 | William Chauvenet - 1893 - 340 pages
...equivalent to a rectangle having the same base and the same altitude. PROPOSITION II.—THEOREM. 5. Two rectangles having equal altitudes are to each other as their bases, Let ABCD and AEFD be two - OOF rectangles having equal altitudes; then are they to each other as AB:... | |
 | George D. Pettee - Geometry, Modern - 1896 - 272 pages
...equal, n FD E' D' Dem. Prove by superposition, noting the coincidence PROPOSITION II 240. Theorem. Two rectangles having equal altitudes are to each other as their bases. a Appl. Cons. E a A kI—:H : L t JI.D Case I. When the bases are commensurable. ^ = ^ ABEF AF measure... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...[If two variables are always equal and each approaches a limit, the limits are equal.] QED 379. COR. Two rectangles having equal altitudes are to each other as their bases. PROPOSITION III. THEOREM 380. Any two rectangles are to each other as the products of their bases and... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 554 pages
...[If two variables are always equal and each approaches a limit, the limits are equal.] QED 379. COR. Two rectangles having equal altitudes are to each other as their bases. Hint. — AD and A' D' may be regarded as the altitudes, and AB and A' B' as the bases. PROPOSITION... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...polygon, to construct a polygon similar to the given polygon. BOOK IV. THEOREMS. 360. The 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.... | |
 | George Washington Hull - Geometry - 1897 - 408 pages
...altitude. 221. COR. 2.—Triangles having equal bases and equal altitudes are equivalent. PROPOSITION II. THEOREM. 222. Two rectangles having equal altitudes are to each other as their bases. CASE I.— When the bases are commensurable. D ,c Given—ABCD and EFGH any two rectangles having equal... | |
 | James Howard Gore - Geometry - 1898 - 232 pages
...terminal points of the former. Thus A'B' 1-1 e projection of AB on XX'. PROPOSITION I. THEOREM. 245. Two rectangles * having equal altitudes are to each other as their bases. D 0 0 Let the two rectangles be AC and AF, having the same altitude AD. m 4.1, , AECD AB To prove that... | |
 | Webster Wells - Geometry - 1898 - 250 pages
...a triangle similar to a given triangle. (§ 262.) BOOK IT. AREAS OF POLYGONS PROP. I. THEOREM. 299. Two rectangles having equal altitudes are to each other as their bases. Note. The words "rectangle," "parallelogram," "triangle," etc., in the propositions of Book IV., mean... | |
 | Harvard University - Geometry - 1899 - 39 pages
...THEOREM I. Parallelograms having equal bases and equal altitudes are equivalent. THEOREM II. The areas of two rectangles having equal altitudes are to each other as their bases. THEOREM III. The areas of two rectangles are to each other as the products of their bases and their... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...segments of the same parallel lines as the respective bases of the other. Proposition 162. Theorem. 198. Two rectangles having equal altitudes are to each other as their bases. CASE I. When the bases are commensurable. CASE II. Wlten the bases are incommensurable. 169 Use the... | |
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Two rectangles having equal altitudes are to each other as their bases. 
