 | 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 : AB :: Va : VA :: Fl : FE;... | |
 | Edward Brooks - Geometry - 1868 - 284 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 the side of the polygon,... | |
 | 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... | |
 | 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... | |
 | Charles P. Florent Baillairgé - Geometry - 1873 - 660 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 relation that the, area... | |
 | 1873 - 192 pages
...6. To circumscribe about a circle a regular polygon similar to a given inscribed regular polygon. 7. Similar polygons are to each other as the squares of their homologous sides. What is the ratio between the areas of two circles ? 8. Prove that the area of a circle of which r... | |
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Now, since the areas of similar polygons are to each other as the squares of their homologous sides... 
