| George D. Pettee - Geometry, Plane - 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 - 556 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 - Geometry - 1896 - 50 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... | |
| 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... | |
| 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 - 1899 - 424 pages
...a triangle similar to a given triangle. (§ 262.) BOOK IV. 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.,... | |
| Charles Austin Hobbs - Geometry, Plane - 1899 - 240 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... | |
| George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...are often used for ' ' area of rectangle, " " area of triangle, ' ' etc. PROPOSITION I. THEOREM. 395. **Two rectangles having equal altitudes are to each other as their bases.** Let the rectangles AC and AF have the same altitude AD. To prove that rect. AC : rect. AF = base AB... | |
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