This is all that needs to be said regarding the description of the proposed geometric bodies. Whoever wishes to clearly see the reasons for their proportions, along with the rules for measuring them—both in terms of surface area and the entire volume—may read the second and fifth books of Cosmo Bartoli on the subject of measurement. There, they will find the clarity of all their parts, along with many other very useful details, both for the science and for the practice of what follows.

RULE FOR FORMING THE PLANS

OF FORTRESSES, WITH THEIR MEASUREMENTS.

C H A P. I.

A decorative woodcut initial 'S' depicts a figure or landscape within a rectangular frame.

Circle necessary for forming the plans of the Fortress.

First plan of eight bastions. Defenses and ease of their measurements.

Rules are generally of no small benefit to everyone because of the great advantage gained from them, especially for beginners in fortification, with whom I assume I am speaking at present. Because from these rules, one comes to possess the true foundation of the science and, at the same time, to keep in memory the most notable parts required in the work. And since pleasure concurs with this, one will come to learn this science with the greatest ease that can be desired, particularly in composing and describing the following plans. Given that these depend on lines and divisions of circles, once one knows the proportion of even a single one of these fortress plans, or body of a bastion, one will be able to know all the others that will need to be made, increasing or diminishing them according to the site, as will be stated in its place.

And first, we will propose wanting to form a plan of a fortress with equal sides, just as the others that follow will be, which is to say that the bastions will be equally distant from one another. It will be necessary to describe a circle upon the paper or other material in which one wishes to form this plan, and to divide it equally into as many parts as there are bastions one wishes to build. And so, we will say we have described with the mobile point of the compass the circle that is seen by the diameter A B, with the dead line made of dots. This circle, for example, is understood to be divided into eight parts to form eight bastions, which will be noted by L, R, S, and the others that follow. And once the straight lines have been drawn from one point to the other, the eight angles will be formed, upon which their bastions must be described, with those measurements and proportions that can bring them the most defense.

It is necessary, however, to first deliberate on the form of the measurement with which one wishes to form and measure the entire body of the fortress. Therefore, to choose the most familiar, we will use the Florentine braccio ell/arm, or the Venetian passo pace, which contains three of these braccia, and the passo contains five feet, just as is seen in the two following drawings: by A B, the measure of a Venetian foot, divided into twelve inches, and by C D, the half Florentine braccio. With these measures, all the drawings of the present work will be formed.

From defenses formed with proportions measured according to the offense, the perfection of the fortress depends. Defenses and their imperfections. The defense of fortresses should not be less than 160 paces, nor more than 180.

And having established (as has been said) the measure that we wish to use, one must then establish the length of the defenses that one wishes to give to this fortress, that is, how great the distance should be from the flank (the place of the artillery) to the point of the interior angle of the other bastion that faces it, which must be guarded and defended by said artillery. The entire perfection and imperfection of the fortress depends on this measure or distance. Because, being made with too long a defense, the artillery of the flanks would not be able to provide the great sweep needed against the earthworks or other material that the enemy might make to traverse and seize the moat. Nor would lead balls from a musket, placed in bags to be fired with the artillery, reach to the offense of the enemy. Conversely, being made with too short a defense (after one would have to build a greater number of bastions), its flanks would be exposed to being targeted, and consequently, the bombardiers would be killed by enemy arquebusiers who remain hidden and covered around the counterscarp. Furthermore, the plazas of the bastions would become small and with quite weak defenses, all the more so by making the flank small in proportion. These are all effects to avoid if one wishes to fortify well and with reason, especially on a plain and in a site exposed to a powerful enemy, as the reasons for all this will be assigned in their place. For now, we will only say that the said defense from the flank to the point of the bastion should be 180 paces, which is among the longest that should be made, which is about 540 braccia. And so, wanting for example to form the eight angles mentioned above, one will make it so that each of the eight parts is the said 180 paces, that is, one will divide, for example, R S into nine equal parts, each of which will be twenty paces, with which the scale A B of one hundred paces will be noted, then dividing it into the most minute parts possible, and at the very least into ten, as is seen. And this will be the just and real measure of said plan with the proposed defense.