 | 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... | |
 | Edward Brooks - Geometry - 1868 - 284 pages
...3.6339124 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 the side of the polygon,... | |
 | Horatio Nelson Robinson - Geometry - 1868 - 276 pages
...therefore 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 : AB :: Va : VA :: Fl : FE;... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 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... | |
 | Charles Davies - Geometry - 1870 - 392 pages
...III. Th. xii). ABC+ADC+ADE : FGN+FIN+FIK : : ÄZ? : FG*; that is, ABCDE : FGNIK : : AT? : FGZ; Hence, the areas of similar polygons are to each other as the squares described on their homologous sides Proportions of Polygons. THEOREM XXII. If similar polygons are... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...Multiplying these ratios, we have (III. 14), ABC AB X AC ADE ~ AD X AE PROPOSITION IX.— THEOREM. 23. Similar polygons are to each other as the squares of their homologous sides. Let ABCDEF, A'B'C'D'E'F', be .two similar polygons; and denote their surfaces by 8 and S'; then, tf_... | |
 | 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 u •''•> by Q1 a °d... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...Multiplying these ratios, we have (III. 14), ABC AB X AC ADE ~ ADX PROPOSITION IX.— THEOREM. 23. Similar polygons are to each other as the squares of their homologous sides. Let ABCDEF, A'B'C'D'E'F', be two similar polygons; and denote their surfaces by S and S', then, /—^\... | |
 | Edward Olney - Geometry - 1872 - 562 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... | |
 | 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... | |
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Now, since the areas of similar polygons are to each other as the squares of their homologous sides... 
