TWO GEOMETRICAL PASSAGES IN THE MEND 299 
acceptance; nevertheless, I think that it is not the right one, 
but that the essentials of the correct interpretation were given 
by S. H. Butcher 1 (who, however, seems to have been com 
pletely anticipated by E. F. August, the editor of Euclid, in 
1829). It is necessary to begin with a literal translation of 
the passage. Socrates is explaining a procedure ‘ by way 
of hypothesis a procedure which, he observes, is illustrated 
by the practice of geometers 
‘ when they are asked, for example, as regards a given area, 
whether it is possible for this area to be inscribed in the form 
of a triangle in a given circle. The answer might be, “ I do 
not yet know whether this area is such as can be so inscribed, 
but I think I can suggest a hypothesis which will be useful for 
the purpose f I mean the following. If the given area is such 
as, when one has applied it (as a rectangle) to the given 
straight line in the circle \jryu SoOtTaav avrov y pa\jifir]v, the 
given straight line in it, cannot, I think, mean anything 
but the diameter of the circle 2 ], it is deficient by a figure 
(rectangle) similar to the very figure which is applied, then 
one alternative seems to me to result, while again another 
results if it is impossible for what I said to be done with it. 
Accordingly, by using a hypothesis, I am ready to tell you what 
results with regard to the inscribing of the figure in the circle, 
namely, whether the problem is possible .or impossible.’” 
Let AEB be a circle on AB as diameter, and let AG be the 
tangent at A. Take E any point on the circle and draw 
ED perpendicular to AB. Complete the rectangles AGED, 
EDBF. 
Then it is clear that the rectangle GEDA is ‘ applied ’ to 
the diameter AB, and also that it £ falls short ’ by a figure, the 
rectangle EDBF, similar to the ‘ applied ’ rectangle, for 
AD : DE = ED : DB. 
Also, if ED be produced to meet the circle again in G, 
AEG is an isosceles triangle bisected by the diameter AB, 
and therefore equal in area to the rectangle AGED. 
If then the latter rectangle, ‘applied’ to AB in the manner 
1 Journal of Philology, vol. xvii, pp. 219-25 ; cf. E. S. Thompson’s edition 
of the Meno. 
2 The obvious ‘line’ of a circle is its diameter, just as, in the first 
geometrical passage about the squares, the ypappy), the ‘ line ’, of a square