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" The areas of two similar triangles (or polygons) are to each other as the squares of any two corresponding sides. "
Observational Geometry - Page 219
by William Taylor Campbell - 1899 - 240 pages
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First lessons in Plane Geometry. Together with an application of them to the ...

Francis Joseph Grund - Geometry, Plane - 1830 - 274 pages
...sides opposite to the equal angles, and also as the squares upon the heights of the triangles. 21. The areas of similar polygons are to each other, as the squares constructed upon the corresponding sides. SECTION IV. OF THE PROPERTIES OF THE CIRCLE.* QUERY I. hi...
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An Elementary Treatise on Geometry: Simplified for Beginners Not ..., Part 1

Francis Joseph Grund - Geometry, Plane - 1834 - 190 pages
...similar triangles are to each other, as the areas of the squares upon the corresponding sides. 23. The areas of similar polygons are to each other, as the squares constructed upon the corresponding sides. ••„ SECTION IV. OF THE PROPERTIES OF THE CIRCLE .*...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...polygon FGHIK, as one antecedent ABC, is to its consequent FGH, or as ABS is to FG2 (Prop. XXV.)j hence the areas of similar polygons are to each other as the squares described on the homologous sides. Cor. If three similar figures were constructed, on the three sides...
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First Lessons in Geometry: With Practical Applications in Mensuration, and ...

Charles Davies - Geometrical drawing - 1840 - 252 pages
...Undecagon, 9,3656404 1,2028437 i 12 Dodecagon, 11,1961524 1,8660254 Mensuration of Surfaces. Now, since the areas of similar polygons are to each other as the squares described on their homologous side (see Part I. VII. Art. 3). we have I2 : tabular area : : any...
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A Practical System of Mensuration of Superficies and Solids ...

J. M. Scribner - Measurement - 1844 - 123 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 of their homologous sides, if the square of the side of a polygon be multiplied by the multiplier of...
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Elements of Drawing and Mensuration Applied to the Mechanic Arts: A Book for ...

Charles Davies - Geometrical drawing - 1846 - 254 pages
...radius of the inscribed circle. 50. How do you find the area of any polygon from the above table ? Since the areas of similar polygons are to each other as the squares described on their homologous sides, we have 1* : tabular area : : any side squared : area. Hence,...
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Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 308 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...
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Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 384 pages
...Decagon .... 10 ... 7.0942088 Dodecagon ... 12 ... 11.1901524 Undecagon ... 11 ... 9.3050399 Now, since the areas of similar polygons are to each other as the squares of their homologous sides (Book IV. Prop. XXVII.), we shall have Or, to find the area of any regular...
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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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