 | William Chauvenet - 1893 - 340 pages
...equivalent. PROPOSITION II. Two rectangles having equal altitudes are to each other as their bases. Corollary. Two rectangles having equal bases are to each other as their altitudes. PROPOSITION III. Any two rectangles are to each other as the products of their bases by their altitudes.... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...areas of two rectangles having equal altitudes are to each other as their bases. 361. Cor. The areas of two rectangles having equal bases are to each other as their altitudes. 362. The areas of two rectangles are to each other as the products of their bases by their altitudes.... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...X b' [Two rectangles having equal altitudes are to each other as their bases.] And —,-=-,' §378 [Two rectangles having equal bases are to each other as their altitudes.] Multiplying, A. J\. R axt> RX ba — x — =— x— , X R' V a' or QED R X t R' a a PROPOSITION IV.... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 554 pages
...Ax. a Hence the rectangles coincide throughout and are equal. § 1 5 QED PROPOSITION II. THEOREM 378. Two rectangles having equal bases are to each other as their altitudes. GIVEN — two rectangles AC and A'C, having equal bases, AD and A'D'. rect. AC AB To PROVE rect. A'C... | |
 | James Howard Gore - Geometry - 1898 - 232 pages
...i 1 ! F Tf QED 246. COR. Since either side of a rectangle may be taken as the base, it follows that Two rectangles having equal bases are to each other as their altitudes. PROPOSITION II. THEOREM. 247. Any tivo rectangles are to each other as the products of their bases... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...are incommensurable. 169 Use the method of proof given in Prop. 79, and consult Prop. 55, Cor. COB. Two rectangles having equal bases are to each other as their altitudes. Proposition 163. Theorem. 199. Any two rectangles are to each other as the products of their bases... | |
 | Edward Brooks - Geometry, Modern - 1901 - 278 pages
...and „, , rect. AC AB We have — 7 — r^=-r^recLAF AE Or ABCD : AEFD = AB : AE. II. 16. COR. — Two rectangles having equal bases are to each other as their altitudes. For their altitudes may be regarded as bases, and their bases as altitudes. PROPOSITION III. — THEOREM.... | |
 | William Chauvenet - 1905 - 336 pages
...for its limit. AE AE Therefore, by II., Theorem, Doctrine of Limits, = - (-H, 42, and III., 14.) 6. COROLLARY. Two rectangles having equal bases are to each other as their altitudes. Note. In these propositions, by " rectangle" is to be understood " surface of the rectangle." PROPOSITION... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...(?), ES EG and — will approach — as a limit (?). ER EF .-. = (?) (242). EG EF JED 369. THEOREM. Two rectangles having equal bases are to each other as their altitudes. (Explain.) 370. THEOREM. Any two rectangles are to each other as the products of their bases by their... | |
 | International Correspondence Schools - Building - 1906 - 634 pages
...40. Since any of the sides of a rectangle can be considered as the base, it follows that the area of two rectangles having equal bases are to each other as their altitudes. 41. The areas of any two rectangles are to each other as the products of their bases by their altitudes.... | |
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Any two rectangles are to each other as the products of their bases by their altitudes. 
