Architettura con il suo commento et figure Vetruvio in volgar lingua raportato

A decorative initial "L" marks the beginning of the text.

Law: that he may have Astrology and know the reasons of the heavens. And so that these things to be known may be thus, these are the causes.

from the aspect of the secret: substance has desired to follow as a science for diligent Painters. But some also desire that Geometry be produced with the doctrine of Arithmetic. Although Aristotle in the first book of the Posterior Analytics says: "It is not appropriate to demonstrate that which is general in another descending particular, such as Geometry in Arithmetic," etc. Whence, in their examples, there could be such zeal that they will represent those things imitated from nature so well that they will almost appear as if they are in agreement with nature itself, as much in quality and quantity as also in motive essence, as we shall say elsewhere. And those propositions are for examples given by Plato, by Aristotle, by Pythagoras, and by many other illustrious ones, and especially by Euclid, of whom Plato said he was more expert in this science, as we have from Valerius Maximus. And not ignorant of Perspective: Furthermore, Vitruvius, beyond the aforesaid, says that with lines they enclose the surfaces and the base lying on a plane. This science of perspective, which he has called Optics, therefore follows. Because optica optics comes from the Greek verb opto to see, or optomai, opsomai, which means "I see," or opticos, which means the visual virtue. This science is precisely that by which every surface is rightly raised into a body, and it demonstrates the most correct foresight and all distances, and the parerga secondary elements or background details in a work of art, even into all the Horizons and in all celestial and terrestrial bodies, and those of the water: this is the true companion of Graphida drawing, and which demonstrates coloring to true Painters, and shadows and lights; this finally can be embraced in all the good liberal sciences, and especially in Mathematics. Trained also in Arithmetic. Since Arithmetic, that is, the act of numbering or what we might call the Abacus, has come from the Arabs, it is a proper and most certain conclusion for the aid not only of the Architect, but of every operator, and mover, and contractor; for without this, one could never calculate nor know the value or the power of another, and what one does by numbering: diligent merchants do not estimate by fortune the gains, nor the dangerous cases by land or by sea, nor do lords or other peoples fear fighting, etc. Therefore, it is necessary for the Architect to know how to discern the quantities of numbers or the common ones, as also those of the courses of water, where much or little is sent, in the order in which they are conducted by closed or open conduits, or even by other vessels for conducting water; also of other things pertaining to measuring fields and moving earth for excavation, or of buildings, or of other things that one intends to produce to the true effect of giving form. This science, in order to be separated from art and the liberal sciences, but the liberal arts seem that they cannot exist without company, Vitruvius has left that this be the remainder of the above-mentioned, because it also behooves one to study with the utmost diligence so that we may ordinarily know how to compose with the order of numbers the proportions measurable to the things that we intend to depict: not only to say the computation of the importance of surfaces and of bodies precisely by number, and also further, it is necessary to be able to say its quantity of weight, and the powers that can sustain it, as we have in the tenth book. And for an example such as what happens with the archiepiscopal and sacred church of Milan, the pyramid or the Hecubal an architectural term for a crowning element or pinnacle title to be made, which, having to be placed entirely of marble above the arches of eight corners divided by the four pilasters raised from the earthly foundations, it is necessary to know most strenuously if that Hecubal top or support can be durable or not because of the very great weight of the marble. Also, by that Arithmetic, to be able to say every necessary expense of each kind of material and workmanship, so as not to be ignorant; so too of many other occurrences of movements and repercussions in power, etc. He must know how to render the reasons as we will say in other places. That he may have understood many histories. This instruction is of great importance, because Architects, or others who have the prompt study of histories, certainly make forseen and provided for occurring cases, and these knowers are excellent counselors not only of the republics in time of peace, but also of war, because the knowledge of history makes a man expert and prudent for the various occurring cases, but he must seek out the noble and noteworthy examples and monuments and many times gather the Rose and leave the thorn. And these ought deservedly to be worthily rewarded by their republics, and also by great princes, for all the time of their life. And that he may have diligently heard the Philosophers. Vitruvius here has said the adjective to the substantive: of great consideration to the Architect or others, saying that he should have diligently heard the Philosophers: because those who go to hear the lectures not only of every kind, but especially those of philosophy, must be joined and intent with great diligence, for if they do otherwise they do not acquire or bring back any fruit of the science: And therefore, he who wants to take those lectures does not need to have removed his intellect, nor his other bodily senses occupied by those hearings: For the animated voice and the worthy demonstrations of excellent readers are those that are founded in the souls of the auditors and of who vivifies, promoting their soul and intellect according to the thing that is treated: and thus the disposed mind takes it to itself like the body, when well-healthy, takes delectable foods, and as 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 an understanding of the writings of the Philosophers, certainly he lacks natural cognitions. That he may know Music, that is, that the Architect has the reason of song: because those proportions of song that sometimes are not found in the measures of Geometry, or of Arithmetic promptly, just as those of common use, this, for the benefit of Architecture, will teach it: and not only will he know how to measure the proportions of buildings, but their resonances: and nominations of every embrace and proportionable number, and from the greater quantities to extract the lesser: as you can have from Euclid: Also what the venerable Franchino Gaffurio has said in his musical commentary for the Euclid and other lecture: there from the simple greater and lesser proportions of equality, precisely composed of one quantity and