[84] It was published at Milan by Bernardo Caluschio, with a dedication—dated 1537—to Francesco Gaddi, a descendant of the famous family of Florence. This man was Prior of the Augustinian Canons in Milan, and a great personage, but ill fortune seems to have overtaken him in his latter days. Cardan writes (Opera, tom. i. p. 107):—"qui cum mihi amicus esset dum floreret, Rexque cognomine ob potentiam appellaretur, conjectus in carcerem, miseré vitam ibi, ne dicam crudeliter, finivit: nam per quindecim dies in profundissima gorgyne fuit, ut vivus sepeliretur."
[85] There is a reference to Osiander in De Subtilitate, p. 523. Cardan gives a full account of his relations with Osiander and Petreius in Opera, tom. i. p. 67.
[86] November 1536.
[87] Ferrari was one of Cardan's most distinguished pupils. "Ludovicus Ferrarius Bononiensis qui Mathematicas et Mediolani et in patria sua professus est, et singularis in illis eruditionis."—De Vita Propria, ch. xxxv. p. 111. There is a short memoir of Ferrari in Opera, tom. ix.
[88] Opera, tom. i. p. 66.
[89] Fra Luca's book, Summa de Arithmetica Geometria Proportioni é Proportionalita, extends as far as the solution of quadratic equations, of which only the positive roots were used. At this time letters were rarely used to express known quantities.
[90] The early writers on Algebra used numerus for the absolute or known term, res or cosa for the first power, quadratum for the second, and cubus for the third. The signs + and - first appear in the work of Stifelius, a German writer, who published a book of Arithmetic in 1544. Robert Recorde in his Whetstone of Wit seems first to have used the sign of equality =. Vieta in France first applied letters as general symbols of quantity, though the earlier algebraists used them occasionally, chiefly as abbreviations. Aristotle also used them in the Physics.—Libri. Hist. des Sciences Mathématiques. i. 104.
[91] Opera, tom. iv. p. 222.
[92] In the conclusion of the Treatise on Arithmetic, Cardan points out certain errors in the work of Fra Luca. Fra Luca was a pupil of Piero della Francesca, who was highly skilled in Geometry, and who, according to Vasari, first applied perspective to the drawing of the human form.
[93] Tartaglia, i.e. the stutterer.