| Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...4.828427 Nonagon, 9 ' 6.181824 Decagon, 10 ' 7.694208 Undecagon 11 ' 9.365639 Dodecagon 12 " 11.196152 Now **the areas of similar polygons are to each other as the squares** of their like sides (Geom., B. IV., th. 11). Hence, to find the area of any regular polygon, we shall... | |
| Benjamin Greenleaf - Geometry - 1868 - 338 pages
...FGHIK, as any one antecedent ABC is to its consequent FGH (Prop. XI. 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. 278. Cor. 1. The perimeters of similar polygons are also to each... | |
| Edward Brooks - Geometry - 1868 - 294 pages
...Octagon 4.8284271 Nonagon 6.1818242 Decagon 7.G942088 Undecagon 9.3656404 Dodecagon 11.1961524 Now, since **the areas of similar polygons are to each other as the squares** of their homologous sides, to find the area of a regular polygon we have the following RULE.—Square... | |
| Horatio Nelson Robinson - Geometry - 1868 - 276 pages
...similar, (Def. 16, B. II). Hence the theorem; a plane passed through a pyramid, etc. Cor , 1. Since **the areas of similar polygons are to each other as the squares** of their homologous sides, (Th. 22, B II), we have area abode : area ABCDE : ab1 : AB*. , . But, ab... | |
| Edward Olney - Geometry - 1872 - 472 pages
...area ABC : area DEF : : CB' : FE" :: Ä~Cз : DT1 : : AB" : DE', QED PROPOSITION IX. 363. Theorem. — **The areas of similar polygons are to each other as the squares** of the homologous sides of the polygons. AREAS OF SIMILAR FIGURES. F1o. 251. DEM.— Let abedef and... | |
| Charles Davies - Geometry - 1872 - 464 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. XXVIL). Denoting the area of a regular polygon whose side... | |
| Edward Olney - Geometry - 1872 - 566 pages
...area ABC : area DEF : : CB~' t FE* :: AC* : DF1 : : ABJ : DE*. QKD PROPOSITION IX. 303. Ttieorem. — **The areas of similar polygons are to each other as the squares** of the homologous sides of the polygons. AREAS OP SIMILAB FIGURES. Flo. 231. DKM.— Let abcdef and... | |
| Charles P. Florent Baillairgé - Geometry - 1873 - 658 pages
...1.2071008 9 1.3737387 II) J. 5388 1 48 11 1.7028430 12 1.8000254 .. 11.1901521 .. 75 And because (565 ft.) **the areas of similar polygons are to each other as the squares** of their homologous sides, the urea of any given polygon will have, to the square of its side the same... | |
| Aaron Schuyler - Measurement - 1864 - 506 pages
...of a similar polygon whose side is 1, as given in the table by kj, and applying the principle that **the areas of similar polygons are to each other as the squares** of the homologous sides, we have the proportion, fc : fc' 1*. k = ¿'s2. 169. Examples. 1. What is... | |
| Benjamin Greenleaf - Geometry - 1873 - 202 pages
...perimeters of similar polygons are also to each other as their corresponding diagonals. 220. Cor. 2. **The areas of similar polygons are to each other as the squares** described on their corresponding diagonals. THEOREM XXII. 221. Regular polygons of the same number... | |
| |