The Operations of the Geometric and Military Compass

versal between the points of this smaller number, this will without any doubt divide the proposed line into the parts ordered for us, as for example.

Having to divide the given line into five equal parts, we take two numbers of which the greater is quintuple original: "quintuplo" of the other, such as 100 and 20, and having opened the Instrument, we adjust it so that the distance already taken with the compass fits transversally to the points marked 100 and 100. And without moving the Instrument any further, one should take the distance, also transversal, between the points of the same lines marked 20 and 20, because undoubtedly this will be the fifth part of the proposed line; and with a similar order, we shall find every other division, taking care to take large numbers provided one does not pass 250, because by doing so the operation will turn out easier and more exact.

We shall be able to achieve the same by operating in another way, and the order will be as such. Wishing to divide, for example, the subjoined line A B, v. g. verbi gratia; for example into 11 parts, I will take a number multiple of the other eleven times, such as 110 and 10, and having taken the entire line A B with the compass, I will accommodate it transversally by opening the Instrument to the points 110. Then, since it is not possible to take the distance between points 10 and 10 upon the same lines, as they are occupied by the size of the nocella the pivot or joint of the compass, in place of this, one will take the interval between points 100 and 100, tightening the compass a little; from which, once an arm is fixed at point B, I will mark point C with the other, wherefore the remaining line A C will be the eleventh part of the whole A B. Similarly, having fixed the arm of the compass in A, I will mark towards the other extremity the point