The first mathematical encyclopaedia of the Renaissance. Second edition of the first mathematical encyclopaedia of the Renaissance, 'the first great general work on mathematics printed' (Smith, Rara arithmetica, p56), and the first printing of any of the works of the great thirteenth-century mathematician Leonardo of Pisa, called Fibonacci (c. 1175-c. 1250), and of Pacioli's friend, the brilliant mathematician and artist Piero della Francesca (1416-92).

The Summa, the writing of which had been completed by 1487, is divided into two volumes, the first dealing with arithmetic and algebra, the second with geometry. The first volume is divided into nine chapters (distinctiones): chapters 1 to 7 on arithmetic (222 pages), chapter 8 on algebra (78 pages), and chapter 9 on business (150 pages). The second volume comprises chapters 1-8 (151 pages), on geometry; it has separate signatures and foliation and a caption title. There is a brief colophon at the end of part 1 referring to the full colophon at the end of part 2.

The first part of the Summa is the first printed comprehensive treatment of algebra and arithmetic, based largely on Fibonacci's 1202 Liber Abaci which famously introduced Arabic numbers to the West, and which was itself in part a translation of the treatises on algebra and arithmetic of the Persian mathematician and astronomer Muhammad ibn Mūsā al-Khwārizmī (c. 780-c. 850) (the word algorithm derives from his name). The second part, on geometry, is based on Fibonacci's Practica Geometriae, but includes at the end a section on stereometric geometry and regular solids taken from the Trattato d'abaco of Piero della Francesca.

This is the first printed text to set out the method of double-entry bookkeeping, the single most influential work in European accounting history, which earned Pacioli the title 'Father of Accounting'; it has been called 'the most influential work in the history of capitalism'. De Computis introduces the 'rule of 72' for predicting an investment's future value, anticipating the development of the logarithm by more than a century.

The Summa is also a work central to the development of Leonardo da Vinci (1452-1519). Pacioli came to Milan where he held the chair of mathematics from 1496 to 1499, during which years he lodged with Leonardo, and taught him mathematics. Leonardo owned a copy of the first edition of the Summa and refers to it in his notebooks.

Second edition; 2 vols in one, folio (30.8 x 20.8 cm); title printed in red and black within a woodcut strapwork border, white on black woodcut initials (including a portrait of the author on A1), woodcut diagrams and illustrations throughout, L2r with full-page woodcut diagram with red printing, frontispiece with partially erased annotations, small tear to right-hand margin on frontispiece and a stain of acid ink puncturing the paper at the bottom of the frame, E4v - E6r with extensive marginal annotations, text underlined and annotated throughout (not affecting legibility of text), S3 with obvious oxidation spots that do not disturb the text, evidence of wormholes, occasional creasing of pages, marginal spotting, very occasional marginal dampstains; 18th-century full vellum, red title piece on spine with gilt border and lettering, warping to upper board, wormholes on boards and spine, some soiling to boards, corners slightly rubbed; [8], [1], 2-224; 76.

Adams P 8; Edit16 28198; Goldsmiths'-Kress 15; Honeyman 2380; Mortimer, Harvard Italian 347; Riccardi ii, 227/228; Sander 5367; Tomash & Williams P2; USTC 846002.