T H E E L E M E N T S |
Book I Proposition 42 | |
And, since BE is equal to EC, the triangle ABE is equal to the triangle AEC, for they are on equal bases BE, EC and in the same parallels BC, AG [I.38]; therefore the triangle ABC is double of the triangle AEC. But the parallelogram FECG is also double of the triangle AEC, for it has the same base with it and is in the same parallels with it; [I.41] therefore the parallelogram FECG is equal to the triangle ABC. And it has the angle CEF equal to the given angle D. |
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