 | William Vogdes - Arithmetic - 1847 - 324 pages
...The areas of circles are to each other as the squares of their diameters, radii, or circumferences. The areas of similar figures are to each other, as the squares of their like sides. 47. The surfaces of all similar solids are to each other as the squares of their... | |
 | James Bates Thomson - Arithmetic - 1848 - 434 pages
...square may be found by dividing the square of its diagonal by 2. (Arts. '285, 578.) 2. The areas of all similar figures are to each other as the squares of their homologous sides, or their like dimensions. (Leg. IV. 25, 27. V. 10.) Hence, The sum of the areas of equilateral or other... | |
 | James Bates Thomson - Arithmetic - 1848 - 432 pages
...square may be found by dividing the square of its diagonal by 2. (Arts. iJ85,578.) 2. The areas of ail similar figures are to each other as the squares of their homologous sides, or their like dimensions. (Leg. IV. 25, 27. V. 10.) Hence, The sum of the areas of c guilateral or... | |
 | John Bonnycastle - Geometry - 1848 - 320 pages
...such as have the same number of sides, and the angles contained by those sides respectively qual. 8. The areas of similar figures are to each other as the squares of their like sides. OF THE MENSURATION OF SUPERFICIES. THE area of any figure is the measure of its... | |
 | Daniel Adams - Arithmetic - 1849 - 142 pages
...be found, by having one side and the number of sides given. It has been shown, If IT 52 and 77, that the areas of similar figures are to each other as the squares of their similar dimensions. It is also true Length of one aide. Number of sides. Names of Solids.... | |
 | George Roberts Perkins - Geometry - 1850 - 332 pages
...triangle, the figure on the hypothenuse will be equivalent to the sum of the other two; for the three figures are to each other as the squares of their homologous sides, and the square of the hypothenuse is equivalent to the sum of the squares of the other two sides. (82.)... | |
 | Daniel Adams - Measurement - 1850 - 144 pages
...be found, by having one side and the number of sides given. It has been shown, Tflf 52 and 77, that the areas of similar figures are to each other as the squares of their similar dimensions. It is also true Length of one side. Number of sides. Names of Solids.... | |
 | Jeremiah Day - Geometry - 1851 - 418 pages
...chain is found to be too long or too short ; the true contents may be found, upon the principle that similar figures are to each other as the squares of their homologous sides. (Euc. 20. 6.) The proportion may be stated thus ; As the square of the true chain, to the square of... | |
 | Benjamin Greenleaf - Algebra - 1854 - 300 pages
...figure may be considered as containing one-fourth of her share. 160-5-4=40 square rods. And, as all similar figures are to each other as the squares of their homologous sides, therefore, as the contents of the assumed figure FBKL is to the exact quantity which it should contain,... | |
 | Thomas Fisher - Mathematics - 1854 - 156 pages
...ratio. The usual axiom is, all circles are to each other as the squares of their diameters. All plane figures are to each other as the squares of their homologous sides. [Homologous is a Greek word signifying similarly described.] But there would be equal truth and propriety... | |
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... similar figures are to each other as the squares of their homologous sides. 
