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" The circumferences of circles are to each other as their radii, and their areas are to each other as the squares of their radii. Let C denote the circumference of one of ^ the circles, R its radius OA, A its area; and let C... "
New Elementary Geometry: With Practical Applications; a Shorter Course, Upon ... - Page 100
by Benjamin Greenleaf - 1873 - 176 pages
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Elements of Geometry and Trigonometry: With Notes

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...
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Elements of Geometry: With Notes

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...
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The New American Grammar of the Elements of Astronomy: On an Improved Plan ...

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...
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The First Six Books of the Elements of Euclid, with a Commentary and ...

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...
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Elements of Geometry and Trigonometry: With Notes

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...
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Railway Locomotives and Cars, Volume 66

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...
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Elements of Geometry and Trigonometry

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...
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Arithmetic on the Productive System: Accompanied by a Key and Cubical Blocks

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...
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Arithmetic on the Productive System: Accompanied by a Key and Cubical Blocks

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...
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Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

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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