 | George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...Proof. Draw the altitudes CO and C'O'. A ACB ABxCO AB CO B' A A'C'B' A'B ' X C'O' A'B' C'O' (two A are to each other as the products of their bases by their altitudes). But §405 AB CO A'B ' C'O' §361 (the homologous altitudes of two similar A have the same ratio as... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...altitude a. But the sum of the bases of the triangular prism equals B. .-.V=Bxa. 570. COR. 1. Prisms are to each other as the products of their bases by their altitudes. i 572. COR. 3. Prisms that have equal altitudes are to each other as their bases. 573. COR. 4. Prisms... | |
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...regarded as bases, and their bases as altitudes. PROPOSITION III. — THEOREM. Any two rectangles are to each other as the products of their bases by their altitudes. Given. — Let R and R' represent two rectangles whose bases are respectively 6 and b', and altitudes... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...altitude a. But the sum of the bases of the triangular prism equals B. .:V=Bxa. 570. COR. 1. Prisms are to each other as the products of their bases by their altitudes. 572. COR. 3. Prisms that have equal altitudes are to each other as their bases. 573. COK. 4. Prisms... | |
 | Education - 1902 - 880 pages
...perpendicular to a chord bisects the chord and its subtended arc. 4 Prove that the areas of two rectangles are to each other as the products of their bases by their altitudes. 5 Prove that two regular polygons of the same number of sides are similar. Second 6 The base of a triangle... | |
 | Education - 1902 - 780 pages
...perpendicular to a chord bisects the chord and its subtended arc. 4 Prove that the areas of two rectangles are to each other as the products of their bases by their altitudes. 5 Prove that two regular polygons of the same number of sides are similar. Second 6 The base of a triangle... | |
 | George Albert Wentworth - Geometry, Solid - 1902 - 246 pages
...altitudes; triangles having equal altitudes are to each other as their bases; any two triangles are to each other as the products of their bases by their altitudes. 410. The areas of two triangles which have an angle of the one equal to an angle of the other are to... | |
 | American School (Chicago, Ill.) - Engineering - 1903 - 390 pages
...; two triangles having equal bases are to each other as their altitudes ; and any two triangles are to each other as the products of their bases by their altitudes. 200. Corollary 111. A triangle is equivalent to one-half a parallelogram having the same base and altitude.... | |
 | Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...(WhyT) QED BOOK IV. PLANE GEOMETRY PROPOSITION II. THEOREM 382. ' The areas of any two rectangles are to each other as the products of their bases by their altitudes. Given the rectangles R and R', having the bases 6 and b', and the altitudes a and a', respectively.... | |
 | Fletcher Durell - Geometry - 1911 - 553 pages
...QED 234 BOOK IV. PLANE GEOMETRY PRGPOSIT ION II . TH EG RKM 382. The areas of any two rectangles are to each other as the products of their bases by their altitudes. Given the rectangles R and Rr , having the bases 1) and V ', and the altitudes a and oJ ', respectively.... | |
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Any two rectangular parallelopipedons are to each other as the products of their bases by their altitudes ; that is to say, as the products of their three dimensions. 
