 | Charles Davies, Adrien Marie Legendre - 1885 - 538 pągines
...equal to AE : hence, ABCD : AEFD :: AB : AE ; which was to be proved. H E C B PROPOSITION IV. THEOREM. Any two rectangles are to each other as th-e products of their bases and altitudes. Let ABCD and AEGF be two rectangles: then ABCD is to AEGF, as ABxAD is to AExAF. For,... | |
 | Charles Davies - 1886 - 352 pągines
...to any other rectangles whose bases are whole numbers : hence, AEFD : EBCF : : AE : EB. THEOREM VI. Any two rectangles are to each other as the products of their bases and altitudes. DC Let ABCD and AEGF be two rectangles : then will ABCD : AEGF : ABxAD : AFxAE For,... | |
 | Webster Wells - 1886 - 392 pągines
...the unit of length. To prove that the area of A, referred to B as the unit, is equal to ax b. Since any two rectangles are to each other as the products of their bases by their altitudes (§ 318), we have A _a xb B~ 1 x 1 = ax b. A But since B is the unit of surface,... | |
 | William Chauvenet, William Elwood Byerly - 1887 - 331 pągines
...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. PROPOSITION IV. The area of a rectangle is equal to the product of its base and... | |
 | William Chauvenet, William Elwood Byerly - 1887 - 332 pągines
...rectangle" is to be understood " surface of the rectangle." ' I '*•-'. - PROPOSITION III.— THEOREM. 7. Any two rectangles are to each other as the products of their loses by their altitudes. Let It and R' be two rectangles, k and It their bases, h and h' their altitudes... | |
 | George Albert Wentworth - 1888 - 272 pągines
...From (1) and (2) rect. AF AE Ax. 1 PLANE GEOMETRY. BOOK IV. PROPOSITION II. THEOREM. 362. The areas of two rectangles are to each other as the products of their bases by their altitudes. b b. b Let R and R' be two rectangles, having for their bases b and b', and for... | |
 | George Albert Wentworth - 1889 - 264 pągines
...altitudes; and two rectangles having equal altitudes are to each other as their bases. 177. Theorem. Any two rectangles are to each other as the products of their bases and altitudes. 178. Theorem. Area of a rectangle = base X altitude. 179. Theorem. Area of a square... | |
 | George Albert Wentworth - 1889 - 276 pągines
...altitudes; and two rectangles having equal altitudes are to each other as their bases. 177. Theorem. Any two rectangles are to each other as the products of their bases and altitudes. 178. Theorem. Area of a rectangle = base X altitude. 179. Theorem. Area of a square... | |
 | Edward Albert Bowser - 1890 - 418 pągines
...yards and whose altitude is the same as that of the first ? Proposition 2. Theorem. 358. The areas of any two rectangles are to each other as the products of their bases by their altitudes. Hyp. Let R and R' be two rectangles, b and b' their bases, a and a' their altitudes,... | |
 | Nicholas Murray Butler, Frank Pierrepont Graves, William McAndrew - 1892 - 544 pągines
...equal to the product of its base and altitude, reference is made to the proposition that " the areas of two rectangles are to each other as the products of their bases by their altitudes" making the former proposition depend upon the latter. To expose the fallacy of... | |
| |
K hag to M the ratio which is compounded of the ratios of the sides ; therefore also the parallelogram AC has to the parallelogram CF the ratio which is compounded of the ratios of the sides. COR. Hence, any two rectangles are to each other as the products... 
