| George Albert Wentworth - Geometry - 1877 - 426 pages
...perimeters. Denote the perimeter of the first by P, and that of the second by P'. Then £, = ¿|, §295 **(the perimeters of two similar polygons have the same ratio as any two homologous sides).** But ^ = ^8; §296 B' 0' A' B' BO P . , . . = — Aх. l B' 0' P' Ex. 1. If any two straight lines be... | |
| George Albert Wentworth - 1881 - 266 pages
...Denote the perimeter of the first by P, and that ~of the second by P'. Then L = AB , § 295 l" A' B' **(the perimeters of two similar polygons have the same ratio as any two homologous sides).** But 2ÎL = Jfjf. : § 296 B'0' A' B'' * BO P . Ax. 1 Bf 0' P' Ex. 1. If any two straight lines be cut... | |
| George Albert Wentworth - Geometry - 1888 - 272 pages
...proportional). In like manner we may prove A ECD and E'C'D' similar. QED PROPOSITION XIV. THEOREM. 333. **The perimeters of two similar polygons have the same ratio as any two homologous sides.** E B c B' C" Let the two similar polygons be ABCDE and A'B'C'D'E', and let P and P' represent their... | |
| James Wallace MacDonald - Geometry - 1894 - 76 pages
...you can from two similar triangles ; from two similar quadrilaterals ; from two similar pentagons. **Proposition IV. A Theorem. 209. Two triangles whose...common point. CASE II. When they are on opposite sides.** NOTE. This principle may be used in finding the sides in Proposition VII. Proposition X. A Theorem.... | |
| George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...number of triangles, similar pair by pair, and similarly placed. 229. Theorem. The perimeters of any **two similar polygons have the same ratio as any two homologous sides.** a mean proportional between the segments of the hypotenuse. 231. Theorem. A leg of a right triangle... | |
| John Macnie - Geometry - 1895 - 390 pages
...similarly placed triangles in P'. .: P and P' may be divided as stated. QED PROPOSITION XIX. THEOREM. 296. **The perimeters of two similar polygons have the same ratio as any two homologous sides.** Given: AB, A'B', any two homologous sides of two similar polygons, P, P', of which p andp' are the... | |
| Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...special case. 307. Def. — The perimeter of a polygon is the sum of its PROPOSITION XIII. THEOREM 308. **The perimeters of two similar polygons have the same ratio as any two homologous sides.** £—'c' »' GIVEN—the perimeters P and P ' of the two polygons ABCDE and A'B'CD'E'. Jr __si tf -o... | |
| George Albert Wentworth - Geometry - 1896 - 68 pages
...they are composed of the same number of triangles, similar each to each, and similarly placed. 333. **The perimeters of two similar polygons have the same ratio as any two homologous sides.** 334. If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse... | |
| Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...case. 307. Def. — The perimeter of a polygon is the sum of its sides. PROPOSITION XIII. THEOREM 308. **The perimeters of two similar polygons have the same ratio as any two homologous sides.** 'GIVEN— the perimeters P and f of the two polygons ABCDE and A'B'C'D'E'. P AB BC CD TO PROVE _=—-—:... | |
| Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 554 pages
...307. Def. — The perimeter of a polygon is the sum of it sides. PROPOSITION XIII. THEOREM 308. TIu **perimeters of two similar polygons have the same ratio as any two homologous sides.** ' GIVEN— the perimeters P and P' of the two polygons ABCDE and A'B'CD'E'. TO PROVE P__A_B__BC_ _CD... | |
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