 | George Albert Wentworth - Geometry - 1895 - 468 pages
...construct R" similar to R. Then R" is the polygon required. Proof. PC? + PH*=OH\ .-., Now and ^L=^^_, §876 (similar polygons are to each other as the squares of their homologous sidei). By addition, R + f = AB + A'B'* = 1. PROPOSITION XV. PROBLEM. 385. To construct a polygon similar... | |
 | Michigan. Department of Public Instruction - Education - 1896 - 710 pages
...radius draw a circle tangent to the sides of a given angle. Demonstrate the solution. 7. Demonstrate: The areas of similar polygons are to each other as the squares of any two homologous sides of the polygons. 8. Define a plane. What determines the position of a plane?... | |
 | International Correspondence Schools - Surveying - 1898 - 518 pages
...: 50 s :: 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...area of a regular hexagon with a side of 10 inches is 250.809 sq. in., the area of a similar hexagon whose side is 15 inches may be found as follows: 10'... | |
 | Webster Wells - Geometry - 1898 - 264 pages
...hypotenuse of a right triangle is 5 ft. 5 in., and one of its s, , J^ PROP. IX. THEOREM. A 322. Two similar polygons are to each other as the squares of their homologous sides. A' B' Given AB and A'B' homologous sides of similar polygons AC and A'C', whose areas are JTand K',... | |
 | George Albert Wentworth - Geometry - 1898 - 462 pages
...1 + PJ2"'= O/T, .-. AI? + A'B* -- Now _ti" A '' J3 ' '' and 4 == j4JL, §376 f>l AI fjl 1 (»imilar polygons are to each other as the squares of their homologous sides). By addition, R" A"B '(t PROPOSITION XV. PROBLEM. 385, To construct a polygon similar to two given similar... | |
 | James Howard Gore - Geometry - 1898 - 232 pages
...each other (by 262) as the squares of their homologous sides. Therefore the sums of the triangles or polygons are to each other as the squares of their homologous sides. PROPOSITION IX. THE PYTHAGOREAN THEOREM.* 265. In any right triangle the square described upon the... | |
 | International Correspondence Schools - Civil engineering - 1899 - 814 pages
...1,600 : area of DEF, or 6,400 : 2,500 :: 1,600 : 625 sq. ft. Hence, area of DEF is 625 sq. ft. 1 189. The areas of similar polygons are to each other as...Thus, if the area of a regular hexagon with a side of 1(1 inches is 259.809 sq. in., the area of a similar hexagon whose side is 15 inches may be found as... | |
 | Webster Wells - Geometry - 1899 - 450 pages
...altitude. Find each of its dimensions. (Let x represent the altitude.) PROP. IX. THEOREM. 322. Two similar polygons are to each other as the squares of their homologous sides. B' Given AB and A'B' homologous sides of similar polygons AC and AC', whose areas are /iTand K', respectively.... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...of their homologous sides. Consult Prop. 166, Cor. V. and Prop. 140. Proposition 178. Theorem. 214. Similar polygons are to each other as the squares of their homologous sides. K Hypothesis. AB and GH are homologous sides of the similar polygons ABCDEF and GHKMNO. Let their areas... | |
 | Webster Wells - Geometry - 1899 - 424 pages
...altitude. Find each of its dimensions. (Let z represent the altitude.) PROP. IX. THEOREM. 322. Two similar polygons are to each other as the squares of their homologous sides. 3~ B A' B' Given AB and A'B' homologous sides of similar polygons AC and AC', whose areas are /fand... | |
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Now, since the areas of similar polygons are to each other as the squares of their homologous sides... 
