DIVISION OF THE

L I N E,

OPERATION I.

A woodcut initial letter 'V' is ornate with white floral scrollwork on a dark background.COMING to the particular 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. Among these, we shall speak first of the innermost ones, denominated Arithmetic Lines, because their divisions are made in arithmetic proportion, that is, with equal excesses, which proceed up to the number 250. From these we shall derive various uses, and firstly:

By means of these lines, we shall be able to divide a given straight line into as many equal parts as we please, by operating in any of the ways described 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 quantity of it with an ordinary compass, and we shall apply this space transversally, opening the Instrument to any number on these Arithmetic Lines, provided that it is such that, above those same lines, there is a smaller one, and contained by it as many times as there are parts into which the proposed line is to be divided. Having adjusted the Instrument in such a way, and having taken the transversal space—