...of any desired size, according to the convenience of the one who wishes it. Furthermore, the rules or branches are, in their bodies, square, flat, and of such thickness that one can make a dovetail groove renure à queue d'hironde: a wedge-shaped joint used to join wood or metal together securely while allowing it to slide along their entire length, into which a slide or shuttle can be well-fitted. Thus, there are two grooves and two shuttles, in the middle of which two other grooves are made across the rules; these two should be shorter and narrower, not reaching the ends of the rules, for they would cause them to split. But so that the use of the placement of these grooves may be understood, it is necessary to know the other parts of the instrument—namely the two shuttles and the nail, along with what is required for it—all being comprised in these five figures which are on the west side The author continues to use cardinal directions—North, South, East, West—to guide the reader's eye across the printed illustration plate..

The first of these, counting from south to north, is the alidade alhidade: a sighting rule used for measuring angles, or demonstrating rule, called by the Latins Osteofor original: "Osteofor", likely a Greek-derived term meaning "bone-bearer" or "pointer"; the second is the head of the nail upon which this alidade turns, having on its edge the points of the altimetric scale eschelle altimetre: a scale used to measure heights or depths which are related to it; the third is one of the shuttles, having a round hole in the middle so that the nail can turn freely within it, and the shuttle consequently rotates around the nail; the fourth is the other shuttle, entirely similar to the aforementioned one, in which the perfectly round nail is seen, its end being threaded like a screw so that by means of the nut escroüe: the internal-threaded piece that twists onto a bolt, which is the fifth part, the instrument can be held tight once it has been set according to the will of the user. These, then, are the parts; which, when well-considered, will bring great clarity to the whole instrument.

PROPOSITION III.

A new compass by means of which one can describe all figures and straight lines, according to the order of pyramids which have such figures as their bases.

EXPLANATION OF THE 3rd FIGURE.

Even though these inventions of compasses may seem useless, given that by several rules—the reasons for which are contained in the sixth book of Euclid’s Elements Euclid's Book VI deals with the theory of proportions and similar figures.—the proposed figures can be made; nevertheless, they are not to be rejected, as much for the subtlety of the invention as for the convenience of being able to make whatever figure one wishes with a single swirling motion tournoyement: a smooth, continuous rotation. And the reason for this is comprised within the doctrine of parallelogrammic and reciprocal figures, as will be seen by the explanation of the parts of this compass.

In this compass are seen several legs, among which the longest and closest to the eastern line (and parallel to it), having three points toward its southern part, is the one we shall call "immobile" or "fixed." This is because when one wishes to use the instrument, this leg must be fixed into the surface by means of its three points so that it cannot move, but acts like an axle around which the rest of the assembly turns freely when in use. On this leg, above the points, appears an inverted pyramid, the base of which is a rectilinear equilateral triangle; the perspective of the drawing prevents this from being fully seen, and said pyramid must be separable—that is to say, able to be removed and attached when needed, being set in its square hole, just as the part of the fixed foot that enters it must also be square.

Besides this pyramid, one must have several others which can also be placed on this fixed leg, these being either square, pentagonal, hexagonal, or of as many sides as one wishes, according to the figures one wants to draw. For one cannot call this instrument a compass except insofar as, in imitation of a compass, it must describe a figure with a single stroke, which will happen according to the pyramid placed upon it. Above the pyramid toward the north, six holes appear in the fixed leg; these are placed there to pass a pin through that comes from the pyramid, in order to raise it when the point can no longer approach it due to its thickness, such as when one wishes to make a small figure.

The rest of the assembly is such that this branch—parallel to the southern line and located 2 paces from the northern line (being the longest of those parallel to it)—can turn freely around the fixed leg by means of the round hole at its eastern end. It is held in proportion by this half-arc, at the end of which is a socket canon: a cylindrical sleeve or tube; so that, being attached to the aforementioned turning branch, it turns with it, so that the branch is better held in place and turns more accurately. On this branch, there are two other smaller parallel branches: the one closest to it at the eastern end has a roller roulette: a small wheel which must always touch the pyramid. On the other, which is the southernmost, is the place or square socket at the eastern end where the point A stylus, pen, or scribing tool. of one's choice is placed. These three branches enter squarely into two rules parallel to the eastern line and to the fixed leg; in this figure, these rules appear to have points, although they serve no purpose there, and it would be better if they were entirely square at the bottom, for they serve greatly to hold the pieces upright, as they rest upon the surface on which the figure is to be described.