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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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First Principles of the Differential and Integral Calculus, Or, the ...

Etienne Bézout - Calculus - 1824 - 222 pages
...kind of demonstration was called reductio ad absurdum. By this means, having first ascertained that the areas of similar polygons are to each other as the squares of their homologous lines, they inferred that circles of different radii are to each other as the square...
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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...QUERY I. In how many points can a straight line, CD, meet the circumference of a circle J A. In two points, M, N, only. For, (f For, letting fall, from...
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An Elementary Treatise on Geometry: Simplified for Beginners Not ..., Part 1

Francis Joseph Grund - Geometry, Plane - 1834 - 206 pages
...of similar polygons are to each other, as the squares constructed upon the corresponding sides. 9* SECTION IV. OF THE PROPERTIES OF THE CIRCLE." QUERY I. In how many points can a straight line, CD, meet the circumference of a circle f A. In two points, only. For, C *%^T^ J> M, N, only. For, letting...
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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...squares constructed upon the corresponding sides. 9* SECTION IV. OF THE PROPERTIES OF THE CIRCLE.* QUERY I. In how many points can a straight line, CD,...
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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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