The Operations of the Geometric and Military Compass

the B A, outside even towards the end A. And thus, if it pleases us, we will come tightening the compass from point to point to 89, 88, 87, etc., and we will transport these intervals from the end C towards A, and one will come degree by degree finding and noting the other particles of the proposed line A B.

A horizontal line segment representing a geometric scale. On the far left, a point is labeled "C". To the right of "C", there are several tick marks indicating equal divisions. Further to the right, a point is labeled "B". Between "B" and the rightmost endpoint "A", the line is marked with many fine, closely-spaced vertical hatch marks, indicating a more precise scale.

But if, finally, the line to be divided were very long, such that it exceeded by much the greatest opening of the Instrument, we could in any way take the part assigned to us, which let it be, for example, the seventh. Now, to find it, having first imagined two numbers, one sevenfold of the other, such as, for example, 140 and 20, let the Instrument be set to any opening whatsoever, and from it, having taken with a compass the transversal distance between points 140 and 140, let it be seen how many times this is comprised in the great proposed line. And however many times it is contained therein, as many times the transversal interval between points 20 and 20 should be replicated upon the great line, and one will have its seventh part; when, however, the interval that was taken between points 140 has measured the given line precisely. But if it had not measured it exactly, it would be necessary to take the seventh part of the remainder according to the manner declared above, and add this to that interval which was replicated multiple times upon the great line, and one will have the seventh part precisely as was desired.