The Operations of the Geometric and Military Compass

A geometric diagram illustrates the proportional scaling of a polygon. An inner irregular hexagon is labeled with vertices A, B, C, D, E, and F. An outer, larger irregular hexagon is labeled with vertices G, H, I, K, L, and M. Dotted lines and arcs are used to show the construction of vertex I based on the orientation and length of the segment BC in the smaller figure. Points N, O, Q, and R are labeled around the dotted arc and construction lines extending from vertex H.

the line G H, and see how many points it contains on the straight scale. Having seen that it contains, for example, 60, take its corresponding A B, and apply it transversally to the points 60, 60, and move the Instrument no more. To then find the line H I, corresponding to the B C, take with the compass that B C and go investigating to which points it accommodates itself upon the transversal scale. Once found to accommodate itself, for example, to the points 46, take immediately the interval of the points 46 upon the straight scale, and you will find the length of the line H I, corresponding to the B C. And note, as much for this as for the preceding 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 directed so that it constitutes the angle H, equal to the angle B. Therefore, once such line H I has been found, with one leg of the compass fixed in the point H, one will note with the other, done subtly, a portion of an arc as shown by the dotted line O I N. Then one will take the interval between point A and point C, and one will search how many points it is upon the transversal scale,