About this Item
First edition, rare, of Borelli's "well received work" (DSB) - not merely a restoration but a thoroughgoing reformulation of Euclid's Elements. "The mathematical work of Giovanni Alfonso Borelli (1608-1679) was entirely devoted to the study and interpretation of the Greek classics. His most important mathematical book is the Euclides restitutus ('Euclid Restored') from 1658, in which Borelli offered a complete rewriting of Euclid's Elements . . . Borelli's Euclides is a masterwork in the foundations of mathematics, and arguably the most important treatise on the subject in the seventeenth century. In it, Borelli reformulated most of Euclid's definitions, modified and expanded the axioms, transformed a great many demonstrations in the Elements, and made in depth changes to the deductive structure of the classical treatise. Euclid's Elements had already been modified many times over the centuries and the text had always remained partially plastic and changeable. Through all these changes, however, the Elements had remained a classical text to which editors had added scholia and local amendments. In times closer to Borelli, such modifications had become bolder: Jesuits and Ramists had abridged the text for students, Aristotelians had reshaped some proofs into syllogistic chains, Herigone and Barrow had formalized the Elements with new symbolisms. None of them, however, had changed the mathematics of Euclid: the ideas behind the demonstrations and their deductive order had remained the same. By contrast, Borelli's book revolutionized the mathematical core of Euclid's work to such an extent that it could be doubted whether it was still Euclid's . . . Borelli had long surpassed Galileo and his contemporaries in both classicism and reformation. He extended the critical approach from the foundations of the theory of proportions to the whole of mathematics, and thus rewrote all of the Elements . . . Book V of Borelli's Euclides mixes together Euclid's theorems belonging to the second, fourth and thirteenth books of the Elements, adding something from the first, sixth and twelfth books. The order of the propositions is generally quite different from Euclid's sequences of the same books . . . These theorems are also interspersed with results from Archimedes, Ptolemy and Pappus. To hold together such a deductive sequence, Borelli also demonstrates therein ten new theorems. As a bonus, Borelli offered a wholly new proof of the important Elements XII.2 (circles are to each other as the squares of the diameters) avoiding the method of exhaustion, which Borelli found hopelessly obscure given its reference to the infinite" (Dr Risi, Euclid Upturned. Borelli on the Foundations of Geometry, Physis 58, 2022). Borelli (1608-79), a Neapolitan, spent the years 1656 to 1667 at the University of Pisa in the chair of mathematics, a period coinciding with the life of the Florentine Accademia del Cimento, of which Borelli was a founder member. In 1665 he established an observatory on the hill of San Miniato in Florence. RBH lists only three copies since 1961. Riccardi I, 157 ('raro'); Steck IV.50. 4to (218 x 153 mm), pp. [8], xxx, [2], 456, woodcut diagrams in text, woodcut initials (light browning and occasional light marginal dampstaining). Later limp vellum. A large copy with the deckle showing on many leaves.
Seller Inventory # ABE-1753266629143
Contact seller
Report this item
