The Operations of the Geometric and Military Compass

How we can take any parts from a proposed line as they are ordered to us. Oper. II.

The present operation is all the more useful and necessary in that, without the help of our Instrument, it would be very difficult to find such divisions, which, however, with the Instrument, will be achieved in an instant. When, therefore, we need to take any parts from a proposed line as they are ordered to us, as for example, from 197 parts we need to take 113: take without delay the length of the given line with a compass, and open the Instrument until such length fits transversally to the points marked 197. And moving it no more, take with the same compass the distance between points 113 and 113; this will, without any doubt, be the portion of the proposed line that equates to 113/197.

How the same lines provide us two, indeed infinite, scales to transfer a plan to another larger or smaller one according to our discretion. Oper. III.

It is manifest that every time we need to extract from one design another larger or smaller one according to whatever proportion is required, it is necessary that we serve ourselves of two scales divided exactly, one of which serves us to measure the design already made, and the other to note the lines of the design to be made, all proportional to their corresponding lines of the proposed design; and such two scales