Operations of the Geometric and Military Compass

E. leaving E B equal to C A. Then, tightening the compass a little more, I will take the transversal interval between the points 90, 90, and I will transport this from B to D and from A to F, and I will have two lines, C D and F E, which are also eleventh parts of the whole. And by the same order, transferring here and there the distances taken between the points 80, 80, 70, 70, etc., we shall find the other divisions, as is seen distinctly in the line below.

A horizontal geometric line diagram depicts a line with eleven equal segments marked by vertical ticks. The points are labeled with letters: B, E, and F on the left side, and D, C, and A on the right side.

But when a very small line is proposed to be divided into many parts, as for example the following line A B, to divide it, for instance, into 13 parts, we shall be able to proceed according to this other rule.

Let that line A B be prolonged secretly up to C, and let us measure upon it as many other lines equal to A B as we please. In the present example, let there be six others, so that A C is seven times A B. It is manifest that, of those parts of which A B contains 13, the whole A C will contain 91. Therefore, having taken the whole A C with a compass, we shall apply it transversally by opening the Instrument to points 91, 91, and then tightening the compass to one point less, that is, to—

A horizontal line diagram is labeled with points C, B, and A. The segment from C to B is divided into several large equal parts, while the segment from B to A contains a much finer scale of many small subdivisions.

—points 90, 90, we shall transport this distance from point C toward A. By marking the limit toward A, one leaves the eighty-first part of the whole C A, which is the thirteenth of the [line A B].