508 
[614 
614. 
ON A PROBLEM OF PROJECTION. 
[From the Quarterly Journal of Pure and Applied Mathematics, vol. xm. (1875), 
pp. 19—29.] 
I measure off on three rectangular axes the distances OX = £lY=£lZ, =6; and 
then, in a plane through O drawing in arbitrary directions the three lines flA, CIB, D.C, 
= a, b, c respectively, I assume that A, B, C (fig. 1) are the parallel projections of 
X, Y, Z respectively; viz. taking OO as the direction of the projecting lines, then 
flA, VLB, 0(7 being given in position and magnitude, we have to find 6, and the 
position of the line OO. 
Fig. l. 
This is in fact a case of a more general problem solved by Prof. Pohlke in 1853, 
(see the paper by Schwarz, “ Elementarer Beweis des Pohlke’schen Fundamentalsatzes der 
Axonometrie,” Grelle, t. lxiii. (1864), pp. 309—314), viz. the three lines OX, OF, OZ 
may be any three axes given in magnitude and direction, and their parallel projection