To construct, in a given rectilineal angle, a parallelogram equal to a given triangle.
作一个平行四边形，使它等于给定三角形，并有一个角等于给定直线角。
在给定角 D 中作平行四边形 EFCG 使其面积等于三角形 ABC。E 为 BC 中点；EF、CG 与 AE 平行；∠CEF = D。
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Let ABC be the given triangle, and D the given rectilineal angle; thus it is required to construct in the rectilineal angle D a parallelogram equal to the triangle ABC. Let BC be bisected at E, and let AE be joined; on the straight line EC, and at the point E on it, let the angle CEF be constructed equal to the angle D; [I. 23] through A let AG be drawn parallel to EC, and [I. 31] through C let CG be drawn parallel to EF.
先在给定点作一个角等于给定角（euclid-elements/book1-prop-023）。
Then FECG is a parallelogram.
作一条通过三角形顶点且平行于底边的直线（euclid-elements/book1-prop-031）。
And, since BE is equal to EC, the triangle ABE is also 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.
在同底同平行线间作平行四边形，使它以给定角为角。
And it has the angle CEF equal to the given angle D.
由 euclid-elements/book1-prop-041，取合适底边时该平行四边形等于给定三角形。