Operations of the Geometric and Military Compass

A geometric diagram depicts two similar irregular hexagons, one nested within the other. The inner hexagon's vertices are labeled A, B, C, D, E, and F. The outer hexagon's vertices are labeled G, H, I, K, L, and M. Near vertex H of the larger hexagon, dashed lines and arcs (labeled N, O, Q, and R) show the geometric construction used to find the corresponding point I and ensure the angle at H is equal to the angle at B using a compass and proportional scales.

the line G H and see how many points it contains on the straight scale. Having seen it contains, for example, 60, take its corresponding A B and apply it transversally to the points 60, 60. Do not move the Instrument further. To then find the line H I corresponding to B C, take that B C with the compass and go investigating at which points it fits upon the transversal scale. Having found it fits, for example, at points 46, immediately take the interval of points 46 upon the straight scale, and you will find the length of the line H I corresponding to B C. And note, as much for this as for the previous operation, that it is not enough to have found the length H I if one does not also find to what point it must be aimed so that it constitutes angle H equal to angle B. However, once that line H I is found, having fixed one leg of the compass at point H, one will note with the other, secretly, a portion of an arc according to what the dashed line O I N shows. Then, take the interval between point A and point C and seek how many points it is upon the transversal scale,