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Italian unworthy of a Milanese, to say nothing of a Tuscan. spite of his mediocrity he was, however, superior to Leonardo in one point he gave the results of his labours to the world, while the greater master jealously guarded his from the knowledge of his contemporaries.

The fact that Pacioli never refers to Leonardo in his preface, while he mentions a crowd of other living artists,1 justifies us in supposing that his acquaintance with the great painter did not begin till later. It was not, in

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of

fact, until 1496 that he
entered the service
the Sforzi. Lodovico
appointed him professor
of arithmetic and geo-
metry in the University
of Pavia. His pay was
modest enough, for while
a professor of civil law
enjoyed an annual salary
of 3,600 lire, he received
no more than 310. From
1496 to 1499 Pacioli
worked side by side with
Leonardo, to whom he
devotes a generous eulo-

gium in his De Divina
Proportione. After the

fall of Lodovico, Pacioli

GROTESQUE HEADS.

(Windsor Library.)

quitted Milan at the same time as Leonardo.

In 1500 we find him

1 I reprinted this preface in Les Archives des Arts, p. 34 et seq. In one of those now incomprehensible memoranda with which he filled his notebooks, Leonardo writes, "Learn the multiplication of roots from Maestro Luca." Richter, vol. ii., p. 433.

2 Finished in December, 1497. The dedication is dated February, 1498. The work was not published until 1509. The Divina Proportione itself is followed by "Libellus in tres partiales tractatus divisus quinque corporum regularium et dependentium, activæ perscrutationis, D. Petro Soderino principi perpetuo populi florentini, a M. Luca Paciolo Burgense Minoritano particularitur dicatus. Feliciter incipit." (27 folios.) Next come

K K

living once more at Perugia, and afterwards with da Vinci at Florence.1 Here, in 1509, he dedicated to the Gonfaloniere Soderini his Divina Proportione, which had previously borne a dedication to Il Moro. In the meantime, between 1500 and 1505,2 he had been teaching at Pisa, and had, in 1508, put in an appearance at Venice. In 1510 we find him again in Perugia, after which all trace of him

is lost.

The following headings will give some idea of the contents of this strange compilation. Perspective, like music, and for the same reason, forms a branch of mathematics (book 1, chapter iii). How to divide a dimension, according to the rules of proportion, into a medium part and two extreme parts (chapter viii). How the hexagon and decagon form between them a dimension susceptible of division according to the rules of proportion (chapter xvi).3

I must make some reference to the figures inserted in the text of the Divina Proportione. Setting aside the separate plates, they are all geometrical diagrams, except those of fol. 25, v°, a man's head in profile, turned to the left, and geometrically divided. We have already said something about Leonardo's share in the production of these engravings.

We know from the evidence of Geoffroy Tory, brought to light by the Marchese d'Adda and M. Dehio, that the initials in Pacioli's the plates, printed only on one side of the leaf. The first, inscribed "Divina Proportio," is the male head described below; next come twenty-three plates numbered from A to Y ; and finally three plates, the first columns, the second entablatures, the third "Porta templi domini dicta speciosa. Hierosolomis." There are besides some geometrical diagrams. Note that the majority of the initials contain those interlaced ornaments so dear to Leonardo.

1 De Architecturâ, ed. Winterberg, p. 144.-Mariotti, Lettere pittoriche perugine,

p. 127.

2 Fabroni, Historia Academia Pisanæ, vol. i., p. 392.

3 A German savant, Herr Winterberg, has had the courage to translate this chaotic work, and to expound its fundamental law, the Golden Section, a magic formula, which, it is asserted, enables the student to establish the value of any work of art by means of three propositions! This was an honour certainly undreamt of by the humble Pacioli !

4 Repertorium für Kunstwissenschaft, 1881, p. 269-279.-" Frère Lucas Pacioli de Bourg sainct Sepulchre, de l'ordre des frères mineurs et théologien, qui a faict en vulgar italien un libre intitulé Divina Proportione, et qui a volu figurer lesdictes lettres Attiques, n'en a point aussi parlé ne baillé raison et je ne m'en ébahis point, car j'ay entendu par aulcuns Italiens qu'il a desrobé sesdictes lettres, et prinses de feu messire

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