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[87a] whether a certain area is capable of being inscribed as a triangular space in a given circle: they reply—“I cannot yet tell whether it has that capability; but I think, if I may put it so, that I have a certain helpful hypothesis for the problem, and it is as follows: If this area1 is such that when you apply it to the given line2 of the circle you find it falls short3 by a space similar to that which you have just applied, then I take it you have one consequence, and if it is impossible for it to fall so, then some other. Accordingly I wish to put a hypothesis, before I state our conclusion as regards inscribing this figure

1 The problem seems to be that of inscribing in a circle a triangle (BDG) equal in area to a given rectangle (ABCD).

2 i.e., the diameter (BF).

3 i.e., falls short of the rectangle on the diameter (ABFE).

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