On the Institution of Arithmetic

subject to the instructions of others, nor do I bind myself by the strictest law of translation; rather, I wander a little more freely upon a foreign path, and I do not insist upon their footsteps. For I have collected with moderate brevity those things which were discussed more diffusely by Nicomachus concerning numbers. And those things which were passed over too quickly and presented a narrower entrance for understanding, I have unlocked with a moderate addition, so that sometimes we might use our own formulas and descriptions for the evidence of things. With what vigils and sweat this has been accomplished for us, the sober reader will easily recognize. Since, therefore, I was to write about arithmetic, which is the first of the four disciplines of mathematics, I saw that you alone were worthy of such a gift, and for that reason I understood that the work was all the more necessary. For even if there were room for easy pardon with you, the insecure safety still feared that very ease. For I believed that nothing should be offered for such reverence that was not elaborated by genius, perfected by study, and finally worthy of such great leisure. I do not doubt, therefore, that through your benevolence toward me, you will prune what is superfluous, fill in the gaps, correct what is wrong, and receive what is spoken well with wonderful alacrity of spirit. This matter has pushed away the sluggish delay of deliberation. For the fruits will restore to me more than I could hope for. I know, indeed, how much more studiously we value our own goods than those of others. Therefore, just as I transmit the sheaves of golden wheat and the mature branches of the vine to Ceres and Bacchus, so have I transmitted the rudiments of this new work to you. You alone shall advance the gift with paternal grace; in this way, you will consecrate the first-fruits of my labor with your most learned judgment, and—

the author will not be considered of greater merit than the approver.

The chapters of the first book begin.

Proem in which the divisions of mathematics are [discussed]. Chapter 1.
On the substance of number. Chapter 2.
Definition and division of number and the definition of even and odd. Chapter 3.
Definition of even and odd number according to Pythagoras. Chapter 4.
Another division of even and odd according to the method of the ancients. Chapter 5.
Definition of even and odd through one another. Chapter 6.
On the principality of unity. Chapter 7.
Division of even number. Chapter 8.
On the evenly-even number i.e., a number divisible by two and its result also divisible by two and its properties. Chapter 9.
On the evenly-odd number i.e., a number which divided by two leaves an odd number and its properties. Chapter 10.
On the unevenly-even number and its properties, and concerning its relationship to the evenly-even and evenly-odd. Chapter 11.
Exposition of the description pertaining to the nature of the unevenly-even. Chapter 12.
On odd number and its division. Chapter 13.
On the first prime and incomposite. Chapter 14.
On the second composite and composite. Chapter 15.
On that which is second and composite in itself, but first and incomposite in relation to another. Chapter 16.
On the procreation of the first and incomposite, and the second and composite, and those which are second and composite in relation to themselves, but first and incomposite in relation to another. Chapter 17.
On the discovery of those numbers which are second and composite in relation to themselves, but first and incomposite in relation to others. Chapter 18.