Operations of the Geometric and Military Compass

—between the points of this smaller number, this will, without any doubt, divide the proposed line into the requested parts, as for example:

Should we need to divide a given line into five equal parts, we take two numbers of which the greater is quintuple the other, such as 100 and 20. Having opened the Instrument, we adjust it so that the distance already taken with the compass is applied transversally to the points marked 100, 100. Without moving the Instrument further, one should take the distance, also transversal, between the points of the same lines marked 20, 20, because undoubtedly this will be the fifth part of the proposed line. A small circular typographic flourish appears here. By a similar order, we shall find every other division, taking care to choose large numbers provided they do not exceed 250, because by doing so, the operation will turn out easier and more exact.

We shall be able to achieve the same result by operating in another way, and the order will be as follows: Wishing to divide, for example, the line A B below into 11 parts, I will take a number that is a multiple of the other eleven times, such as 110 and 10. Having taken the whole line A B with the compass, I will accommodate it transversally by opening the Instrument to the points 110. Then, since it is not possible to take the distance between the points 10 on the same lines (which are occupied by the size of the nocella hinge/pivot), instead of this, one shall take the interval between the points 100, 100, tightening the compass a little. Once an arm is fixed at point B, I will mark with the other the sign C, where the remaining line A C will be the eleventh part of the whole A B. Similarly, having fixed the arm of the compass at A, I will mark point E toward the other extremity.