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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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The National Arithmetic on the Inductive System: Combining the Analytic and ...

Benjamin Greenleaf - Arithmetic - 1850 - 368 pages
...the diameter of a circle to its inscribed square is as 1 to .707106; we have also seen in Problem IV. that the ratio of the circumference of a circle to its diameter is as 3.141592 to 1; therefore, the ratio of the circumference of a circle to its inscribed square is...
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An elementary treatise on plane trigonometry

Richard Dunkley Beasley - Plane trigonometry - 1858 - 144 pages
...circumferences of the circles, and we have circumference ABCD : A О = circum. abed : ao, or the ratio of the circumference of a circle to its diameter is the same for all circles. This ratio is generally denoted by the symbol tr ; so that if r be the radius of a circle, and 2r its...
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Elements of Natural Philosophy, Elementary Statics and Dynamics

Physics - 1862 - 496 pages
...surface in 22 the circle is -y- r*, or rather (3.14159) r2. It has been proved in a variety of ways that the ratio of the circumference of a circle to its diameter is about 22 : 7, or, rather, 3.14159 : 1 ; wherefore, if c be the circumference, 22 c : 2r :: 22 : 7,...
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An Elementary Course of Plane Geometry

Richard Wormell - Geometry, Modern - 1868 - 286 pages
...approaches more and more nearly the circumference of the circle circumscribing it. We conclude therefore that the ratio of the circumference of a circle to its diameter is always the same. The constant number which expresses the value of this ratio cannot be found exactly....
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An Elementary Course of Plane Geometry

Richard Wormell - Geometry, Plane - 1870 - 304 pages
...approaches more and more nearly the circumference of the circle circumscribing it. We conclude therefore that the ratio of the circumference of a circle to its diameter is always the same. The constant number which expresses the value of this ratio cannot be found exactly....
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876 - 268 pages
...approaches more and more nearly the circumference of the circle circumscribing it. \Ve conclude, therefore, that the ratio of the circumference of a circle to its diameter is always the same. The constant value of this ratio cannot be expressed exactly by any finite number....
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The Complete Arithmetic

Milton Browning Goff - Arithmetic - 1876 - 462 pages
...a circle equals the product of the circumference, by one-half the radius. It is proven in Geometry, that the ratio of the circumference of a circle to its diameter is 3.14159, nearly. By means of this truth we deduce various rules for determining different parts of...
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Examination Papers for Science Schools and Classes

Great Britain. Education Department. Department of Science and Art - 1877 - 562 pages
...root itself? (20.) 34. Find in degrees and decimals, an arc equal in length to the radius, assuming that the ratio of the circumference of a circle to its diameter is 355 : 113. By how much does the length of arc, thus found, differ from that given by assuming the ratio...
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First Public Examination in Literis Graecis Et Latinis

University of Oxford - Greek language - 1879 - 412 pages
...Inscribe an equilateral and equiangular hexagon in a given circle. II. Elements of Geometry. II. 1. Prove that the ratio of the circumference of a circle to its diameter is invariable. Taking this ratio as 2T2, find the length of an arc, subtending an angle of i at the...
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A treatise on elementary trigonometry. [With] Key, by H. Carr

John Bascombe Lock - 1882 - 384 pages
...else; just as 180 stands for the number one hundred and eighty, and for nothing else. 30. We proceed to prove that the ratio of the circumference of a circle to its diameter is the same for all circles. The proof depends on the following important principle ; The length of the circumference of a circle...
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