PACIOLI, LUCA. C.1445-1517.
Divina proportione Opera a tutti glingegni perspicaci e curiosi necessaria Oue ciascun studioso di Philosophia. Venice: Paganinus de Paganinis, June 1, 1509. Edited by M.A. Capella. A6 b6 C-D8 E10 a-b8 c10. , 33, [1 blank], 27 [i.e. 26] ll. And 87 plates not included in collation, comprising: proportion head, 23 alphabet plates, 3 architectural plates; LXI [i.e. LIX] shape plates; 1 plate, "Arbor proportio et proportionalitas." Title and last plate printed in red and black. Woodcut initials, illustrations and plates. Folio (290 x 195 mm). Red jansenist levant by Trautz-Bauzonnet, wide gilt dentelles, a.e.g. Title with minimal strengthening in margin, one leaf skilfully repaired near gutter with 20 x 20 mm woodcut initial supplied in facsimile (and the words on its verso), another leaf with unobtrusive repair touching initial and a few letters, one or two further very minor marginal repairs, spine extremities lightly rubbed.
First edition. The Hoe copy of this landmark work of Renaissance geometry, with illustrations by Leonardo da Vinci.
Pacioli taught at the University of Perugia and published his Somma di aritmetica before joining the court of Ludovico Sforza, Duke of Milan, around 1496, as a mathematics tutor. There, he met Leonardo da Vinci who was court painter and engineer. When the French captured Milan three years later, Pacioli and da Vinci fled south together, to Florence.
The result of their acquaintance was the Divina proportione, written while Pacioli was in Milan but not published until a decade later, in Venice. The work contains a summary of the properties of divine proportion (the "golden ratio"), based on Euclid's theorems and demonstrated with examples of polyhedra and the human head. The shapes are shown in both skeletal and solid forms. Vitruvian architecture, da Vinci's stunning Roman capitalsalso exhibiting their geometric proportionsand an Italian version of Piero della Francesca's De quinque corporibus regularibus make up the remainder of the work.
Tipped onto a binder's blank is a leaf of autograph notes by Theodore Low de Vinne [1828-1914], printer, typographer, and fellow founding member of the Grolier Club with Hoe. De Vinne critiques da Vinci's capitals: "lower half stands out too far ... unnecessarily wide ... lower half deficient in serif...."
Provenance: morocco book label of Robert Hoe [1839-1909]; his sale, Anderson Auction Company, New York, November 20, 1912, lot 2476, sold for $75.