With this vantage ground beneath his feet Cardan raised the study of Algebra to a point it had never reached before, and climbed himself to a height of fame to which Medicine had not yet brought him. His name as a mathematician was known throughout Europe, and the success of his book was remarkable. In the _De Libris Propriis_ there is a passage which indicates that he himself was not unconscious of the renown he had won, or disposed to underrate the value of his contribution to mathematical science. "And even if I were to claim this art (Algebra) as my own invention, I should perhaps be speaking only the truth, though Nicomachus, Ptolemaeus, Paciolus, Boetius, have written much thereon. For men like these never came near to discover one-hundredth part of the things discovered by me. But with regard to this matter--as with divers others--I leave judgment to be given by those who shall come after me. Nevertheless I am constrained to call this work of mine a perfect one, seeing that it well-nigh transcends the bounds of human perception."[111] FOOTNOTES: [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, misere 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 e 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.