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" It follows that the ratio of the circumference of a circle to its diameter is the same for all circles. "
Yale University Entrance Examinations in Mathematics: 1884 to 1898 - Page 186
1898 - 208 pages
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Arithmetic

George Albert Wentworth - Algebra - 1892 - 312 pages
...doubled ; or, if the diameter be trebled, the circumference will also be trebled ; and so on. It follows that the ratio of the circumference of a circle to its diameter is the same for all circles. The exact value of this ratio cannot be expressed by numbers, but the value near enough for most practical...
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A History of Mathematics

Florian Cajori - Mathematics - 1893 - 476 pages
...by approaching it from a different direction and by newly discovered paths. Lambert proved in 1761 that the ratio of the circumference of a circle to its diameter is incommensurable. Some years ago, Lindemann demonstrated that this ratio is also transcendental and...
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"Wentworth & Hill's Exercise Manual: Arithmetic, Volume 1

George Albert Wentworth - 1894 - 318 pages
...doubled ; or, if the diameter be trebled, the circumference will also be trebled ; and so on. It follows that the ratio of the circumference of a circle to its diameter is the same for all circles. The exact value of this ratio cannot be expressed by numbers, but the value near enough for most practical...
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Plane and Solid Geometry: Suggestive Method

Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 522 pages
...diameters. If D and U represent their diameters, ^L C "= D' ' 312. COROLLARY II. The ratio of the circumference of a circle to its diameter is the same for all circles. For, by Cor. 1, = 7 , C C' and by alternation ~f=, = ~jy • This ratio is represented by the...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 570 pages
...the cir cle is the common limit of 5 and s. 185 QED PROPOSITION' X. THEOREM 49 1. The ratio of the circumference of a circle to its diameter is the same for all circles. GIVEN — any two c1rcles with radii R and r, and circumferences Cand c respectively. C c To PROVE...
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Elements of Geometry: Plane geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...the civ cle is the common limit of J> and s. 185 PROPOSITION X. THEOREM QED 491. The ratio of the circumference of a circle to its diameter is the same for all circles. GIVEN—any two circles with radii R and r, and circumferences C and c respectively. To PROVE — =...
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Exercises in Arithmetic

George Albert Wentworth, George Anthony Hill - Arithmetic - 1897 - 476 pages
...doubled ; or, if the diameter be trebled, the circumference will also be trebled ; and so on. It follows that the ratio of the circumference of a circle to its diameter is the same for all circles. The exact value of this ratio cannot be expressed by numbers, but the value near enough for most practical...
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An Algebraic Arithmetic: Being an Exposition of the Theory and Practice of ...

Silas Ellsworth Coleman - Arithmetic - 1897 - 180 pages
...diameter (d) is the distance across it measured through the centre. Hence d - 2 r. 97. The ratio of the circumference of a circle to its diameter is the same for all circles, and is generally denoted by the Greek letter v (pronounced pie). That is, - = TT. The value of IT is...
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Entrance Examinations in Mathematics, 1884 to 1898 [with Supplements to 1900]

Yale University - 1898 - 212 pages
...with the diameter through A. (). If each of these angles is 30, prove that the points A, B, and С trisect the circumference. 3. In two similar triangles...the method of determining this value. JUNE, 1900. (В). 1. The legs of a right triangle are 6 and 8. Find the length of the perpendicular from the right...
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A History of Elementary Mathematics

Florian Cajori - Mathematics - 1898 - 512 pages
...by approaching it from a different direction and by newly discovered paths. Lambert proved in 1761 that the ratio of the circumference of a circle to its diameter is incommensurable. Some years ago, Lindemann demonstrated that this ratio is also transcendental and...
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