In Geometria Male Restaurata ab authore A.S.L. rimae detectae a Petro Paolo Caravagio

Milan: Ludovici Montiae, 1650. Soft cover. Very Good. 4to - over 9¾ - 12" tall. 4to. [23 x 16.5 cm], (4) ff., 79 pp., 1 folded plate. Bound in contemporary limp vellum; faint waterstain at upper corner of first 8 leaves, small inkstain on one preliminary leaf; otherwise excellent.Extremely rare first and only edition of this polemical volume of Italian geometry, responding to recent appropriations of the work of great French mathematician François Viète. In 1644 and 1648, respectively, the Venetian amateur astronomer Antonio Santini had published Supplementi Francisci Vietae and Inclinationum Appendix, which utilized Viète's algebra to solve the geometric mean, as well as such celebrated problems as the multisection of the angle and duplication of the cube. In this fierce attack on the 'bad renewal' of Viète's work, Caravagio presents point-by-point replies to the supposed 'solutions' of Santini, which he buttresses with his own solutions to solvable problems. The volume also contains a large folding engraved plate with 54 geometrical diagrams.Antonio Santini (1577-1661) is best known for his early corroboration of Galileo regarding the observation of Jupiter's moons. In June 1610, three months after the publication of Siderius Nuncius, Santini wrote to Galileo announcing that he had confirmed the presence of satellites around Jupiter. Renn speculates that Santini might have also conducted observations with Galileo in Padua or Venice, where he then lived.Petro Paolo Caravagio (1617-1688) was a Milanese mathematician.OCLC: NYPL and Michigan. *Riccardi I.242-3; Renn, Galileo in Context, p. 283