 | Joseph Ray - Arithmetic - 1880 - 420 pages
...All equilateral triangles are similar; the same is true of all squares, all circles, all spheres. 3. The areas of similar figures are to each other as the squares of their like dimensions. 4. The solidities of similar solids are to each other as the cubes of their... | |
 | Alexis Claude Clairaut - 1881 - 184 pages
...figure ABCDE, is the same as that of the squares x contained in the figure abode, and consequently, the areas of similar figures are to each other as the squares of their homologous sides. 48. All that has been said as to similar figures may be reduced to this single principle, that similar... | |
 | William George Spencer - Geometry - 1881 - 116 pages
...surfaces together, and say whether the ratio the less has to the greater accords with the law, .. " The areas of similar figures are to each other as the squares of their homologous sides." 367. Can you erect an hexagonal pyramid whose slant sides shall be equilateral triangles \ 368. Make... | |
 | H. Bryant - 1881 - 574 pages
...figures have their corresponding angles equal and the sides including those angles proportional. 5. The areas of similar figures are to each other as the squares of their corresponding linear dimensions, and the volumes of similar solids are to each other as the... | |
 | Indiana. State Board of Education - 1886 - 360 pages
...Illustrate Art. 437 by an original problem. ART. 438.—Comparison of Similar Figures. Principles.—1. The areas of similar figures are to each other as the squares of their like dimensions. 2. The dimensions of similar figures are to each other as the square roots... | |
 | Daniel Carhart - Surveying - 1888 - 536 pages
...drawing referred to any convenient scale and computing the area from these determined lengths. Then, since the areas of similar figures are to each other as the squares of their homologous sides, the true scale may be obtained by the proportion, computed area _ square of assumed scale * known area... | |
 | George Washington Hull - Arithmetic - 1895 - 408 pages
...Figures are those which have the same form, but difler in area. It is proved in Geometry that — 1. The areas of similar figures are to each other as the squares of their like dimensions. 2. The like dimensions of similar figures are to each other as the square... | |
 | William Frothingham Bradbury - Arithmetic - 1895 - 398 pages
...Similar Figpires are figures that are of precisely the same form, without regard to their magnitude. The areas of similar figures are to each other as the squares of their corresponding lines ; and, conversely, the corresponding lines of similar surfaces are to... | |
 | George Albert Wentworth - Arithmetic - 1897 - 396 pages
...cubical vessel that will hold 1 ton of water. 403. Similar Figures are figures that have the same shape. The areas of similar figures are to each other as the squares of their corresponding dimensions, and their volumes are to each other as the cubes of their corresponding... | |
 | George Albert Wentworth - Arithmetic - 1897 - 440 pages
...as a rectangular cistern 12' X 8' X 5£'. 403. Similar Figures are figures that have the same shape. The areas of similar figures are to each other as the squares of their corresponding dimensions, and their volumes are to each other as the cubes of their corresponding... | |
| |
... similar figures are to each other as the squares of their homologous sides. 
