T H E E L E M E N T S |
Book VI Proposition 20 | |
And, since the angle BAM is equal to the angle GFN, and the angle ABM is equal to the angle FGN, therefore the remaining angle AMB is also equal to the ramaining angle FNG; [I.32] therefore the triangle ABM is equiangular with the triangle FGN. Similarly we can prove that the triangle BMC is also equiangular with the triangle GNH. Therefore, proportionally, as AM is to MB, so is FN to NG, and as BM is to MC, so is GN to NH; so that, in addition, ex aequali, as AM is to MC, so is FN to NH. |
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