Arithmetica

an image, there all things in truth. Indeed, there is nothing divine or human, nothing small or great, nothing lower or higher, and finally nothing so arduous or so difficult that it has not taken upon itself through this brightness of numbers. And that which fell away and was lost from itself for another reason, it gathers and repairs by this method. And he who distinguishes things by a threefold interval will not be alienated from the truth. For some things, which are filled with the highest peak of honor, are indeed expressed, but they are not themselves the expressions or signs of anything else. Others, on the contrary, are signs and expressions in a good part, in which class are numbers. Nor are there lacking those things which remove their own calculation from both, such as the entities of nature. For the wise man himself considers these equally, as well as numbers, as images, expressions, and symbols. Such is the dignity of both things and numbers, insofar as they are appropriate symbols of the divine intelligences. Indeed, he who, in mathematics, embraces only numbers, weighing their mystical meaning as nothing, is nearly like an eye which, though in darkness, has made light of no value. And for these reasons I have been led to spend the strengths of my talent, even if they are small (for I know well how short my furniture is a Latin idiom for having little intellectual equipment), in drawing out the mystical meaning of numbers. I preferred to risk my talent in this matter rather than leave this part untouched, especially since in these times mathematics has begun to emerge and lift its head again. Nor have I been delayed or deterred by those imbued with backwards letters, whose minds nourish thorns and monsters, for whom even a single Hercules would not be enough to pluck them away. For, as is said in the proverb of the Wise Man the proverb of the Wise Man, the net is cast in vain before the eyes of those with wings. I am well aware that the minds of men are of the same fate as fields: if they are cultivated, they bring forth good things; if neglected, they produce bad weeds. Yet in this matter, I did not wish to proceed without a leader. But whom could I choose more suitable than him who made these arts known to Latin ears? Therefore, I have examined Boethius's Arithmetic, divided into two books, with what diligence I could. And those things which seemed to desire light and clarity, I have made passable by a cursory glance and the light of a brief annotation. I have added here and there many ascents and examples. In which matter, if I have achieved what I wished, let others be the judges. I wished these first fruits of our talent to be dedicated to your name, Reverend Father, so that you might clearly understand the gratitude of our soul for the innumerable benefits with which you have long overwhelmed me, and continue to overwhelm me daily. And because it is not given otherwise, I revere you as my benefactor. Nor indeed do I revere you for any other reason than that you are most worthy of all praise.

THE PREFACE OF ANICIUS MANLIUS SEVERINUS BOETHIUS,

ARITHMETIC.

Ornamental woodcut drop cap I featuring scrolling vines and floral motifs within a square border.

In giving and receiving gifts, duties are rightly estimated, especially among those who value each other greatly, if it is clearly established that nothing more liberal could be brought forth as an invention by the one, nor anything more pleasant could be embraced with benevolence when received by the other. Considering these things myself, I have brought not the dull weight of wealth, for which nothing is more equipped for crime when the thirst for possessing burns, and nothing is viler to merit when the victorious mind has trampled it underfoot. Rather, I bring those things which we have gathered from the wealth of Greek literature into the treasury of Roman speech. For in this way, the account of my work will be established for me: if those things which I have drawn from the teachings of wisdom are approved by the judgment of the wisest man. You see, therefore, that the effect of such great labor awaits only your examination, nor should it go forth into the public ears unless it is supported by the agreement of a learned opinion. In this, nothing ought to seem strange, since that work which pursues the inventions of wisdom relies not on the author's judgment, but on that of another. For a matter of reason is weighed by its own instruments when it is forced to undergo the judgment of a prudent person. But for this small gift, I do not establish the same defenses that threaten other arts. For there is almost no science so absolute in all its parts, needing nothing and relying only on its own protections, that it does not also desire the help of other arts. For in shaping marble statues, the labor of cutting the mass is one thing, and the method of forming the image is another. Nor does the brightness of the polished work expect the hand of the same craftsman. And tablets to be painted by hands are committed to the labor of smiths; waxes are gathered by the rustic observation of farmers; the dyes of colors are sought out by the skill of merchants; and linens are elaborated by industrious weavers. All these provide a manifold material. Is not the same also seen in the instruments of war? Here one sharpens the points for arrows, there a strong breastplate groans on the black anvil. Yet another purchases the coverings of a raw shield boss to be fixed to the circle of his own labor. By so many arts is one art perfected. But the completion of our labor runs toward a far easier outcome. For you alone will lay your hand upon the final work, in which there is no need to labor for the consensus of those deciding. For although this judgment may be proven cultivated by many arts, it is nevertheless fulfilled by a single examination. You may therefore experience how much labor the long stretch of leisure has added to us in this study; whether the speed of a practiced mind can grasp the escapes of subtle things; whether the meager thinness of speech is sufficient to explain those things which are hindered by darkened sentences. In which matter, the gains of another's judgment are also sought by me, since