A DEMONSTRATIVE DECLARATION OF THE MACHINES OF THIS THEATRE.

PROPOSITION I.

Certain instruments and machines invented for dimensions and foundations, upon which the inventions following in this book are for the most part based.

HERE first occur six instruments to be considered, of which the two that look to the East are the compass and the rule, upon which the whole practice of mathematics depends; the two next are parts of a screw, one the male, which we shall call the inner part, and the other, which here turns to the South, the female, which we shall call the outer part; and the remaining two, the Western ones, by which the screw is made: these are the principal instruments of this whole book, and they provide great use for the remaining figures.

PROP. II.

A new and singular instrument suitable for measuring all parts of any proposed body, to perceive their symmetry in the structure of that body.

This instrument consists of two rules, either of wood or bronze or any other material, of which the one that shall be called the superior turns from the angle of the East and South toward the angle of the West and North; the other extends perpendicularly from the North to the South. Each of these is divided into fifteen equal parts, and these again into five, so that there are seventy-five parts in total.
On the superior rule appears the head of a nail, the inner parts of which—as also the parts of the whole instrument—are depicted particularly toward the West: the first and more southerly of these is the Alhidada; the other part, or head of the nail in its figure, is that on whose rim’s circle are drawn the parts of the altimetric or measuring scale. The third is the Tessella, which is placed into the slit of the inner and continuous superior rule; in it is a hole in which the part of the nail moves freely, which protrudes from the other, similar tessella, which is placed in the continuous slit of the other rule; the remaining part of the nail, with the fifth figure, is the screw by which the instrument is fastened. There is also in each rule another, shorter and narrower slit, through which the nail is led and drawn back, so that the tessellae may move in the continuous slits. This, however, is very similar to the Euclidean compass invented by our author, and can be adapted to many uses, as I shall demonstrate elsewhere (God favoring).

PROP. III.

A new and universal compass, for describing by the order of pyramids and rectilinear figures, any plane curvilinear figures that correspond to the order of those same rectilinear figures.

These are the parts of this excellent compass. In the East is the first leg, extending from North to South, the southern part of which has three cusps by which the pyramid is struck, the base of which to the North is an equilateral rectilinear triangle. This, however, is fixed or revolves around the fixed leg; if it is moved, quadrilaterals and other multilaterals will not be able to be described by this compass in one stroke, for the side of the pyramid will have to be subtended to the side of the proposed figure; if, however, it is fixed, many pyramids will be necessary for the construction of the lines of the figure.