| Adrien Marie Legendre - Geometry - 1822 - 367 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 - 208 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
...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 - 359 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 - 1842 - 306 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 - 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... | |
| James Bates Thomson - Geometry - 1844 - 237 pages
...polygons will ultimately become equal to the circle, and equal to each other. PROPOSITION X. THEOREM. **The circumferences of circles are to each other as their radii ; and their areas are** as the squares of their radii. Let the circumference whose radius is CA, be designated by circ. CA... | |
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