 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 554 pages
...Prove the last proposition by means of Proposition VIII. PROPOSITION X. THEOREM 401. The areas of two similar polygons are to each other as the squares of any two homologous sides. GIVEN— the similar polygons ABCDE and A'B'C'D'E', with sides a. b, c, d, e, and a', b', c', d', e',... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...• = — x - = — x- = — i A'B'C a'xb' a b' b' QED PROPOSITION X. THEOREM 401. The areas of two similar polygons are to each other as the squares of any two homologous sides. GIVEN—the similar polygons ABCDE and A'B'C'D'E', with sides a, b, c, d, e, and a', V, c', d', e '... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...polygons are to each other as the squares of any two homologous sides. 377. Cor. 1. The areas of two similar polygons are to each other as the squares of any two homologous lines. 378. Cor. 2. The homologous sides of two similar polygons have the same ratio as the square... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...Prove the last proposition by means of Proposition VIII. PROPOSITION X. THEOREM 401. The areas of two similar polygons are to each other as the squares of any two homologous s1des. GIVEN— the similar polygons ABCDE and A'B'C'D'E', with sides a, b, c, d, e, and a', b', c',... | |
 | George Washington Hull - Geometry - 1897 - 408 pages
...similar triangles (§ 272), M-£-£ §217 But '• £-j|, §273 PROPOSITION XXIX. THEOREM. 275. Two similar polygons are to each other as the squares of any two homologous sides. D K Given — P and P ' the areas of the similar polygons EB and LG respectively. To Prove— i- =... | |
 | International Correspondence Schools - Surveying - 1898 - 518 pages
...1,600 : area of DEF, or 6,400 : 2,500 :: 1,600 : 025 sq. ft. Hence, area of DE F.vs, 025 sq. ft. 1189. The areas of similar polygons are to each other as the squares of their homologous sides. Thus, if the area of a regular hexagon with a side of 10 inches is 250.809... | |
 | William Taylor Campbell - Geometry - 1899 - 264 pages
...sides makes the area of the polygon four times as great; and so on. This is expressed by saying that " the areas of similar polygons are to each other as the squares of any two corresponding sides." The square of a number is the number multiplied by itself; thus the square of... | |
 | George Albert Wentworth - Geometry, Plane - 1899 - 278 pages
...A'C'B' ™ A'B' A'B' A'B'2 QBD COMPARISON OF POLYGONS. PROPOSITION IX. THEOREM. 412. The areas of two similar polygons are to each other as the squares of any two homologous sides. Let S and S' denote the areas of the two similar polygons ABC etc. and A'B'C' etc. To prove that S... | |
 | George Albert Wentworth - Geometry, Solid - 1899 - 246 pages
...other are to each other as the products of the sides including the equal angles. 412. The areas of two similar polygons are to each other as the squares of any two homologous sides. 414. The homologous sides of two similar polygons have the same ratio as the square roots of their... | |
 | George Albert Wentworth - Geometry - 1899 - 498 pages
...AABE _ AB* v. .,„„ S <5Ot> AA'B'U' + AB'C'E' + AC'D'E' A A'B'E' A'B' 413. COR. 1. The areas of two similar polygons are to each other as the squares of any two homologous lines. \j 194 BOOK IV. PLANE GEOMETRY. PROPOSITION X. THEOREM. 415. The square on the hypotenuse of... | |
| |
The areas of two similar polygons are to each other as the squares of any two homologous sides. 
