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ON RECIPROCAL FIGURES AND DIAGRAMS OF FORCES. 



The conditions are that the four intersections of corresponding sides of 

 opposite quadrilaterals in fig. V. shall lie in one straight line, parallel to the 



Fig. V. Fig. 5. 



line joining the opposite points of fig. 5 which correspond to these quadrilaterals. 

 There are three such lines marked x, y, z, and four points of intersection lie on 

 each line. 



We may express this condition also by saying that fig. V. must be a per- 

 spective projection of a plane-sided polyhedron, the intersections of opposite 

 planes being the lines x, y, z. 



In fig. 6, let ABCDE be a portion of a polygon bounded by other polygons 

 of which the edges are PQRST, one or more of these edges meeting each angle 

 of the polygon. 



In fig. VI., let abcde be lines parallel to ABCDE and meeting in a point, 

 and let these be terminated by the lines pqrst parallel to PQRST, one or 

 more of these lines completing each sector of fig. VI. 



In fig. 6 draw Y through the intersections of AC and PQ, and in fig. 

 VL draw y through the intersections of a, p and c, q. Then the figures of 

 six lines ABCPQY and dbcpqy will be reciprocal, and y will be parallel to Y. 

 Draw X parallel to x, and through the intersections of TX and CE draw Z, 

 and in fig. VI. draw z through the intersections of ex and et; then CDETXZ 



