 | Thomas Holliday - Surveying - 1838 - 404 pages
...4 : : 800000 : 16. Hence the plan was drawn by a scale of 4 chains to an inch. Note 1. The areas of similar figures are to each other as the squares of their homologous sides. 2. Always draw in the bottom of your plan the scale plotted by, or insert the same in writing, as much... | |
 | Joseph Gwilt - Architects - 1842 - 1114 pages
...DCB is to the radius AB as the circumference deb is to the radius ai. 96 1 . PROP. LXXX 1 1. Amito figures are to each other as the squares of their homologous sides. Let the two similar figures be A, a (fig. 316.) Upon the homologous sides CD, cd form the squares B,... | |
 | Anna Cabot Lowell - Geometry - 1846 - 206 pages
...triangle a dc= triangle 2 g 2 2 ADE : triangle ade = AB : a6 = BC : be , &c., that is, The surfaces of similar figures are to each other as the squares of their homologous sides. 15* 290. Upon the 3 sides of a right-angled triangle construct similar figures, in which the sides... | |
 | James Bates Thomson - Arithmetic - 1847 - 432 pages
...may be found by dividing the square of its hypothenuse 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 si> ji of the areas of equilateral... | |
 | George Roberts Perkins - Geometry - 1847 - 326 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. (... | |
 | 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... | |
 | 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... | |
 | 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.)... | |
 | Jeremiah Day - Geometry - 1851 - 418 pages
...triangle, circle, &c. the contents may be found by the rules in Mensuration, Sec. I, and II. 125. The erea of a field which has been plotted, is sometimes found...the computed area of the field, to the true area. .5 Ex. If the area of a field measured by a chain 66-4 feet long, be computed to be 32^.6036 acres... | |
 | 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,... | |
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It will be sufficient to lay the edge of a rule on C, so as to be parallel to a line supposed to pass through B and D, and to mark the point of intersection G. 126. If after a field has been surveyed, and the area computed, the chain is found to be too... 
