Pacioli, Luca | A foundational text on "Divine Proportion" illustrated with designs after Da Vinci

Pacioli, Luca

Divina proportione. Opera a tutti glingegni perspicaci e curiosi necessaria. Ove ciascun studioso de philosophia: prospective picture sculptura: architectura: musica: e alter mathematice. Venice: Alessandro and Paganino de’ Paganini, June 1509

4to (288 x203 mm). Title printed in red and black with red woodcut initial letter, blank E10 present, 87 woodcut plates including 59 woodcuts after designs by Da Vinci, diagrams in margin of text, white-on-black woodcut initials throughout; minor soiling and effaced old signature to title with two small repairs, minor worming along inner margin of E3-a4, some faint soiling and occasional stray spot, but generally a handsome, crisp example. Eighteenth-century vellum; top edge rubbed.

First edition of a foundational text on "Divine Proportion" illustrated with designs after Da Vinci and a key work in the study of the polymath. 

Pacioli, a native of Borgo Sansepolcro, entered the Franciscan order sometime between 1470 and 1476, and taught mathematics first as a tutor to a merchant's family, and then as a lecturer at the University of Perugia, during which time he published his Somma di aritmetica (Venice 1494).

The Divina proportione is a compendium of contemporary mathematical ideas organized in three parts. The first, a discussion of “divine proportion” with a focus on the proportion we now call the “golden ratio,” in seventy-one chapters, was completed in 1498 while Pacioli was employed in Milan as a public lecturer in mathematics in the Scuole Palatine; the printed edition retains the dedication to Ludovico Sforza of the two surviving manuscripts (Geneva, Bibliothèque de l’Université, Ms 210; Milan, Biblioteca Ambrosiana, Ms 170). The second part is a “Trattato dell’architettura,” in twenty brief chapters, treating the proportions of Vitruvian architecture and the art of perspective; it is dedicated by Pacioli to his students in Sansepolcro. The third part is an Italian translation of Piero della Francesca’s unpublished work on the five regular solids, the Libellus de quinque corporibus regularibus; it is dedicated to the Florentine gonfaloniere Piero Soderini, who receives the dedication of the entire book (1 May 1509), and presumably supported its publication.

In the text, Pacioli identifies his close friend Leonardo da Vinci as the artist who drew the regular and semi-regular polyhedra (although sixty appear in the two presentation manuscripts, one is omitted in the printed book). The name of Leonardo da Vinci is mentioned repeatedly in various passages of this book, and his Last Supper, painted for Ludovico at Milan, is mentioned particularly in Chapter XIII. Pacioli does not identify who drafted the equally celebrated series of twenty-three Roman capital letters, each measuring about 95 mm and printed on separate pages: several critics conjecture they also were drawn by Leonardo, others propose the painter Andrea Mantegna, who knew Pacioli and who had worked with Felice Feliciano on his geometrically constructed alphabet; and some promote Leon Battista Alberti. A woodcut profile of a netted head (f. 25v) is believed to be copied from a manuscript of Piero della Francesca’s. At the end is a woodcut genealogical tree of proportion and proportionality, copied from the block in Pacioli's 1494 Somma di arithmetica. All the illustrations presumably were cut by an artisan working for the Paganini.

Divina proportion was at last published in Venice in 1509, the same year in which his edition of Euclid appeared, with the addition of a short tract on architecture and an Italian version of Piero della Francesca's De quinque corporibus regularibus.

Only edition, with illustrations cut from designs by Leonardo da Vinci.

REFERENCES:

Censimento 16 CNCE 28200; Riccardi ii, 228; Smith p. 87; Mortimer, Harvard Italian 346; Sander 5365/6; Essling 1645; Dyson Perrins, Italian book-illustrations and early printing 190

PROVENANCE: 

Gian Giacomo Trivulzio (bookplate, book-label, and three other small stamps, "Duplicate" stamp at end) — Ladislao Reti (noted Leonardo da Vinci scholar, bookplate) — Giancarlo Beltrame (his sale, Christie's London, 13 July 2016, lot 80, £194,500)