 | Etienne Bézout - 1824 - 222 sider
...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 - 1834 - 202 sider
...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... | |
 | Francis Joseph Grund - 1834 - 204 sider
...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... | |
 | Francis Joseph Grund - 1834 - 212 sider
...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,... | |
 | Adrien Marie Legendre - 1836 - 394 sider
...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 - 1840 - 262 sider
...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 - 1844 - 130 sider
...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 - 1846 - 254 sider
...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 - 1847 - 326 sider
...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... | |
 | Charles Davies - 1849 - 372 sider
...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... 
