The preface to Boethius’ Institutio arithmetica implies an intention to write introductions to all four mathematical disciplines. Declarations of intent are not always fulfilled. At one time Augustine intended to write treatises on all seven liberal arts, but he completed only his projects on grammar, rhetoric, dialectic, something on geometry, and the six well­ known books on music. His Grammar was already lost from his own library at Hippo before he came to write his Retractations (i, 6) near the end of his life. A comparable misfortune seems early to have struck Boethius’ writings on geometry and, especially, astronomy.
Nothing by Boethius on astronomy has been transmitted by the medieval manuscript tradition, nor is any such work mentioned by Cassiodorus in his Institutiones. In the tenth century Gerbert of Aurillac, to be Pope Sylvester II from 999 to his death in 1003, speaks of Boethius as author of eight books on astronomy (astrologia) which he had seen in a manuscript at Bobbio. But the work (if really that by Boethius) failed to find copyists. Students preferred to find their astronomy in Macrobius’ commentary on Cicero’s Dream of Scipio or from Martianus Capella or from Cassiodorus. However, one likely model for Boethius’ treatise is the summary of Ptolemy’s Mathematike Syntaxis (the `Almagest’) composed by Proclus, a work which is still extant, though not edited since L. Allatius’ edition (Leyden, 1635). If Boethius’ work followed this precedent, he will have taken the earth as the static centre of a spherical cosmos, the Ptolemaic system assumed in his commentary on the Categories (212BC), and will have explained how the heavenly bodies move in relation to it; the solar year and its relation to the lunar months; the design and use of the astrolabe (an instrument in whose use Ammonius’ high skill is reported by Simplicius, In de Caelo, p. 462, 20); eclipses, fixed stars, the precession of the equinoxes; finally the courses of the planets. How far he comprehended Ptolemy’s trigonometry we cannot guess, and it is idle to speculate further. The allusion to Ptolemy’s astronomical geography in the Consolation of Philosophy (ii, 7, 4) as a work specially studied by Boethius is no doubt to be interpreted as an allusion to Boethius’ treatise on the subject.

Henry Chadwick. Boetius. ‘The Consolations of Music, Logic, Theology, and Philosphy’, II – Liberal Arts in the Collapse of Culture. Geometry and Astronomy, p. 102. Clarendon Paperbacks, 1981.