Page - 311 - in The Complete Plato

line? Remember that I am not speaking of an oblong, but of a figure equal every way, and twice the size of this—that is to say of eight feet; and I want to know whether you still say that a double square comes from double line? BOY: Yes. SOCRATES: But does not this line become doubled if we add another such line here? BOY: Certainly. SOCRATES: And four such lines will make a space containing eight feet? BOY: Yes. SOCRATES: Let us describe such a figure: Would you not say that this is the figure of eight feet? BOY: Yes. SOCRATES: And are there not these four divisions in the figure, each of which is equal to the figure of four feet? BOY: True. SOCRATES: And is not that four times four? BOY: Certainly. SOCRATES: And four times is not double? BOY: No, indeed. SOCRATES: But how much? BOY: Four times as much. SOCRATES: Therefore the double line, boy, has given a space, not twice, but four times as much. BOY: True. SOCRATES: Four times four are sixteen—are they not? BOY: Yes. SOCRATES: What line would give you a space of eight feet, as this gives one of sixteen feet;—do you see? BOY: Yes. SOCRATES: And the space of four feet is made from this half line? BOY: Yes. 311