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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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Chauvenet's Treatise on Elementary Geometry

William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...the circle is the limit of the areas of these polygons. PROPOSITION VIII. The circumferences of two circles are to each other as their radii, and their...areas are to each other as the squares of their radii. Corollary I. The circumferences of circles are to each other as their diameters, and their areas are...
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A Collection of Mathematical Rules and Tables: Including Interest, Equation ...

James Morton - Mathematics - 1887 - 236 pages
...GB is 16 yards, and the square of BF is 9 yards, and the sum of their squares is 25 yards. GEOMETRY. The circumferences of circles are to each other as their radii, and the areas are to each other as the squares of their radii. The circumferences of circles are to each...
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The Colliery Engineer Pocket-book of Principles Rules, FormulŠ, and Tables ...

Thomas J. Foster - Coal mines and mining - 1891 - 444 pages
...two lines, and the point of intersection of the perpendiculars will be the center of the circle. 26. The circumferences of circles are to each other as their radii, and their areas are to each other aa the squares of their radii. EXAMPLES. If the circumference of a circle is 62-83 in. and its radius...
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Yale Examination Papers

Yale University - 1892 - 200 pages
...given straight line to construct a polygon similar to a given polygon ? 6. The circumferences of two circles are to each other as their radii, and their...areas are to each other as the squares of their radii. II. — SOLID AND SPHERICAL GEOMETRY. 7. If a straight line and a plane are parallel, the intersection...
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Elementary Geometry

William Chauvenet - 1893 - 340 pages
...the circle is the limit of the areas of these polygons. PROPOSITION VIII. The circumferences of two circles are to each other as their radii, and their...areas are to each other as the squares of their radii. Corollary I. The circumferences of circles are to each other as their diameters, and their areas are...
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Yale University Entrance Examinations in Mathematics: 1884 to 1898

Mathematics - 1898 - 228 pages
...following: — 6. Two triangles are similar when they are mutually equiangular. 7. The circumferences of two circles are to each other as their radii and their areas are as the squares of their radii.] JUNE 1887. (The candidate may omit any two propositions.) 1. To inscribe...
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Entrance Examinations in Mathematics, 1884 to 1898 [with Supplements to 1900]

Yale University - 1898 - 212 pages
...following: — 6. Two triangles are similar when they are mutually equiangular. 7. The circumferences of two circles are to each other as their radii and their areas are as the squares of their radii.] JUNE 1887. (The candidate may omit any two propositions.) 1. To inscribe...
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A Treatise on Navigation and Nautical Astronomy

William Robert Martin - Nautical astronomy - 1899 - 474 pages
...of latitude. 1 Described in Norwood's Seaman's Practice, 1637. Then since by a property of geometry the circumferences of circles are to each other as their radii, and the same is true of equivalent arcs of those circles, it follows that — u V : AB :: ou : CA : : o...
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Plane Geometry: A Complete Course in the Elements of the Science

Edward Brooks - Geometry, Modern - 1901 - 278 pages
...by the hypothetical introduction of the infinite into the statement." PROPOSITION VII. — THEOREM. The circumferences of circles are to each other as...areas are to each other as the squares of their radii. To Prove. — Then we are to prove that Circ. OA : Circ. ffM ::R:R, Circle OA : Circle ffM : : I? :...
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Treatise on Elementary Geometry

William Chauvenet - 1905 - 336 pages
...the circle is the limit of the areas of these polygons. PROPOSITION VIII. The circumferences of two circles are to each other as their radii, and their...areas are to each other as the squares of their radii. Corollary I. The circumferences of circles are to each other as their diameters, and their areas are...
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