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The ratio of AD original: 甲丁 to DB original: 丁乙 is the same as the ratio of AE original: 甲戊 to EC original: 戊丙; therefore, the ratio of triangle AED original: 甲戊丁 to triangle DEB original: 丁戊乙 is also the same as the ratio of AE to EC. Book 15, Proposition 11 Furthermore, since the ratio of the two bases AE to EC is the same as the ratio of triangle AED to triangle DEC since they lie between two parallel lines, see Proposition 1 of this volume, then the ratio of triangle AED to triangle DEB is also equal to the ratio of triangle AED to triangle DEC. Book 15, Proposition 11 And triangle DEB and triangle DEC are equal. Book 5, Proposition 39 If two triangles have the same base DE and are equal, then they lie between the same parallel lines. Book 1, Proposition 39
A geometric diagram displays a large triangle divided by internal lines. Points are labeled with celestial stems: 甲 (Jia) at the top vertex, 戊 (Wu) on the left side, 丁 (Ding) on the right side, 丙 (Bing) at the bottom left, and 乙 (Yi) at the bottom right. A horizontal line connects 戊 and 丁, and diagonal lines connect 戊 to 乙 and 丁 to 丙, intersecting in the center.