H
E
E
L
E
M
E
N
T
S
therefore the circle described with center G and distance one of the straight lines GE, GF, GH, GK will not cut the straight lines AB, BC, CD, DA.
Therefore it will touch them, and will have been inscribed in the square ABCD.
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T H E E L E M E N T S |
Book IV Proposition 8 | |
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For,
if the circle cuts AB, BC, CD, DA, the straight line drawn at right angles to the diameter of the circle from its extremity will fall within the circle: which was proved absurd; [III.16] therefore the circle described with center G and distance one of the straight lines GE, GF, GH, GK will not cut the straight lines AB, BC, CD, DA. Therefore it will touch them, and will have been inscribed in the square ABCD. |
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