On the Institution of Arithmetic

Another division of the even number according to perfect and imperfect numbers, beyond those that are perfect. Chap. 19.
On the generation of the perfect number. Chap. 20.
On quantity related to something. Chap. 21.
On the species of greater and lesser inequality. Chap. 22.
On the multiple ratio and its species, and their generations. Chap. 23.
On the subparticular ratio and its species, and their generations. Chap. 24.
On a certain useful principle happening to subparticulars regarding cognition. Chap. 25.
A description through which it is taught that the multiple is older than the other species of inequality. Chap. 26.
Reason and exposition of the arranged formula. Chap. 27.
On the third species of inequality which is called superpartient ratio: and concerning its species and their generations. Chap. 28.
On the multiple superparticular. Chap. 29.
On the examples of them to be found in the formula above. Chap. 30.
On the multiple superpartient. Chap. 31.
A demonstration of how every inequality has proceeded from equality. Chap. 32.

Preface in which the division of mathematics is set forth. Chapter 1.

A large ornamental drop cap 'I' features a white vine-stem or foliate pattern against a dark, hatched background, enclosed in a double-line rectangular frame.
Among all men of ancient authority who flourished with a clearer reason of mind under the leadership of Pythagoras a Greek philosopher (c. 570–495 BC) who emphasized mathematical order in the universe, it is manifest that no one arrives at the peak of perfection in the disciplines of philosophy unless that nobility of prudence is sought through a certain quadrivium the four-fold path of study: arithmetic, music, geometry, and astronomy. This will not escape the correct skill of an observer. For wisdom is the comprehension of truth regarding those things which possess an immutable substance. We say those things "are" which do not grow by intention, nor diminish by retraction, nor change by variations, but are always preserved in their own power, resting on the supports of their own nature. These are qualities, quantities, forms, magnitudes, smallnesses, equalities, relationships, acts, dispositions, places, times, and whatever is found in some way united to bodies. These things, indeed, are incorporeal by nature and flourish by the reason of immutable substance; yet, they are changed by participation in a body and pass into a mutable inconstancy through the touch of a variable thing. Therefore, since these...