 | William Chauvenet - Geometry - 1871 - 380 pages
...which AEFD will contain 4 ; consequently, we have ABCD 1 AEFD ~ 4' and therefore ABCD AS AEFD ~ AE The demonstration is extended to the case in which...understood " surface of the rectangle." PROPOSITION II.— THEOREM. 5. Any two rectangles are to each other as the products of their bases by their altitudes.... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...which AEFD will contain 4; consequently, we have ABCD = 7 AEFD ~~ 4and therefore ABCD AB AEFD ~~ AE The demonstration is extended to the case in which...the altitudes, it follows that two rectangles having 9qual bases are to each other as their altitudes. Note. In these propositions, by " rectangle" is to... | |
 | George Albert Wentworth - Geometry - 1877 - 436 pages
...rect. AF are always equal .'. their limits are equal, namely, AE rect. AC §199 AB QED 314. COROLLARY. Two rectangles having equal bases are to each other as their altitudes. By considering the bases of these two rectangles AD and AD, the altitudes will be AB and A E. But we... | |
 | George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...their limits ; rect. AF .-. their limits are equal, namely, = ., § 199 rect. AC AB QED 314. COROLLARY. Two rectangles having equal bases are to each other as their altitudes. By considering the bases of these two rectangles AD and AD, the altitudes will be AB and A E. But we... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...equal. Hence, ABCD _ AD 153 317. COROLLARY. 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. 318. Any two rectangles are to each other as the products of their bases by... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 336 pages
...its limit. Therefore, by II., Theorem, Doctrine of Limits, (-II-, 42, and III., 14.) 6. COROLLARY. Two rectangles having equal bases are to each other...understood " surface of the rectangle." PROPOSITION III.— THEOREM. 7. Any two rectangles are to each other as the products of their bases by their altitudes.... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 332 pages
...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.... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...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.... | |
 | William Chauvenet - Geometry - 1888 - 826 pages
...which AEFD will contain 4; consequently, we have ABCD 1 AEFD ~ 4' and therefore ABCD _ AB AEFD ~ AE The demonstration is extended to the case in which...incommensurable, by the process already exemplified in (II. 61) and (III. 15). 4. Corollary. Since AD may be called the base, and AB and AE the altitudes, it follows... | |
 | George Albert Wentworth - Geometry - 1888 - 264 pages
...are constantly equal, and each approaches a limit, the limits arc equal). a ED 361. COB. The areas of two rectangles having equal bases are to each other as their altitudes. For AB and AE may be considered as the altitudes, AD and AD as the bases. PROPOSITION II. THEOREM.... | |
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Any two rectangles are to each other as the products of their bases by their altitudes. Let R and R... 
