 | 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
...will also be doubled ; or, if the diameter be trebled, the circumference will also be trebled ; and so on. It follows that the ratio of the circumference...the value near enough for most practical purposes is J*j?. Concentric circles are circles having the same centre. Circumference of a circle = ^ X radius.... | |
 | 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... | |
 | George Albert Wentworth - Arithmetic - 1896 - 318 pages
...octagonal floor, one side of which is 12 ft., with carpet 29 in. wide, and costing $1.70 per square yard. A Circle is a plane figure bounded by a curved line...the value near enough for most practical purposes is If-. Concentric circles are circles having the same centre. Circumference of a circle = ty X radius.... | |
 | 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 — =... | |
 | 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... | |
 | George Albert Wentworth, George Anthony Hill - Arithmetic - 1897 - 476 pages
...will also be doubled ; or, if the diameter be trebled, the circumference will also be trebled ; and so on. It follows that the ratio of the circumference...the value near enough for most practical purposes is Zf-. Concentric circles are circles having the same centre. Circumference of a circle = ~4^ x radius.... | |
 | 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... | |
 | Mathematics - 1898 - 228 pages
...proportional, and in two equivalent triangles the bases and altitudes are inversely proportional. 4. (a). Prove that the ratio of the circumference of a circle to its diameter is the same for all circles. What is the approximate value of this ratio ? (b) Explain briefly (without proofs) the method of determining... | |
 | Yale University - 1898 - 212 pages
...proportional, and in two equivalent triangles the bases and altitudes are inversely proportional. 4. (a). Prove that the ratio of the circumference of a circle to its diameter is the same for all circles. What is the approximate value of this ratio ? (b) Explain briefly (without proofs) the method of determining... | |
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It follows that the ratio of the circumference of a circle to its diameter is the same for all circles. 
