| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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 — =... | |
| 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... | |
| 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... | |
| Yale University - 1898 - 212 pages
...with the diameter through A. (ó). 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... | |
| 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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