BORGHI, Pietro

Qui comenza la nobel opera de arithmethica ne la qual se tracta tute cosse amercantia pertinente facta...

      [colophon:] Venice, Erhard Ratdolt, 2 August, 1484 4to (185 x 145 mm), ff [1] 2-116 [1], with woodcut initials;annotations throughout in a later hand, coloured pencil numbering on a few leaves, some minor worming in b lank margins and gutter, some early repairs and reinforcement at gutter, not affecting text, a very fresh, honest copy, eighteenth-century blue paper wrappers, with paper label on spine, spine splitting, embossed stamps of 'Giosue Pagani Ragioniere' on several leaves, in a morocco-backed box. £60,000 First edition, rare, of the second commercial arithmetic published in Italy and 'the first great commercial arithmetic' (Smith). Borghi's text covers 'operations with integers, fractions, compound numbers, mercantile rules, currency, commercial problems, barter, and matters relative to partnership' (Stillwell). It was a staple of the Abbaccho classroom of fifteenth-century Italy, with its chapters on currency exchange and barter, providing the computational skills on which the trading and financial empires of all the Italian city-states depended. In his Commercial Revolution and the Beginnings of Western Mathematics, Van Egmond has argued for a close causal link between the techniques described in mercantile arithmetics and the historical advent of capitalism. (See also the similar line pursued by Frank J. Swetz, Capitalism and Arithmetic. The New Math of the 15th century.) 'This work is more elaborate than the Treviso arithmetic, and had a far greater influence on education. More than any other book it set a standard for the arithmetics of the sixteenth century, and none of the early textbooks deserves more careful study. Borghi first treats of notation, carrying his numbers as far as "numero de million de million de million" and making no mention whatever of the Roman numerals. In the same spirit he eliminates all of the medieval theory of numbers, asserting that he does this because he is preparing a practical book for the use of merchants' (Smith). 'The boys (there is no record of any girls attending these schools) began their training in the abacus schools around the age of 10 or 11, usually immediately after two years in an elementary grammar school where they learned the basic skills of reading and writing. They generally stayed in the abacus schools for about two years and were taught the basic principles of arithmetic and practical mathematics: how to write the numbers, how to multiply and divide, how to deal with fractions, and how to solve the basic mathematical problems. Sections of the course were also devoted to understanding the complex Florentine monetary system. The school even followed a familiar routine of lessons, exercises, recitations and even an occasional holiday party. It appears that nearly all the educated men of the Renaissance gained their basic understanding of mathematics in schools such as these, including, for example, such notables as Leonardo da Vinci and Niccoló Macchiavelli. When grouped with the earlier schools of reading and writing, higher schools of Latin grammar, and the educational apex of the university, it is apparent that the abacus schools were an integral part of an educational system' (van Egmond, pp 8-9). BMC V 289; Goff B1034 (Burndy Library (Boston), Chicago, Columbia, Huntington, Lehigh, Morgan, Yale) Smith, Rara pp 19-20 and 'The first great commercial arithmetic' Isis 8 (1926) pp 41-49; Stillwell 151; Van Egmond, p 293; facsimile, introduction and bibliography by Kurt Elfering (Munich 1964)