On the Principles of Arithmetic and On the Principles of Music

PRINCIPLES OF ARITHMETIC, BOOK I, PREFACE. 5

I have collected these matters with brevity, and those points which, being passed over too quickly, offered too narrow an entrance to the understanding, I have opened up with a moderate addition, so that eventually, for the sake of clarity, we might even use our own formulas and diagrams. How much sleeplessness and sweat this effort has cost us, the sober reader will easily recognize. Therefore, as I was writing about arithmetic—which is the first of the four disciplines of mathematics Boethius refers to the Quadrivium: arithmetic, music, geometry, and astronomy. He argues arithmetic is the foundation for the others.—you alone seemed worthy of such a gift, and I understood all the more that the work must be free of error. For although there was room for easy forgiveness from you, nevertheless a suspicious sense of security sometimes dreaded that very ease. For I judged that nothing ought to be offered to such great reverence which did not seem elaborated by genius, perfected by study, and finally worthy of such great leisure.

Therefore, I do not doubt that, out of your kindness toward me, you will cut back the superfluous, fill the gaps, correct the errors, and receive what is aptly said with a wonderful eagerness of spirit. This reality drove away the sluggish delay of my planning. For these works, if they please you, will return excessive fruits to me. Indeed, I know how much more zealously we love our own good works than those of others. Justly, therefore, as if offering golden stalks to Ceres The Roman goddess of agriculture and grain. and ripe vine-branches to Bacchus The Roman god of wine and fertility., so I have sent these first fruits of a new work to you. May you only promote our gift with your fatherly grace. Thus you will consecrate the first fruits of my labor with your most learned judgment, and the author shall be deemed to have no greater merit than the one who approved the work.

I. Preface, in which is the division of mathematics.
II. On the substance of number.

The following notes represent variations found in different historical manuscripts of this text, labeled a, b, c, etc., by the 19th-century editor Gottfried Friedlein.

1—3 which... I have opened up: this phrase is in the margin of manuscript c following a correction. 1 more quickly: manuscript a uses a different spelling for "velocius." 3 eventually: found in manuscript c. 6 Therefore, as... arithmetic: this phrase is written twice in manuscript s. || four: written as the Roman numeral IIII in manuscript c. 7 which is the first: omitted in manuscript c. 9 For although: original: "Nametsi" in manuscript a, with a mark indicating a correction to "Tametsi" (although), which is found in edition f. || sometimes: original: "aliquanto" found in manuscripts b, c, d, f, l, r, s. 10 itself: found in manuscript a. || dreaded that very: word order flipped in edition f. 11 to be offered: alternative grammatical forms in a and b. Manuscript r has a different ending. 13 finally: spelled "suppremo" in a and c; "supremo" in f. 16 wonderful: omitted in c and s; deleted in d; added by correction in l. 20 and: omitted in c and r. 23 lesser: found in b and c. 25 The prologue of the book of Boethius ends here: found in manuscript a. Here begin: omitted in manuscript r. || of Book I: found in a and c. of the first book: found in edition f. || The entire heading is omitted in b, d, l, s. 26 of mathematics: omitted in manuscript a.