FRIENDS. 131 



letter 1 . Gaddi, who, as we have seen, fell among princes, 

 ten years afterwards died in a dungeon, wretchedly. 



Ludovico Madio was another friend to whom Cardan 

 was introduced by the warm-hearted Archinto. Of 

 Madio we know only that he was kind, and that the 

 young struggler obtained from him ready help in times of 

 need. Girolamo Guerrini, a jeweller, was at the same 

 time an associate from whom Jerome obtained much 

 curious information, and from whose experience he was 

 able to enrich some of his books 2 . 



The works upon which Jerome was occupied in the 

 months immediately following his return to Milan, were 3 

 a volume suggested by Sacrobustus upon Spheres, of 

 which he wrote nine or ten books; a little work on 

 Circles ; three dissertations founded on the first and 

 seventh books of Ptolemy's Geography ; and one on the 

 elements of Euclid, which grew in after-years till it con- 

 tained three books, then was enlarged to seven, then to 

 nine, then to fifteen, when it contained more than forty 

 new propositions. 



Very soon after his appointment as a lecturer Jerome 

 had taken a house, and received his mother as a portion 

 of his family. Since Clara had been hitherto depending 



1 The letter is included in his published works. Cardan relates the 

 fate of his friend in the last of the three books De Libris Propriis. 

 Opera, Tom. i. p. 107. 



- De Vit. Prop. p. 69. 



3 De Sapientia, &c. p. 424. 



K2 



