[TAGLIENTE, Giovanni Antonio and Girolamo.]

Remarkably good copy of this very scarce edition of a most important treatise on arithmetic. There were few textbooks as influential as this in shaping the subsequent teaching of arithmetic (Smith, Rara , p. 114). The brothers Giovanni Antonio (c.1460-1524) and Girolamo (fl. late C15-early C16) Tagliente were Venetian mathematicians; the former was also a printer known for the production of very successful manuals on calligraphy, embroidery patterns, methods for learning reading and accounting. First published in 1515 and reprinted at least twenty times in the course of the C16, Libro was addressed to Venetians wishing to learn the virtu della Arithmetica and the arte de la Geometria in order to practice the arte de la mercantia . After a discussion of notation and the ancient practice of counting with finger symbols, illustrated with woodcut tables, it proceeds to the four mathematical operations (addition, subtraction, division, multiplication) discussing additionally the proof of seven, fractions and the rule of three. Specific applications to problems are presented in narrative form and illustrated with woodcuts of everyday life situations: e.g., a Jewish moneylender s interest for a given time and a given sum, the differing speed of a boat heading to Cyprus using 40 or 36 oars and gain from the sale of a variety of goods. A second section explains how to use geometry to measure allotments or buildings, whilst the final pages present a conversion table for Venetian ducats in relation to Italian and foreign currencies. A fascinating work illuminating arithmetical education for the Venetian mercantile classes at the commercial apex of the Serenissima.