The Operations of the Geometric and Military Compass

E, leaving E B equal to C A. Then, tightening the compass again a little, I will take the transversal interval between points 90 and 90, and this I will transport 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 with the same order, transferring back and forth the distances taken between points 80 and 80, 70 and 70, etc., we will find the other divisions, as is seen distinctly in the subjoined line.

A horizontal line segment marked with vertical ticks. Labels B, E, and F appear under the left side, and D, C, and A appear under the right side. Above the line, the number "1" is repeated above several segments to indicate equal units of measurement.

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

Let the line A B be secretly prolonged until C, and measure within it other lines as many as we like equal to A B, and in the present example let there be six others, so that A C is sevenfold of that A B. It is manifest that of those parts of which A B contains 13, the whole A C will contain 91. Wherefore, having taken the whole A C with a compass, we shall apply it transversally by opening the Instrument to points 91 and 91, and then tightening the compass to one point less, that is to

A horizontal line segment divided into seven larger equal parts by vertical tick marks. The leftmost point is labeled C. The sixth tick mark is labeled B, and the final point on the right is labeled A. The segment between B and A contains numerous smaller subdivisions.

points 90 and 90, we will transport this distance from point C towards A, because by noting the end towards A, one will leave the ninety-first part of the whole C A, which is the thirteenth of the