Operations of the Geometric and Military Compass

of B A, further out toward the end A. And in this way, if we please, we shall go on tightening the compass from point to point to 89, 88, 87, etc., and we shall transport these intervals from the end C toward A, and we shall gradually find and mark the other segments of the proposed line A B.

A horizontal line segment is marked with ticks of varying frequency. The left end is labeled 'C', and the right end has two labels 'B' and 'A' very close together. There are six main segments marked between C and B, and a series of very small increments between B and A.

But if, finally, the line to be divided were very long, such that it greatly exceeded the maximum opening of the Instrument, we could in any case take the assigned part of it, which might be, for example, the seventh. Now, to find it, having first imagined two numbers, one seven times the other, such as 140 and 20, the Instrument is set to any opening, and from it, with a compass, one takes the transversal distance between points 140, 140. One sees how many times this is contained in the great proposed line, and as many times as it is contained, so many times the transversal interval between points 20, 20 should be repeated upon the great line, and one will have its seventh part. This holds when the interval taken between the points 140 has measured the given line precisely. But if it had not measured it exactly, one would need to take the seventh part of the remainder according to the method declared above, and add this to that interval which was repeated several times over the great line, and one will have the seventh part exactly as desired.