The Arithmetica is not an original work and does not present itself as one: it is Boethius's Latin adaptation of the Introductio arithmetica of Nicomachus of Gerasa, made in the early sixth century. What matters for this volume is what the adaptation carries with it. Nicomachus is a Neopythagorean, and the doctrine that number is prior to and constitutive of the things numbered enters the Latin West through this book, in this form, and reaches the Middle Ages with no competing arithmetic to correct it. When a twelfth-century master says that music is a species of number he is not reasoning independently to a Pythagorean conclusion; he is reading Boethius reading Nicomachus. [C] The dependence is not concealed — the work names its source — but its consequence is rarely stated: the Latin tradition inherited an arithmetic already committed to a metaphysics.
Boethius, De institutione arithmetica libri duo · De institutione musica libri quinque, ed. Gottfried Friedlein (Leipzig: Teubner, 1867) — read from page images, with the critical apparatus separated from the text
The original is shown on its own: no English is held for this issue yet.
INST. ARITHM. I, 32. (1l quadripartiens statim quantitas procreabitur, ut est ea forma, quam subpositam vides. XXV. XX. | XVI («— XXV. XLV. LXXAXIL Restat, quemadmodum ex superparticularibus et super- 5 partientibus multiplices superparticulares vel multiplices superpartientes nascantur ostendere, quorum binas tan- tum faciam descriptiones. Namque si rectum et non con- versum sesquallerum ponimus, duplex superparticularis excrescit. Sit enim hoc modo: 10 ] III. VI. VIII. Ponatur secundum superiorem modum primo primus ae- qualis, id est -IIII-, secundus primo et secundo, id est -X., tertius primo, duobus secundis et tertio aequalis, id est XXV. IE. Iti. VI. VHII. IIl. X. XXV. | Atque haec quidem duplex sesqualtera summa pro- ducta est; si vero sesquitertium non conversum pona- mus duplex sesquitertius invenitur, ut subiecta descriptio 20 docet: VIIII. XII. XVI. VIIIT. XXI — XLVIII. | AÀt vero si ad superparlientes animum convertamus eos- que ordinatim secundum superiora praecepta disponamus, 25 multiplices superpartientes ordinatim progenitos repperie- mus. Disponatur enim superpartientis haec formula: VIII. XV. XXV.
This issue carries a scholarly apparatus: 422 notes on the editor’s variant readings. Scholar · $29 a month, by application — see what it adds →