| Adrien Marie Legendre - Geometry - 1822 - 394 pages
...subtended by one of its sides is an aliquot part of the circumference. 94 PROPOSITION XI. THEOREM. The circumferences of circles are to each other as their radii, and their surfaces as the squares of those radii. For the sake of brevity, let us designate the circumference... | |
| John Radford Young - Euclid's Elements - 1827 - 228 pages
...oo2 : : AO-iABCD : ao^abcd, whence (Prop. I. Cor. B. VI.) AO : ao : : $ ABCD : i abed. Consequently the circumferences of circles are to each other as their radii, and therefore their surfaces are as the squares of the circumferences. Cor. 2. It follows also, that similar... | |
| James Ryan - Astronomy - 1827 - 408 pages
...inserted in the table. The reason of the preceding calculation is evident from this principle, that the circumferences of circles are to each other as their radii ; and that the radius of any parallel of latitude is equal to the cosine of that latitude ; hence, if the... | |
| Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...before, have — - =: a, and — •%• = /3. Hence r T c: c' :: r : r1, and s : s1 :: r3 : r1* ; hence the circumferences of circles are to each other as their radii, and the surfaces are as the squares of those radii. Let us now examine a sector whose radius is r. A being... | |
| Adrien Marie Legendre - Geometry - 1830 - 344 pages
...we shall, as before, have l=a, and -^=g. Hence c: c : : r : r', and * : ,f . . j.2 . p/2 . nence fag circumferences of circles are to each other as their radii, and their surfaces as the squares of those radii. Let us now examine a sector whose radius is T. A being the... | |
| Railroad engineering - 1892 - 610 pages
...circle, and its velocity at this instant is the velocity of the crank-pin circle. Bearing in mind that the circumferences of circles are to each other as their radii, and that the 7-ft. circle of the driving-wheels moved 88 ft. per second, we have the proportion 3i : i... | |
| Adrien Marie Legendre - Geometry - 1836 - 394 pages
...circumscribed circles, or as the squares of OD, od,the radii of the inscribed circles. PROPOSITION XI. THEOREM. The circumferences of circles are to each other as their radii, and the areas are to each other as the squares of their radii. Let us designate the circumference of the... | |
| Roswell Chamberlain Smith - Arithmetic - 1841 - 324 pages
...diameters of the circles. The same is true of the arcs and chords of similar segments. 57. Circles, or their areas are to each other as the squares of their radii, diameters ot circumferences. 58. To find the area of a regular polygon, or any regular figure : Multiply... | |
| Roswell Chamberlain Smith - Arithmetic - 1842 - 320 pages
...diameters of the circles. The same is true of the arcs and chords of similar segments. 57. Circles, or their areas are to each other as the squares of their radii, diameters or circumferences. 58- To find the area of a regular polygon, or any regular figure : Multiply... | |
| Roswell Chamberlain Smith - Arithmetic - 1843 - 320 pages
...diameters of the circles. The same is true of the arcs and chords of similar segments. 57. Circles, or their areas are to each other as the squares of their radii, diameters or circumferences. 58. To find the area of a regular polygon, or any regular figure: Multiply... | |
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