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论述等积问题,以割补为上策。试举例说明如下: 甲.同底等高的平行四边形及矩形,二者等积。胡敦复、吴在渊:高中几何学(中华书局)(§334),周宣德:现代初中几何(商务印书馆)(§209),及Stone-Millos:Plane and Solid Geometry(§214)三书对这个定理的证明,大意是(图1): III≌I, II≌II, ∴ III+II=I+II, 乙.斜棱柱与以其正截面为底、侧棱为高的直棱柱等积。黄元吉:共和国立体几伺(商务印书馆)(§.365),胡敦复、吴在渊高中几何(中华书局)(§549),Wentworth(§612) Wentworth-Smith (§525) Ford-Ammerman(§284) 诸书对这个定理的征明,大意是(图2):
Discuss the equal-volume problem and take the cut-up as the best policy. The example is illustrated as follows: A. Parallelograms and rectangles with the same height as the bottom, the equal product of the two. Hu Dunfu, Wu Zaiyuan: High School Geometry (Zhonghua Book Company) (§334), Zhou Xuande: Modern Junior Middle School Geometry (Commercial Press) (§209), and Stone-Millos: Plane and Solid Geometry (§214) The proofs are as follows (Figure 1): III≌I, II≌II, ∴III+II=I+II, B. Equal product of an oblique prism and a straight prism with the front cross section as the base and the side edge as the height. Huang Yuanji: Republic of the Three-dimensional (The Commercial Press) (§ 365), Hu Dunfu, Wu Zaiyuan High School Geometry (Zhonghua Book Company) (§549), Wentworth (§612) Wentworth-Smith (§525) Ford-Ammerman (§284 The significance of the book’s examination of this theorem is (Figure 2):