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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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Report of the Superintendent of Public Instruction

Michigan. Department of Public Instruction - Education - 1896 - 718 pages
...radius draw a circle tangent to the sides of a given angle. Demonstrate the solution. 7. Demonstrate: The areas of similar polygons are to each other as the squares of any two homologous sides of the polygons. 8. Define a plane. What determines the position of a plane?...
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A Textbook on Surveying and Mapping ...: Arithmetic, formulas, geometry and ...

International Correspondence Schools - Surveying - 1898 - 518 pages
...1,600 : area of DEF, or 6,400 : 2,500 :: 1,600 : 025 sq. ft. Hence, area of DE F.vs, 025 sq. ft. 1189. The areas of similar polygons are to each other as the squares of their homologous sides. Thus, if the area of a regular hexagon with a side of 10 inches is 250.809...
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Observational Geometry

William Taylor Campbell - Geometry - 1899 - 264 pages
...sides makes the area of the polygon four times as great; and so on. This is expressed by saying that " the areas of similar polygons are to each other as the squares of any two corresponding sides." The square of a number is the number multiplied by itself; thus the...
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The Elements of Civil Engineering: Prepared for Students of the ..., Volume 3

International Correspondence Schools - Civil engineering - 1899 - 798 pages
...1,600 : area of DE F, or 6,400 : 2,500 :: 1,600 : 625 sq. ft. Hence, area of DE Fis 625 sq. ft. 1189. The areas of similar polygons are to each other as the squares of their homologous sides. Thus, if the area of a regular hexagon with a side of 10 inches is 259.809...
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Surveying, land surveying, mapping, railroad location, railroad construction ...

International Correspondence Schools - Civil engineering - 1899
...1,600 : area of DEF, or 6,400 : 2,500 :: 1,600 : 625 sq. ft. Hence, area of DEF is 625 sq. ft. 1 189. The areas of similar polygons are to each other as the squares of their homologous sides. Thus, if the area of a regular hexagon with a side of 1(1 inches is 259.809...
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Surveying, Land Surveying, Mapping, Railroad Location, Railroad Construction ...

International Correspondence Schools - Cartography - 1903 - 846 pages
...1,600 : area of DEF, or 6,400 : 2,500 :: 1,600 : 625 sq. ft. Hence, area of DEF is 625 sq. ft. 1189. The areas of similar polygons are to each other as the squares of their homologous sides. Thus, if the area of a regular hexagon with a side of 10 inches is 259.809...
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Hodgson's Estimator and Contractor's Guide for Pricing Builder's Work ...

Frederick Thomas Hodgson - Architecture, Domestic - 1904 - 364 pages
...showing the multipliers of the ten regular polygons, when the sides of each are equal 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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Second-year Mathematics for Secondary Schools, Volume 2

George William Myers - Mathematics - 1910 - 304 pages
...=. (Why?) See 128. Therefore -•-. QED FIG. 277 Areas of Polygons PROPOSITION IX 247. Theorem: The areas of similar polygons are to each other as the squares of the homologous sides. Hypothesis: Polygon ABC .... ^polygon A'B'C'. . . . (Fig. 278). Let P denote...
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Builders' Reliable Estimator and Contractors' Guide: A Complete Guide for ...

Frederick Thomas Hodgson - 1917 - 716 pages
...showing the multipliers of the ten regular polygons, when the sides of each are equal 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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A Geometry Reader

Julius J. H. Hayn - Geometry, Plane - 1925 - 328 pages
...the hypothenuse and a side of the one are proportional to the hypothenuse and a side of the other. 5. The areas of similar polygons are to each other as the squares of any two homologous sides. 6. The area of a circle is equal to one-half the product of its radius...
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