DIVISION OF THE

LINE,

OPERATION I.

A decorative woodcut initial 'V' featuring ornate floral patterns and scrolling vines.

Coming to the detailed explanation of the operations of this new Geometric and Military Compass, we shall first begin with that face of it upon which are noted four pairs of lines with their divisions and numbers; and among them, we shall first speak of the most interior ones, named Arithmetic Lines, as their divisions are made in arithmetic proportion, that is, with equal differences, which proceed up to the number 250, from which we shall draw various uses, and firstly:

By means of these lines, we will be able to divide a proposed straight line into as many equal parts as we please, by operating in any of the ways written below.

When the proposed line is of moderate size, such that it does not exceed the opening of the Instrument, we shall take the entire length of it with an ordinary compass, and we shall apply this space transversally, opening the Instrument to any number of these Arithmetic Lines, provided it is such that, upon the same lines, there is a smaller number, and contained within it as many times as are the parts into which the proposed line must be divided. Having adjusted the Instrument in such a way, and having taken the space trans-