Ten Books on Architecture by Vitruvius

the unlearned might be able to educate themselves by reading and become good. This is a thing that seems to be the only goal of all the laws of the universal world: that we should be good, and learned if possible, for our own well-being. This precept of being literate is of the utmost importance, because Vitruvius stated in the sixth prologue that "a life cannot be worthy without literature," as you will see in the ninth prologue and in this same chapter 3. Therefore, this being the foundation and origin of all universal sciences and letters of the good, discipline-able studies, it appears certain that no science can be known without literature. Nor can men ascend to greater things, nor execute the most lofty tasks, whether in philosophy, civil law, business, contracts, or other notes—neither mediocre nor minimal tasks—without the aid of literature, as will be said appropriately in the seventh prologue. Therefore, it is easy to believe that "a life cannot be perfect without literature," nor could the things done and said in the past be known so conveniently if this literary element had not existed. Because the account of the past makes the intellect and the soul know and be illuminated. Therefore, it is necessary that these things be instructed—whether by us ourselves or by those who possess them—so that our animated intelligence may be refined, for the more we know, the more excellent and divine we shall become.

¶ Skilled in graphida drawing/drafting. This word, grapho to write/draw, signifies in Latin not only to write, but also to paint, and at times to sculpt. Therefore, it is fitting that the architect knows how to read, write, and design or represent, as is the custom in painting. Because, as we have said, if we possess all the opportune sciences but do not know how to demonstrate them, they will appear as nothing, or we will grasp only the shadow of the thing enigmatically or confusedly, and not the effect. And for that reason, it is sometimes better to know how to signify a thing than to speak of it. Furthermore, it is a thing to be known for such a purpose: the Greeks, in their institutions, proposed that noble children, and not those who were freedmen or slaves, should learn the science of antographida drawing/design—that is, painting—before any other discipline. And this was so that they might better have the cognition of universal things in order to know how to express them, and also so that they, being noble, could always be better in soul and in bodily honesty. And for this reason, this was taught in the school of letters, as we shall say of many most famous men in the lower reading. And thus, being trained in this, which was placed in the first degree of the liberal arts, they were then able to judge and represent the other liberal or active sciences with the easiest comprehension. Whence it has come about that these Greeks, who were founded in the good sciences, have appeared as Gods among learned men; the testimony to this is their works, which have reached posterity. Therefore, to this science, honor and the greatest rewards have always been given as long as it remained in the hands of noble and most diligent students. But since then—as it is even now in great quantity, because it has been taught to slaves and the lowest people—the good professors are so disparaged by the idiots and the slothful that they are almost reputed to be worse than the working cobblers or building masons. Whence, there no longer appears anyone who wishes to acquire it with true study, as did many most famous men—not only philosophers, but primary Romans and Emperors—if we believe Valerius Maximus and Pliny.

Learned in geometry: Because all things of the world are universally and generally figured and comprehended superficially and corporally by lines of diverse qualities and proportional quantities. Vitruvius, after drawing, wished to make this substantive science follow, because they—just like diligent painters, although geometry is, as some would have it...

Learned in Geometry: and not ignorant of optics. Also instructed in Arithmetic: and that he has knowledge of many Histories: and has diligently heard the Philosophers: also that he knows Music: and is not ignorant of medicine. And has known the responses of the Jurisconsults: also has known astronomy and the reasons of the heavens.

brought forth with arithmetical doctrine. Although Aristotle says in the first of the Posterior Analytics: "It is not possible to demonstrate by descending from one genus into another, as geometry into arithmetic, etc." This can be for the sake of only demonstrating proper figures by continuous quantities and not discrete or numerable ones. Whence, in their examples, there can be such zeal that they will delineate those things so well-imitated from nature that they will almost appear as if they were concordant with nature itself, as much in quality and quantity as even in motive essence, as we shall say elsewhere. And therefore, you will not only understand that it is necessary to know how to make examples by hand, but also how to understand exquisitely those propositions given as examples by Plato, by Aristotle, and Pythagoras, and by many other most famous men, and especially by Euclid, whom Plato said was more expert in that science than himself, as we have from Valerius Maximus.

