Arithmetic Geometry

Ch. i. What number is.
Ch. ii. On the definition of number.
Ch. iii. On the division of number into even and odd.
Ch. iiii. On the description of even and odd through various means.
Ch. v. On the species of even number.
Ch. vi. On the evenly even.
Ch. vii. On the evenly odd.
Ch. viii. On the oddly even.
Ch. ix. On those that relate to one another in another way: and on abundant, deficient, and perfect number.
Ch. x. On inequality: and its primary species.
Ch. xi. On the definition of the multiple: and its species and descriptions.
Ch. xii. On the superparticular: and its species and descriptions.
Ch. xiii. On the superpartient: and its species and descriptions.
Ch. iiii. On the multiple superparticular: and its species and descriptions.
Ch. xv. On the multiple superpartient: and its species and descriptions.
Ch. xvi. On those things that relate to one another in part of another part.
Ch. xvii. On those things found in relation to one another by difference.
Ch. xviii. On the theory of multiplication.
Ch. xix. On the parts of a number.
Ch. xx. On even and odd numbers.
Ch. xxi. On the species of inequality: how they proceed from equality.
Ch. xxii. Example of the first species of inequality.
Ch. xxiii. On the second species of inequality.
Ch. iiii. On the third species of inequality.
Ch. xxv. On the fourth species of inequality.
Ch. xxvi. On the fifth species of inequality.
Ch. xxvii. On the conversion of the species of inequality to equality.
Ch. xxviii. On multiplications to infinity.

and Music of Boethius

Among all the ancient authors who have written on the mathematical disciplines, it is undisputed that the most illustrious Boethius appears to hold the first place. He expressed not only the subtlety of the Greeks but also the eloquence of the Latins in these books. For when certain Greeks, such as Nicomachus and others, had written about arithmetic, music, and geometry, Boethius translated these books into the Latin language in such a way that he was not merely a translator, but as if he were an author who added much of his own. It is fitting to briefly note here what is contained in these books. In Arithmetic, therefore, he first treats of the essence of number and its definitions, then of the species of number, and of those that relate to one another. Also, of abundant, deficient, and perfect numbers. Afterward, of inequality and its species, and how they proceed from equality. Then, of proportions and of means in music/mathematics, a "mean" is an intermediate value between two quantities. In Music, however, he treats of the differences of sounds and of their proportions. Then, of the genera of melodies. Also, of the monochord a one-stringed musical instrument used for measurement and its division. In Geometry, moreover, he treats of geometric principles, of lines, of plane figures, and of solids. Also, of measures and weights. He teaches all these things so clearly and openly that nothing can be desired in them. But because this art is not only useful but also necessary for understanding other sciences, especially theology, it is therefore deservedly placed in the first position in this work. For as Isidore says: "Without these disciplines, no one can attain the perfection of wisdom." Whence we also have decided, not without cause, that this Boethius must be placed at the beginning of this volume, so that he who desires to tend toward higher things may begin from these, as if from the foundations.