Theater of Mathematical and Mechanical Instruments

Declaration
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The fixed western head should be a point where the work-piece is placed: and the two mobile heads should be split, not to hold a board, as in the previous example, but the handle of the tool original: "vtil" (outil); the cutting instrument or chisel, which rests upon the cams original: "orbes"; circular discs or eccentric wheels used to guide the tool's movement, and by them is raised and lowered to create the shape of the oval, or any other type of figure that might be required. As for the square holes in the mobile head toward the east, they serve to hold a peg to support the tool when there is only one cam; however, it is better that there be two cams, for the reason already mentioned.

PROPOSITION IX.

A third type of lathe, not yet seen, and which is not without subtlety, for engraving bit by bit a screw thread around any long and round piece, even an oval one.

DESCRIPTION OF THE NINTH FIGURE.
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The ease found in this machine shows that what many would find difficult to believe is possible, seeing as the nature of the screw original: "vis" is not that its ridge is made of parallel circles, but that it moves in the manner of a spiral line. As for its utility, this lathe has much to offer, in that it dispatches in a short time what would otherwise consume a great deal, as common practice shows. But so that we may understand the whole, let us come to the parts.

This lathe differs in many parts from the preceding ones, although its base is always similar, being the most suitable, most certain, and most stable—seeing as one could not make one with fewer parts that could serve as well. But the heads are different, for their feet are raised above the lathe toward the north original: "septentrion"; the back side of the machine in this layout by about two measures, thus establishing toward the west and the east the two fixed heads, as in the others. One of these, namely the western one, contains the point upon which one end of the work-piece turns, being 23 parts away from the base of the lathe. Between these two fixed heads are three mobile heads: the two toward the east are small and like common ones; but the western one is taller, and of such a size that it can carry the point upon which the other part of the work-piece turns. The two small and similar heads serve to carry a lead screw, which causes the movement that drives the iron of the instrument in the same manner as the screw is turned. This lead screw is held within a hollowed piece of wood, where it is supported in all its parts. In the middle of the hollowed wood is a fixed nut original: "escroüe" in which the screw moves, such that it approaches and recedes through its rotation. The western end of the screw pushes a square piece, in which it is held by a pivot; and by means of a peg, the pivot remains notched so that it cannot come out, much like the screws in printing presses original: "presses des libraires" in the part that is entirely round. At the end of the said wood pushed by the screw is the handle of the tool, which (different from how it is portrayed here) must have an up-and-down motion so that it can be pulled away from the work-piece or pushed against it. For when the craftsman turns [the lathe], the iron must catch the work, and when he turns back, the said iron must withdraw—as turners well know how to practice. The rest of what is depicted here belongs to the movement of both the screw and the work-piece, and of the instrument. To understand this well, it is necessary to know the parts that are specific and adapted to it in this portrait. At the top of the fixed heads toward the north is a straight, round pole original: "perche" parallel to the northern line, which can move freely within the holes in the said heads where it enters, having in its middle and toward its ends three drums where cords are wound, as appears in the figure. In the middle drum, the wound cord has a counterweight at one end, and at the other, it is held by the hand of the craftsman, who, by pulling it, provides the motion that is returned by the counterweight. For the cord at the eastern drum is attached by one end, then, encircling the eastern end of the lead screw, has a counterweight at its other end; and the other cord at the western drum is also held there; then, being wound around one end of the work-piece, as is usually done, it has a counterweight at its other end which, along with the others, brings back the motion. For the craftsman, pulling his cord, causes the pole and the drums to turn, and consequently the work-piece and the lead screw. As the work-piece turns, it prepares itself to be cut by the iron; for the iron does not cut unless it is pushed, or if the object to be cut is not moved. Then, when the craftsman brings his hand back up, the counterweights pull back, and thus the lead screw recedes, which previously pushed the tool, pushing it as much as the work-piece turns, and receding as much as it turns back. There is at this time, for the movement of the tool, a crossbeam original: "solineau" under the lathe parallel to the ground, which is seen here 7 parts from the base of the lathe, and is 2 measures and 14 parts long, passing from one side to the other through the legs of the lathe, which are split to the size of its thickness. At each end of the said crossbeam, there is a square piece of wood, 1 measure and 8 parts long, at the end of each of which is a cord that passes through two rotating pulleys on the rods that emerge from the fixed heads, 10 parts from the end of those which face north, having at their other ends...