76 JEROME CARDAN 



Leonardo was a trader, who had learned the art during 

 his voyages to Barbary, and his treatise and that of 

 Mahommed were the sole literature on the subject up to 

 the year 1494, when Fra Luca Pacioli da Borgo 1 brought 

 out his volume treating of Arithmetic and Algebra as 

 well. This was the first printed work on the subject. 



After the invention of printing the interest in Algebra 

 grew rapidly. From the time of Leonardo to that of 

 Fra Luca it had remained stationary. The important 

 fact that the resolution of all the cases of a problem 

 may be comprehended in a simple formula, which may 

 be obtained from the solution of one of its cases merely 

 by a change of the signs, was not known, but in 1505 

 the Scipio Ferreo alluded to by Cardan, a Bolognese 

 professor, discovered the rule for the solution of one 

 case of a compound cubic equation. This was the 

 discovery that Giovanni Colla announced when he went 

 to Milan in 1536. 



Cardan was then working hard at his Arithmetic 

 which dealt also with elementary Algebra and he was 

 naturally anxious to collect in its pages every item of 

 fresh knowledge in the sphere of mathematics which 

 might have been discovered since the publication of the 

 last treatise. The fact that Algebra as a science had 

 made such scant progress for so many years, gave to 

 this new process, about which Giovanni Colla was 

 talking, an extraordinary interest in the sight of all 

 mathematical students ; wherefore when Cardan heard 

 the report that Antonio Maria Fiore, Ferreo's pupil, 

 had been entrusted by his master with the secret of 



1 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. 



