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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

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...

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...

"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...

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...

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...

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 — =...

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...

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...