Chap. VII. PIETRO PERUGINO. 173 that Leonardo should add to the imperfect method of Piero della Francesca the atmosphere in which it was wanting, and ascend gradually to the culminating point of his career in the production of the Mona Lisa, whilst Perugino should arrive at a height almost equally sur prising in the Madonna of the Certosa; 1 * the first attaining depth by calculation, the second yielding the same qua lity by an innate sense of the value of tone, and by-pe culiar knack of handling, both succeeding in that smooth ness of tints which “caused the crowd to gather round their work and think it was a marvel.’ 72 But the community of thought and of aim in Peru gino and Leonardo would not end there. Perugino is justly celebrated for his proficiency in perspective. 3 He might have learnt the elements of it from Piero della Francesca, and have sought to master its intricacies under Luca Pacioli who held the chair of mathematics at Peru gia in 1478. 4 But he would be sure to find a congenial spirit in Leonardo who was to show the students of his academy at Milan all the secrets of perspective that were known to that age. Da Vinci, and Perugino are named in one sentence by Caporali. He says, they both knew the use of “two centres of vision”; 5 and it is quite as certain of Leonardo that he taught that rule, as it is of Perugino that he put it into practise. We shall see how the latter adopted Da Vinci’s principles of composition; how both in different ways excelled in giving atmosphere to landscape. That they were together under Verrocchio, is only stated by Vasari; 5 but Vasari is confirmed by the creations of the three painters; and he speaks of them in conjunction too frequently to permit a doubt as to his conviction. Nothing can be clearer, or more true than that Perugino and Da Vinci gave the last 1 Now in the National Gallery. * Vasari, Proemio (VII. 6). 3 Vas. (VI. 3) says truly that Pe rugino “ne faceva professione par- ticolare”. 4 See Tirahoschi, Stor. della Letteratura. 5 Caporali. Vitruv. uh. sup. p. 1G. c Ih. VI. 32.