THE SOLUTION ATTRIBUTED TO PLATO 257 
produced. Then slide the movable strut KL, which remains 
always parallel to GH, until its edge (towards GH) passes 
through A. If now the inner angular point between the 
strut KL and the leg FG does not lie on BO produced, 
the machine has to be turned again and the strut moved 
until the said point does lie on BO produced, as M, care being 
taken that during the whole of the motion the inner edges 
of KL and HG pass through A, B respectively and the inner 
angular point at G moves along AO produced. 
That it is possible for the machine to take up the desired 
position is clear from the figure of Menaechmtis, in which 
MO, NO are the means between AO and BO and the angles 
AMN, MNB are right angles, although to get it into the 
required position is perhaps not quite easy. 
The matter may be looked at analytically thus. Let us 
take any other position of the machine in which the strut and 
the leg GH pass through A, B respectively, while G lies on AO 
produced, but P, the angular point between the strut KL and 
the leg FG, does not lie on OM produced. Take ON, OM as 
the axes of x, y respectively. Draw PR perpendicular to OG, 
and produce GP to meet OM produced in S. 
Let AO = a, BO = h, OG — r. 
s 
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