De institutione arithmetica.

[Augsburg, Erhard Ratdolt, 20 May 1488.]


FIRST EDITION. 4to. 47 unnumbered ff., a-e8 f8, double column. Small woodcut tables and geometrical diagrams throughout, white-on-black decorated initials. Minimal marginal spotting, 7 ms. pages in a near contemporary hand with scientific diagrams and explanatory text in black-brown ink, bound at end, slightly foxed at margins. A very fine, clean, well-margined copy in modern crushed crimson morocco, raised bands, gilt lettered spine, bookplate of Erwin Tomash to front pastedown. In modern slip case.

A very fine, clean, well-margined copy of the first edition of this major work in the history of arithmetic. One of the most influential early Christian philosophers, Severinus Boethius (477-524AD) was a Roman politician at service of Theodoric, King of the Ostrogoths. He probably studied in Athens where he became fluent in Greek and acquainted with important Hellenic philosophers. Imprisoned by Theodoric upon charges of high treason, he famously penned in jail his ‘De Consolatione philosophiae’, a milestone of Western thought. ‘Arithmetica’ was one of his earliest works—an adaptation of the introduction to arithmetic written in Greek by the first-century mathematician Nicomachus of Gerasa. Like Nicomachus, Boethius perceived mathematics and philosophy (imbued with Platonism) as like-minded disciplines interested in abstract ideas and principles. In Boethius’s introduction, arithmetic is introduced as one of the disciplines in the ‘quadrivium’ (with geometry, music and astronomy), a term attributed to Boethius himself which would become the standard continuation of the traditional ‘trivium’ in faculties of arts. ‘Arithmetica’ discusses the substance of numbers, their subdivisions into odd and even, following Pythagoras, and the latter’s subdivisions, positive integers (‘compositi’), perfect numbers (‘perfecti’) as well as ‘an elaborate theory of ratios and […] figurate numbers, such as the triangular, square, pentagonal, and cubic’ (Smith-de Morgan, p. 28). The mathematical terms Latinized by Boethius were current for many centuries and the work was ‘the standard reference book for arithmetic in the West for a millennium’ (Guillaumin, ‘Boethius’s “De Institutione”’, 161). The ms. annotations show geometrical diagrams for calculations of the ‘true position’ of individual planets within the eighth sphere. They appear to be written in the form of exercises, each beginning with ‘ponas’ followed by data allowing the calculation of ellipsis and triangulation: e.g., ‘place in 𝛽 the body of the Sun in that month as shown in the figure of the eighth sphere’, which suggests the figure and its main reference points were provided probably by a teacher. A very fine, fresh copy of this fundamental work.

ISTC ib00828000; Riccardi I/1, 139: ‘prima e rara’; Smith-de Morgan, pp. 25-28; Goff B828. J.-Y. Guillaumin, ‘Boethius’s De Institutione’, in A Companion to Boethius in the Middle Ages, ed. N.H. Kaylor et al. (Leiden, 2012), 135-62.

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