| Daniel Alexander Murray - Plane trigonometry - 1899 - 226 pages
...circle two angles at the centre are in the same ratio as their intercepted arcs. (b) The ratio of a **circumference of a circle to its diameter is the same for all circles.** [See Art. 9 (6).] For the proof of (a), reference may be made to any plane geometry ; for instance,... | |
| Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...polygon, and less than the perimeter of any regular circumscribed polygon. § 361. (2) The ratio of the **circumference of a circle to its diameter is the same for all circles.** C = ird = 2 irr. § 362. (3) The area of a circle is equal to one-half the product of its circumference... | |
| University of St. Andrews - 1903 - 762 pages
...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... | |
| Elmer Adelbert Lyman - Arithmetic - 1905 - 268 pages
...could be made, the quotient in each case would be the same and equal to 3.14159 + , ie the ratio of the **circumference of a circle to its diameter is the same for all circles.** The ratio is denoted by the Greek letter TT (pi). The value of TT found in geometry is 3. 14159+ .... | |
| Daniel Alexander Murray - 1906 - 466 pages
...circle two angles at the centre are in the same ratio as their intercepted arcs. (6) The ratio of a **circumference of a circle to its diameter is the same for all circles.** [See Art. 9 (6).] For the proof of (a), reference may be made to any plane geometry ; for instance,... | |
| Daniel Alexander Murray - Plane trigonometry - 1908 - 358 pages
...circle two angles at the centre are in the same ratio as their intercepted arcs. (6) The ratio of. a **circumference of a circle to its diameter is the same for all circles.** [See Art. 9 (6).] For the proof of (a), reference may be made to any plane geometry ; for instance,... | |
| Euclid - Mathematics, Greek - 1908 - 456 pages
...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... | |
| Geometry, Plane - 1911 - 192 pages
...the work will not be accepted unless the constructions are made accurately with ruler and compass. **1. Divide a line externally in extreme and mean ratio...(without proofs) the method of determining this value.** GEOMETRY (A), JUNE, 1901 1. State and prove a theorem relating to the squares of the sides of an obtuse-angled... | |
| William Ernst Paterson - Logarithms - 1911 - 262 pages
...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... | |
| Clara Avis Hart, Daniel D. Feldman - Geometry - 1912 - 504 pages
...of circle ABCD in terms of its diameter; ie to compute the value of TT. ARGUMENT 1. The ratio of the **circumference of a circle to its diameter is the same for all circles.** 2. Since the diameter of the given circle is ' unity, the side of an inscribed square will be V2. REASONS... | |
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