| 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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