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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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Scribner's Engineers' and Mechanics' Companion: Comprising United States ...

J. M. Scribner - Mechanical engineering - 1849 - 264 pages
...showing the multipliers of the ten regular polygons, when the sides of each are eqflal to 1 : Now, since the areas of similar polygons are to each other as the squares of their homologous sides, if the square of a side of a polygon be multiplied by the multiplier of...
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Mensuration, Mechanical Powers and Machinery: The Principles of Mensuration ...

Daniel Adams - Arithmetic - 1849 - 142 pages
...feet, and the altitude of one of its equal triangles is 8'660254 feet ? Ans. 259>80762 sq. ft. IT 54. The areas of similar polygons are to each other as the squares of one of their sides. H 52. Hence, the areas of regular polygons may be more readily found by the...
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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 218 pages
...of each is equal to 1 : it also shows the length of the radius of the inscribed circle. Now, since the areas of similar polygons are to each other as the squares described on their homologous sides (Bk. IV. Th. xx), we have I2 : tabular area : : any side squared...
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Mensuration, Mechanical Powers, and Machinery: The Principles of Mensuration ...

Daniel Adams - Measurement - 1850 - 144 pages
...and the altitude of one of its equal triangles is 8<660254 feet ? Ans. 259<80762 sq. ft. ^T ęS4Lę The areas of similar polygons are to each other as the squares of one of their sides. If 52. Hence, the areas of regular polygons may be more readily found by the...
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Elements of Geometry: With, Practical Applications

George Roberts Perkins - Geometry - 1850 - 332 pages
...GHKLM, as any one antecedent ABC, is to its corresponding consequent GHK, or as AB' is to GH' Hence the areas of similar polygons are to each other as the squares of their homologous sides. Cor. If three similar rectilineal figures are constructed on the three sides...
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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 236 pages
...of each is equal to 1 : it also shows the length of the radius of the inscribed circle. Now, since the areas of similar polygons are to each other as the squares described on their homologous sides (Bk. IV. Th. xx), we have 1 : tabular area : : any side squared...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...polygons whose sides are unity, or 1, be calculated and arranged in the following TABLE. Now, since the areas of similar polygons are to each other as the squares of their homologous sides (B. IV., P. 27), we have, n 1 : any side squared : : tabular area : area....
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...polygons whose sides are unity, or 1, be calculated and arranged in the following TABLE. Now, since the areas of similar polygons are to each other as the squares of their homologous sides (B. Iv., r. 27), we have, o 1" : any side squared : : tabular area : area....
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Arithmetic and Its Applications: Designed as a Text Book for Common Schools ...

Dana Pond Colburn - Arithmetic - 1855 - 396 pages
...squares, and parallelograms are to each other as the product of their bases by their altitudes. (/.) The areas of similar polygons are to each other as the squares of their like dimensions. (u.) The circumference of a circle equals very nearly 3.1416 * times its...
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1855 - 336 pages
...side of each is equal to 1 : it also shows the length of the radius of the inscribed circleNow, since the areas of similar polygons are to each other as the squares described on their homologous sides (Bk- IV Th- xx), we have I2 : tabular area : : any side squared...
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