 | Florian Cajori - 1893 - 476 σελίδες
...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 σελίδες
...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... | |
 | George Albert Wentworth, George Anthony Hill - 1897 - 476 σελίδες
...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... | |
 | Florian Cajori - 1898 - 512 σελίδες
...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... | |
 | Yale University - 1898 - 212 σελίδες
...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... | |
 | 1898 - 228 σελίδες
...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... | |
 | University of St. Andrews - 1903 - 762 σελίδες
...cuts orthogonallv any circle through a pair of harmonic conjugates to A, B. TRIGONOMETRY. 7. Assuming that the ratio of the circumference of a circle to its diameter is a constant, -n say, show that the circular measure of two right angles is ir radians, and prove that... | |
 | Euclid - 1908 - 456 σελίδες
...explanation, gives out that gives approximate values for the square roots of several large numbers, and proves that the ratio of the circumference of a circle to its diameter is less than 37- but greater than 3^, (4) that the first approach to the rapidity with which the decimal... | |
 | William Ernst Paterson - 1911 - 262 σελίδες
...17. Assuming that a circle may be treated as a regular polygon with an infinite number of sides, show that the ratio of the circumference of a circle to its diameter is constant. What is the circular measure of the least angle whose sine is J, and what is the measure... | |
 | 1911 - 192 σελίδες
...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... | |
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It follows that the ratio of the circumference of a circle to its diameter is the same for all circles. 
