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

angular things to which the terminations of lines and divisions are expected. Therefore, to better clarify the Greek word εὐθύγραμματος straight-lined, considering that the Greek letter 'r' in opening is of an angular figure, for this reason, Martianus Capella, in his designations of geometry, says this: "But when the lines between themselves equally hold the angle and have been straightened, it will be called a straight-line angle, which is in Greek εὐθύγραμμα euthygramma." From which a rectilinear will be caused. But know, reader, that we have found more Latins to have said EVTHIGRAMIS. But εὐθεῖα eutheia means straight, and γραμμή gramme means line, almost as if it conducts the lines straightly. Now, you will side with whomever you like, for other than what we have explained, it does not seem to us to signify anything else in this place. Therefore, if Vitruvius in the Sesto varies even a minimum space or plinth, certainly he falsifies the adapted form of the figure, and so much the more as the multiplication is greater due to the inequality of the points, as is most known to expert delineators, of which the Perspective artists are special. From which the designs of buildings are made with much greater ease in the areas, that is, terrestrial surface or flattened spaces, in which we intend to make the directions of the lines with the NORMS, that is, that which we vulgarly call a square, an instrument made like a right angle, of iron or of wood, which masons and stonecutters of squared stone use to straighten the lines. And Plumb line, that is, that instrument which is called the Level of wood, made of rules, that is, a plumb line made equiangularly, and in the middle of it, we place the perpendicular lead with a thread, in the middle of which the Plumb line demonstrates at the end of the hole, cathodically with the movement and points, the equal and unequal spheres and the importance of the lines. Of which most known instrument to operate with, we have made the figure upon the marble Amusio leveling board on page 34, and upon the Chorobate leveling instrument. And with this, one can use it in every thing to make equal or air lines that are straight and direct, in which it is necessary to pull some important alignments for a terminated or continued distance. And so, through these two lines, you will be able to accompany, content, and likewise make by straight or direct, that is, by extended plane and by plumb line, as many lines as you wish, made equally. Similarly, for Perspective, or indeed what we wish to call Optics, we have spoken above on page 5, letter E, which is also the companion of the Gnomonic science, through which some lights are conducted with reason from certain regions of the Sky, where the lights are conducted rightly. Vitruvius speaks the truth because nature certainly does not give light except through the course of the Sun, that is, from the summer sunrise to the sunset. And for this, sometimes someone can, to his neighbor from the North region, make it so that he walls up and closes some window or other views, when in another place he could have the living light. And if that one stands resistant, he can be made with reason an anti-wall, which the Greeks call ἀβατὸν abaton/inaccessible and the Latins paliprando, by the way it is constituted by the public laws or statutes of the Cities. But also, when it is for good neighboring, considering that it is given by the rules of the laws, what does not harm you and helps others is easily to be conceded. If the ceiling of the floor will be high from the pavement up to under that floor, or one might say ceiling, from five cubits upward, the windows should be made so that there is not a facility to fail upon a chest or other thing to see into the house or outside of the neighbor. And these windows can also be made as much longer as the capacity that the air rendered first. And this does not seem to us to be to be regarded otherwise to long antiquity and custom, because the divisions of the walls and of the hedges and ditches have been made from neighbor to neighbor, so that everyone lives free and secure in his house and upon his own, etc. But it happening that in the buildings there is some place replicated, making it dark or of weak light, it will be necessary to know how to illuminate it from some places from above, just as the first commentator of Vitruvius says his preceptor, Donato, nicknamed Bramante from Urbino, did in the sacristy of the sacred church of Santo Satyro in Milan, whose lights of the Sun descend from above. Also, it can be made so that by celestial reflection from the living light from the opposite side, through that reflection opposed and entertained in some part, it makes that effect. Or knowing how to diverge or avoid some opening that can make that light enter, just as there are light-wells, or what we wish to call the balustrades that are made upon the roofs, to give light into another secondary or included place in the middle of the two. That tertiary place it is necessary to know how to illuminate with plasters and whitewashings upon the whole walls, which are very easy and better to take the light of the day and of the night, because through the whiteness of the surface, the light is easily imprinted, just as it happens through the snow when it lies happily upon the ground. When, therefore, these places have taken that reflection, they render so much light that it satisfies them, and these enclosed places are always tempered by the extremes of the annual variation of the weather and course of the Sun. And some of our Citizens, from certain times, in some narrow neighborhoods and which have high buildings and walls, or one street surrounded by another, these not only are always shadowy and melancholic due to the accident, but also unhealthy and contaminated by cold airs, etc.; they have whitewashed the walls of one and the other neighbor outside. Thus, to the district they offer happiness, and to them themselves, and to those walking there. And therefore, it is necessary to know the science of Perspective also for many other universal and particular cases, which sometimes happen unexpectedly, and not knowing how to discern them, they will seem to be truly confused and obscurely speaking, and persevering to stay as in dark shadows, of which things we will speak in this book.

Catheta is the plumb line.