 Halma ; of. the reproduction in Cantor's Oesch. d. Mathematik, I. (1894), p. 389). Ptolemy's object is to connect by an equation the lengths of the chord of an arc and the chord of half the arc. Substantially his procedure is as follows. Suppose AP, PQ...  Trigonometry - Page 27by Arthur Graham Hall, Fred Goodrich Frink - 1909 - 239 pagesFull view - About this book
 | Isaac Todhunter - Measurement - 1869 - 312 pages
...we obtain -4Z>=3771, and therefore AB=T542. Thus the chord of the arc is about 7-542 feet. 97. Given the chord of an arc and the chord of half the arc, to find the diameter of the circle. Here we know AD and AE. We first obtain ED by Art. 60, and then... | |
 | Edward Olney - Geometry - 1882 - 262 pages
...perimeter of the regular inscribed polygon of 24 sides ; then of 48, etc. In order to do this, let us find the relation between the chord of an arc and the chord of £ the arc in a Fio. sea. circle whose radius is 1. Call the chord of an arc as AB, O, and the chord... | |
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...to each other as their radii, and as their diameters (390). PROPOSITION X. 418. Problem. — To find the relation between the chord of an arc and the chord of half the arc in a circle whose radius is r. SOLUTION. Let O be the centre of the circle, AB any chord, and CB the... | |
 | Building - 1888 - 164 pages
...ч/В~Ёi— (B E— BD)2 Chord ADC = 2AD = 2 ъ/ТГЁ?— (BE — ВТ5)s с = 2 vVhR— h1 (4.) Given, the chord of an arc and the chord of half the arc, to find the length of the arc, 8AB — ADC . __, . . = arc ABC (very nearly). (5-) To find the number... | |
 | Archimedes - Geometry - 1897 - 528 pages
...Gesch. d. Mathematik, I. (1894), p. 389). Ptolemy's object is to connect by an equation the lengths of the chord of an arc and the chord of half the arc. Substantially his procedure is as follows. Suppose AP, PQ to be equal arcs, AB the diameter through... | |
 | Arthur Graham Hall, Fred Goodrich Frink - Plane trigonometry - 1909 - 272 pages
...42. Find the lengths of the chords of the following arcs in terms of the radius : 30°, 36°, 40°, 45°, 60°, 75°, 90°, 120°. Compute, given R =...the chord of an arc and the chord of half the arc. 45. Compute and tabulate the perimeter and the circumferences of the circum- and in-circles of a regular... | |
 | Arthur Graham Hall, Fred Goodrich Frink - Trigonometry - 1910 - 204 pages
...45°, 60°, 75°, 90°, 120°. Compute, given R = 100. l> FIG. 18. 43. Express in terms of the «we and radius the relation between the chord of an arc...circumscribed circle, the radius r of the inscribed circle, the side s, and the number of sides n of a regular polygon. « = 35°, « = 42; « = 72°, b = 125;... | |
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...Oesch. d. Mathematik, I. (1894), p. 389). Ptolemy's object is to connect by an equation the lengths of the chord of an arc and the chord of half the arc. Substantially his procedure is as follows. Suppose .11', PQ to be equal arcs, AB the diameter through... | |
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