WITH MS. WORKINGS

** ***De institutione arithmetica.*

[Augsburg, Erhard Ratdolt, 20 May 1488.]

**£42,500**

FIRST EDITION. 4to. 47 unnumbered
ff., a-e^{8} f^{8}, 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 **? 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.

K166