opus novum, containing Cardano's work on the relation between the densities of air and water, the second edition of the Ars magna, his great work on algebra first published in 1545, in which he had published Tartaglia's method for solving third-degree equations and the De aliza regula, about the third-degree equation, here published for the first time.
"In his Opus novum de proportionibus, Cardano turned to problems of mechanics, with the principal aim of applying quantitative methods to the study of physics. His use of the concept of moment of a force in his study of the conditions of equilibrium in balance and his attempt to determine experimentally the relation between the densities of air and water are noteworthy" (DSB III, p.66).
"It was only in 1570, in a new edition of the Ars magna, that he added a section entitled 'De aliza regula' ... devoted to the 'irreducible case' of the cubic equation, in which Cardano's rule is extended to imaginary numbers. This was ... important for the algebraic transformations which it employed and for the presentation of the solutions of at least three important problems" (DSB III, p.65). - Visit our website to see more images!