 | David Munn - 1873 - 160 pages
...angles 47 IX. The areas of similar triangles are to each other as the squares of their like sides 48 X. The areas of similar polygons are to each other as the squares of their like sides 49 PXOPOSITIOH PACE XI. The area of a regular polygon is equal to its perimeter... | |
 | Adrien Marie Legendre - Geometry - 1874 - 512 pages
...on the supposition that each side is equal to 1, and the results are given in the following TABLE. The areas of similar polygons are to each other as the squares of their homologous sides (Book IV., Prop. XXVII.). Denoting the area of a regular polygon whose side... | |
 | Benjamin Greenleaf - Geometry - 1874 - 206 pages
...as any one antecedent ABC is to its consequent FGH(Theo. X. Bk. II.), or as ~AB* is to FG* • hence the areas of similar polygons are to each other as the squares described on their homologous sides. 219. Cor. 1. The perimeters of similar polygons are also to each... | |
 | Charles P. Florent Baillairgé - Measurement - 1876 - 306 pages
...1 .4619022 Decagon 1.6180340 Undecagon. . . 1 .7747324 Dodecagon. ..1.9318517 And because (56G G.) the areas of similar polygons are to each other as the squares of their homologous sides, the area of any given polygon will have to the square of its side the same... | |
 | Simon Newcomb - Geometry - 1881 - 418 pages
...of the common ratio of each side of the one to the homologous side of the other. THEOREM XXIII. 425. The areas of similar polygons are to each other as the squares upon their homologous sides. Hypothesis. A BCD and A'B'C'D', two similar polygons, in which AB and... | |
 | Edward Olney - Geometry - 1883 - 354 pages
...area~EFG AB' we have area ABC ACJ area EFG ~ ' EG' BC8 'FG' AB5 EF' BC PROPOSITION VIII. 409. Theorem. — The areas of similar polygons are to each other as the squares of any two homologous sides of the polygons. * The only object in taking the largest angles is to make... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...Decagon, ... 10 ... 7.6942088 TTndecagon, . . 11 . . . 0.3656399 Dodecagon, . . 12 . . . 11.1861524 The areas of similar polygons are to each other as the squares of their homologous sides (Book IV., Prop. XXVII.). Denoting the area of a regular polygon whose side... | |
 | Edward Albert Bowser - Geometry - 1890 - 420 pages
...of a similarlyshaped lot containing 4 times as much ? Ans. 80 rods. Proposition 1 O. Theorem. 379. The areas of similar polygons are to each other as the squares of their homologous sides. Hyp. Let S and S' denote the areas of the two similar polygons ABCDE and... | |
 | William Shaffer Hall - Measurement - 1893 - 88 pages
...4.8284271 Nonagon 9 6.1818242 Decagon 10 7.6942088 Undecagon 11 9.3656399 Dodecagon . 12 11.1961524 The areas of similar polygons are to each other as the squares of their homologous sides (Ww. Geom., 343). Denoting the area of a regular polygon whose side is s... | |
 | Adelia Roberts Hornbrook - Geometry - 1895 - 224 pages
...NOTE. — Demonstrative geometry will show you the truth of the following principle : PEINCIPLE 55. — The areas of similar polygons are to each other as the squares of their homologous sides. 137. The area of a heptagon, one of whose sides is 6 inches long, is 100... | |
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Now, since the areas of similar polygons are to each other as the squares of their homologous sides... 
