302 
PLATO 
it about E until it passes through a point P of the circle such 
that, if EP meets AB and AC produced in T, R, PT shall be 
equal to ER. Then, since RE=PT, AD —AIT, where M is 
the foot of the ordinate PAL 
Therefore DT — A AT, and 
AAI-.AD = DT-.A1T 
— ED: PM, 
whence PM . MA = ED. DA, 
and APAI is the half of the required (isosceles) triangle. 
Benecke criticizes at length the similar interpretation of the 
passage given by E. F. August. So far, however, as his objec 
tions relate to the translation of particular words in the 
Greek text, they are, in my opinion, not well founded. 1 For 
the rest, Benecke holds that, in view of the difficulty of the 
problem which emerges, Plato is unlikely to have introduced 
it in such an abrupt and casual way into the conversation 
between Socrates and Meno. But the problem is only one 
of the same nature as that of the finding of two mean 
proportionals which was already a famous problem, and, as 
regards the form of the allusion, it is to be noted that Plato 
was fond of dark hints in things mathematical. 
If the above interpretation is too difficult (which I, for one, 
do not admit), Benecke’s is certainly too easy. He connects 
his interpretation of the passage with the earlier passage 
about the square of side 2 feet; according to him the problem 
is, can an isosceles right-angled tri 
angle equal to the said square be 
inscribed in the given circle 1 ? This 
is of course only possible if the 
radius of the circle is 2 feet in length. 
If AB, DE be two diameters at right 
angles, the inscribed triangle is ADE; 
the square ACDO formed by the radii 
AO, 0D and the tangents at D, A 
is then the ‘ applied ’ rectangle, and 
the rectangle by which it falls short is also a square and equal 
1 The main point of Benecke’s criticisms under this head has reference 
to toiovtco )((Oj>La> oiav in the phrase iWe'nuiv rotovrco ^copt« OLOV * IV ovro to 
TTapnr.Tafifvov y. He will have it that toiovtco olov cannot mean ‘ similar to ’,