9.6 Sector Compasses About 1597. Galileo perfected the sector compasses, an instrument that enjoyed considerable popularity for more than two centuries. The instrument consists of 2 arms fastened together at one end by a pivot joint, as shown in Figure 84 On each arm, there is a simple scale radiating from the pivot and having the 0 of the scale at the pivot. In addition to these simple scales, other scales have often been used, some of which will be described below. Many problems can readily be solved using the simple scales of the compasses, the only theory required being that of similar triangles. (a) Show how the sector compasses may be used to divide a given line segment into 5 equal parts. (b) Show how the sector compasses may be used to change the scale of a drawing. (c) Show how the sector compasses may be used to find the fourth propor- tional x to 3 given quantities a, b, c (that is, to find x where a: b = c:x), and thus applied to problems in foreign exchange