Arithmetic, Geometry, and Music

¶ The two books on Arithmetic by Anicius Manlius Severinus Boethius, most illustrious and noble man, former consul, ordinary, and patrician, to the patrician Symmachus, begin.

In giving and receiving gifts, duties are considered rightly performed—especially among those who hold each other in high esteem—if it is clearly established that the giver brought nothing more generous, and the receiver accepted nothing more joyfully embraced by benevolence. Considering this myself, I have brought not idle weights of work, for nothing is more instructed for a deed when the thirst for having inflames it, and nothing is more worthless for merit when the mind, having conquered itself, has subjected its passions to being trampled; rather, I have brought those things which I have gathered from the wealth of Greek literature into the treasury of the Roman language. For the logic of my work will also be consistent for me if those things which I have elicited from the doctrines of wisdom are approved by the judgment of the most wise. You see, therefore, how the result of such great labor awaits only your examination, nor should it proceed to public ears unless it relies on the stipulation of a learned opinion. In which nothing should seem surprising, since this work, which pursues the discoveries of wisdom, relies not on the authority of its author but on another's judgment. For the matter of reason is weighed by its own instruments when it is compelled to undergo the judgment of a prudent man. But for this small gift, I do not establish the same defenses that I do for other arts. For our knowledge is not so absolute in all its parts that it does not desire the assistance of other arts. For in fashioning statues from marble, the labor of carving the mass is one thing, and the method of forming the image is another; nor does the hand of the same craftsman await the shine of the polished work. And the tablets committed to the hands of painters, the wax accepted by the rustic observation of the makers, the dyes of colors sought out by the skill of merchants, and the linens worked by laborious weaving-houses provide a manifold material. Is not the same thing also seen in the instruments of war? One sharpens missiles for arrows; for others, a sturdy breastplate groans on a black anvil. Yet another buys the coverings of a raw boss to be fixed to the circle of his own labor; thus one art is perfected by many arts. Yet the completion of our labor runs to a much easier outcome. For you alone will place your hand on the supreme work, in which it is not necessary to labor for the consensus of deciders. For however much this judgment is proven to be cultivated by many arts, it is nevertheless accumulated by one examination. You may therefore experience how much the labor of drawn-out leisure has added to us in this study. Whether the speed of an exercised mind comprehends the flights of subtle things, whether the leanness of a sparse speech suffices to explain those things which are obscured by difficult sentences. In which matter, the gains of another's judgment are also sought by me, since you, most skilled in both literatures, can prescribe by your pronouncement alone how much those who are without Greek speech should dare to judge of me. But I do not bind myself to the instructions of another, nor do I constrain myself by the strictest law of translation, but having wandered a little more freely, I do not insist upon the footsteps of another's journey. For I have collected with moderate brevity even those things which were discussed at length by Nicomachus regarding numbers. And those things which, having been passed over too quickly, provided a narrower entrance for understanding, I have unlocked with a moderate addition, so that we might sometimes use our own formulas and descriptions for the clarity of things. The sober reader will easily recognize with what vigils and sweat this has been constituted for us. Since, therefore, I was prescribing regarding arithmetic, which is the first of the four mathematical disciplines, you alone seemed worthy of that gift, and I understood that there was all the more need for it in the narration. For even if there were a place for easy pardon with you, nonetheless, suspicious security sometimes feared that very ease. For I thought that nothing should be offered for such great reverence that was not elaborated by genius, perfected by study, and finally worthy of such great leisure. I do not doubt, therefore, that because of your benevolence toward

me, you will cut away the superfluous, fill in the gaps, correct errors, and receive what is said conveniently with wonderful alacrity of mind. This matter pushed away the slow delay of counsel. For things that will please me will return the smallest fruits. I know, indeed, how much more studiously we cherish our own goods and those of others. Rightly, therefore, just as one transmits the stalks of wheat to Ceres and the ripened shoots to Bacchus, so have I transmitted the rudiments of a new work to you. You alone, with paternal grace, shall promote our gift; thus you will consecrate the first-fruits of my labor with the most learned judgment, and the author will be valued no more by his own merit than by the examiner's.

The chapters of the first book begin.