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" Now, since the areas of similar polygons are to each other as the squares of their homologous sides... "
First lessons in Plane Geometry. Together with an application of them to the ... - Page 129
by Francis Joseph Grund - 1830 - 12 pages
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Elements of Plane and Solid Geometry: And of Plane and Spherical ...

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...
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Elements of Geometry: With Practical Applications to Mensuration

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...
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The Normal Elementary Geometry: Embracing a Brief Treatise on Mensuration ...

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...
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Elements of Geometry, Plane and Spherical: With Numerous Practical Problems

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...
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A Treatise on Special, Or Elementary Geometry

Edward Olney - Geometry - 1872 - 472 pages
...area ABC : area DEF : : CB' : FE" :: ─~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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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

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...
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A Treatise on Special Or Elementary Geometry, Volumes 1-2

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...
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Geometry, mensuration and the stereometrical tableau: lecture read before ...

Charles P. Florent BaillairgÚ - 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...
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Surveying and Navigation, with a Preliminary Treatise on Trigonometry and ...

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...
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New Elementary Geometry: With Practical Applications ; a Shorter Course Upon ...

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...
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