BOETHIUS, Anicius Manlius Torquatus Severinus (c.480-524/525). De institutione arithmetica. Augsburg: Erhard Ratdolt, 20 May 1488.
Chancery 4 (199 x 142mm). Collation: a-f8 (a1 title, a2r Boethius's dedication to his father-in-law and teacher, Q. Aurelius Memmius Symmachus, a2v chapter index, a3r text, f8r colophon, f8v blank). 48 leaves. 40 lines, double column. Type: 4:76G (text), 9:130G (title). Full-page woodcut diagram, numerous woodcut text diagrams and tables, woodcut white vine initials in several sizes. (Occasional light marginal spotting, light dampstain at extreme margins.) Modern brown morocco panelled in blind in an antique style, red edges. Provenance: a few early annotations and underlining.
FIRST EDITION of the basic mathematical text of the middle ages. De institutione arithmetica was conceived as one of four treatises, each devoted to a branch of the 'quadrivium', a term coined by Boethius and first used in this work, comprising arithmetic, music, geometry and astronomy. Together with the trivium (grammar, rhetoric, dialectic), they form the seven liberal arts. Of Boethius's treatises on the quadrivium only his works on arithmetic and music survive; a work on geometry is spurious.
One of Boethius's aims in writing his works on the quadrivium was to make available to the Latin world the great works of Greek learning. De institutione arithmetica is in essence an expanded translation of the work of the Alexandrine Nicomachus of Gerasa, whose Arithmetics was as celebrated as Euclid's Geometry. De institutione arithmetica treats of the properties of numbers and sets forth practical applications. It became the basic mathematical textbook of the middle ages, explaining arithmetical theory: 'prime and composite numbers, proportionality, numeri figurati (linear, triangular, etc.; pryamidal and other solid numbers), and ten different kinds of medietates (arithmetical, geometrical, harmonic, counterharmonic, etc.)' (DSB 2, p.233). De arithmetica is imbued with the neo-Pythagorean theory of number as the divine essence of the world and was embraced in the Renaissance for its view of unity as the constitutive element of plurality. The humanist Jacques Lefvre d'taples wrote an epitome of the Arithmetica and Poliziano praised Boethius, writing, 'Who is more accurate than Boethius in dialectic, or subtler in mathematics, or richer in philosophy, or more sublime in theology?' (Opera omnia, Misc., Basel: 1533, p.225; cf. M. Gibson, ed., Boethius, Oxford: 1981, esp. J. Caldwell 'The De institutione arithmetica and the De institutione musica' and A. White 'Boethius in the medieval quadrivium'). Goff B-828; HC *3426; BMC II, 381 (IA. 6659-60); BSB B-592; GW 4586; Klebs 191.1; Riccardi I, 139; Smith, Rara Arith. p.25; Schreiber 3511.