 | 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... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...B in the given polygons. The polygon itself may then be constructed on x, by the last problem. 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... | |
 | William Kennedy Maxwell - 1871 - 148 pages
...inner rectangle, will equal the area of the walk round it, will equal 8000 -i- 2 = 4000 feet. Again, similar figures are to each other as the squares of their homologous sides ; therefore the breadth of the lesser rectangle will be as 8000 : 4000 : : 802 : 3200, the square of... | |
 | James Stewart Eaton - Arithmetic - 1873 - 182 pages
...for the proportion 4:2:: CE2 : CB2, is based on the principle (Art. 330, Prop. 5) that the areas of similar figures are to each other as the squares of their homologous sides ; but circles and circular -ings are not similar figures. For a like reason it is necessary to und... | |
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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... 