¶ And not ignorant of Optics: Vitruvius, beyond the aforesaid—which are those that close the surfaces and bases lying on a plane with lines—adds this science of optics, which in Latin we call perspectiva perspective. For optica comes from the Greek verb optomai I see. This science is precisely that by which every surface is rightly raised into a body, and it indicates the most correct foresight and every distance, and the Parerga secondary features/details. Down to all the horizons and in every celestial, terrestrial, and aquatic body, this is the true companion of drawing, and it indicates how to color for true painters, as well as shadows and lights. This, finally, can be encompassed in every good liberal science, and especially in the mathematical ones.

¶ Also instructed in Arithmetic: Since arithmetic—that is, number or the abacus, which came from the Arabs—is a proper and most certain conclusion, not only for the help of the architect but of every operator, mover, and contractor. For without this, one could never calculate nor know the value or the power of others. And those who know the expert merchants do not worry about fortune, neither by land nor by sea, for the dangerous cases, nor do lords or other peoples fear the combat, etc. Thus, the architect needs to know numerable quantities, whether direct or continuous, such as are also those of the flow of water through emitters, whether much or little, how it is conducted either by pipes, tubes, or other water-conveying vessels. Also of other things pertaining to the operation of surveying, terrestrial motions, excavations, or buildings, or other things that he intends to produce to a true, performable effect. This science is powerful enough to stand separate from the other liberal arts and sciences, but the other liberal arts seem as if they cannot exist without company. Vitruvius has left this to be posterior to the above-mentioned, because one must also study it with the greatest diligence so that one knows how to compose, with numerable series, the symmetries proportional to the things one intends to represent. Not only to say precisely the important superficial and corporal importance with number and computation, but furthermore, if necessary, to know how to tell its ponderous quantity and the powers that can sustain it, as we shall have in the tenth book. And for such an example, as happens with our archiepiscopal and sacred house of Milan, the pyramid or the future Hecubalean vault (which is all of marble), having to place it upon the octagonal arching pulled by the four pillars erected from the terrestrial substructures, one must most strongly know the permanence or not of that Hecubalean pinnacle or vault because of the very heavy marble weight. Also, by this arithmetic, [one must] know how to state every opportune expense of every sort of material and manufacturing, so that one does not appear ignorant, just as with many other accidents of motion, repercussion, power, etc., [so that] he knows how to render the reasons, as we shall say in another place.

¶ And that he has knowledge of many Histories: This precept is of great importance, insofar as architects or others who have a prompt study of histories certainly know how to foresee and provide for occurring cases, and these knowers are excellent counselors not only for republics in times of peace, but also of war. And these should deservedly be rewarded by their republics and even by great princes worthily for all the time of their life.

¶ And has diligently heard the philosophers: Vitruvius here has given the adjective to the substantive, of great consideration for the architect or another, saying that he must have "diligently heard" the philosophers. Because those who go to hear lessons—not only of every sort, but especially those of philosophy—must stand quiet and intent, with great diligence. If they act otherwise, they do not acquire nor report any fruit of that science. And therefore, whoever wishes to take up these lessons does not need to have a distracted intellectual mind, nor other bodily senses occupied by those hearings. Because the animated voice and the worthy demonstrations of the excellent readers are those that infuse themselves into the soul of the listeners and quicken them, promoting their soul and intellect according to the thing that is treated, and thus the disposed mind assumes them just as the healthy body assumes delectable foods. And as it is written by Aristotle in the book On Sense and Sensible Objects. And it is a thing to be known: that if the architect does not have intelligence of philosophical writings, he certainly lacks natural cognition.

¶ Also, it is necessary that the architect knows Music, because those proportions that sometimes cannot be found in geometric or arithmetical symmetries are those of common use, and this will teach them for the benefit of architecture. And he will not only know how to modulate the proportions of the buildings, but...