 | 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
...original figure. The area of the triangle may then be found by multiplying its base into half its height ; and this will be the contents of the field. In practice,...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,... | |
 | 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... | |
 | Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...will be equal to 11.1961524. If it is required to find the area of any other regular decagon, since similar figures are to each other as the squares of their homologous sides, we have simply to 2. * = Л« • 10 8. In like manner, if r denote the radius of the inscribed sphere,... | |
 | George Roberts Perkins - Geometry - 1856 - 460 pages
...7*6942088 0'8861640 Undecagon .11 9'3656399 0'97l5375 Dodecagon 12 11.1961524 1*0490687 Since the areas of similar figures are to each other as the squares of their homologous sides, we may find the area of any regular polygon whose number of sides is not greater than 12 by this SECOND... | |
 | James Stewart Eaton - Arithmetic - 1857 - 376 pages
...octagon is 10 and its apothem 12.071068; what is its area ? Ans. 482.84272. '171. The arcas of all similar figures are to each other as the squares of their homologous sides (330, 9), .-. we may more readily obtain the areas of regular polygons by reference to a table in which... | |
 | George Roberts Perkins - Geometry - 1860 - 472 pages
...7'6942088 0-8861640 Undecagon 11 9'3656399 0-9715375 Dodecagon 12 11-1961524 1'0490687 Since th.e areas of similar figures are to each other as the squares of their homologous sides, we may find the area of any regular polygon whose number of sides is not greater than 12 by this SECOND... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...in the given polygons. The polygon itself may then be constructed on x, by the last problem. y For similar figures are to each other as the squares of their homologous sides ; but the square of the side x is equal to the sum or the difference of the squares described upon... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...polygons. The polygon itself may then be constructed on x, by the last problem. ELEMENTS OF GEOMETRY. For similar figures are to each other as the squares of their homologous sides ; but the square of the side x is equal to the sum or the difference of the squares described upon... | |
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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... 
