Theatre of Instruments and Machines

The remaining structure concerns the motion or firmness of the machine. Its northern arm, parallel to the southern line, drawn from East to West and 20 parts of our 2 measures long, revolves around the fixed leg. In that part which is distant from the cusps by 12 parts of 2 measures, two small arms parallel to the leg move in this square; in the middle of these moves a square, oblong rule, in whose eastern extremity the center of a small wheel is fixed. For the wheel revolves around each side of the pyramid, so that the movable cusp (which is on the third rule from the North) is moved toward the East and removed from it. An arc, in the manner of a Turkish bow, is imposed so that one hand is placed upon it, and the other on the fixed leg, and a figure is described that becomes larger or smaller as the movable cusp is moved toward the pyramid or removed from it. Note this, however: the middle of the arc is always joined to the middle small arm.

PROP. IIII.

A new compass, the opposite of the former, suitable for describing rectilinear figures from the order of certain inverted pyramids which have as a base the preceding plane and curvilinear figures.

The parts of this compass differ in some way from the parts of the preceding one, although they agree with each other in certain respects. For it has a similar immovable leg and a northern arm revolving around it; however, if the structure of both compasses were the same and as it is in this one, it would be far better, for they ought to differ between themselves only in the pyramid. But those tubes which are in each perpendicular rule (within which the arms can be led and drawn back to move the movable cusp to and fro) are useful for depressing and elevating that same cusp if the center and circumference are not on a flat surface. Experience will teach the diligent reader this.

PROP. V.

A new and universal compass for delineating in one stroke an oval figure whose diameter, whether long or short, can be as much extended or contracted as one wishes.

This compass has certain things in common with the others, namely the immovable leg, the superior revolving arm, and those two parallel rules which verge from North to South, for the rest is particular to it. For to the South, it has an arm parallel and similar to the aforementioned superior one; then there are two globes on the fixed leg, of which the first is 7 parts of 1 measure distant from the cusps, the other 2 parts of 1 measure from it, around which two flat orbs of moderate thickness revolve freely, so that the inner part of the screw, which is visible, may be able to enter into its solid, and to set each orb at the discretion of the operator. In the middle of each orb is a cavity so fashioned that the lower part is wider than the upper, and it is said to be shaped in the manner of a swallow's tail, in which a tessella is adapted, moving circularly and freely around the fixed leg. From each tessella of this and that orb, two similar and parallel rules are produced, in the middle of which is a slit in which the middle arm, in which the movable cusp is, can be freely led and drawn back; the motion of the cusp in it toward the center or immovable leg is checked by the operation of that tube in which the screw is, for retaining its motion; the remaining arm, however, is for the firmness of the machine. Now, if the revolving parts are led around the immovable one, an oval will be made, the small orbs being so disposed that one part is lower, the other higher; for then the diameters in the plane in which the immovable leg is elevated at right angles are smaller in the elevated and depressed part, which the diligent explorer will easily perceive.

PROP. VI.

Our compass, like the others also of our own invention—long since communicated to many—for describing any spiral line on a plane without the wrapping of a cord or other deceptive method.

In the South of this compass is the entire machine. The remaining northern parts are its parts, which I am pleased to explain. The round, long, and hollow part, which I prefer to call a cannon from its similarity to a bombard, is the sheath in which, toward the West, is the cusp around which the compass revolves to describe a spiral; the next part is the screw, on whose outer part a rule adheres, at whose western end is the movable cusp; the remaining others, which are the northern parts, are the inner parts of the screw.