Operations of the Geometric and Military Compass

How to take any number of parts from a proposed line as ordered. Operation II.

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This present operation is all the more useful and necessary because, without the help of our Instrument, it would be very difficult to find such divisions, which, however, will be obtained in an instant with the Instrument. When, therefore, we need to take whatever parts of a proposed line are ordered—for example, if we must take 113 parts out of 197—take the length of the given line with a compass without hesitation, and open the Instrument until that length fits transversally between the points marked 197 and 197. Without moving it further, take with the same compass the distance between the points 113 and 113; that portion of the proposed line will, without any doubt, be equal to one hundred and thirteen one-hundred-and-ninety-sevenths.

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

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It is manifest that whenever we need to draw another plan from a drawing, either larger or smaller according to any proportion, it is necessary to use two exactly divided scales. One of these should serve to measure the drawing already made, and the other to mark the lines of the drawing to be made, all proportional to their corresponding lines of the proposed drawing. Such two scales