 | 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... | |
 | 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...SECTION IV. OF THE PROPERTIES OF THE CIRCLE.* QUERY I. hi how many points can a straight line CD, cut the circumference of a circle ? A, In two points M,... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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,... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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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Now, since the areas of similar polygons are to each other as the squares of their homologous sides... 
