 | Francis Nichols - Plane trigonometry - 1811 - 162 pages
...cosines and secants of two arcs, and also the sines and cosecants, are reciprocally proportional. 43. The sine of any arc is equal to half the chord of double that arc. For the radius CA, perpendicular to BE, bisects the chord BE in F (3. 3), and also the arc BAE subtended... | |
 | Charles Butler - Mathematics - 1814 - 528 pages
...quadrant be computed, and the whole arranged in a table, this table will serve for the whole circle. 34. The sine of any arc is equal to half the chord of double that arc; and conversely, the chord is double the sine of half the arc. Because CA cuts BG at right angles BD... | |
 | Miles Bland - Euclid's Elements - 1819 - 444 pages
...= ^/(l + tang*. A), tang. ^ = 7 (sec*. A - 1), cos. ^/ = , tang. ^xcotang. A = l. PROP. III. (62.) The sine of any arc is equal to half the chord of double the arc. Let the arc PB be double of PA. Join OA, PB intersecting each other in E. Since PB is double... | |
 | Miles Bland - Euclid's Elements - 1819 - 442 pages
...^(sec*. A - 1), cos. A = ^(1 +t'ng, ^ and sin. A = ^"fan, A , tang. A x cotang. A -I. PROP. III. (62.) The sine of any arc is equal to half the chord of double the arc. Let the arc PB be double of PA. Join OA, PB intersecting each other in E. Since PB is double... | |
 | Miles Bland - Geometry - 1821 - 898 pages
...cos. Л = I • 4 tatlK- -^ Л 4 and sm. ^ = /^1. > tang- A x cotang. Л= 1. PROP. III. (62.) I'Ae sine of' any arc is equal to half the chord of double the arc. Let the arc PB be double of PA. Join О А, РВ intersecting each other in E. Since PB is... | |
 | Thomas Keith - 1839 - 498 pages
...side of a hexagon, which is the chord of 60°, is equal to the radius of the circumscribing circle. f The sine of any arc is equal to half the chord of double that arc ,• thus let BF and BH (Plate I. Fig. 1.) be equal arcs, then FOB is the chord of the double arc FBH;... | |
 | William Scott - Measurement - 1845 - 288 pages
...Now, from the definition of the sine of an arc (Art. 30. a.), and from Eue. ш. 3. it follows that the sine of any arc is equal to half the chord of twice that arc. Therefore the sine of an arc of 18° is equal to half the chord of an arc of 36°.... | |
 | Nathaniel Bowditch - 1846 - 854 pages
...bisecting a chord at right angles, unust pass through the centre, and consequently be a diameter. XL VI. The sine of any arc is equal to half the chord of tieice that arc. For (in the last scheme) AD is the sine of the arc AF, and AF is equal to half the... | |
 | Samuel Alsop - Surveying - 1865 - 440 pages
...methods if the protractor in similar cases of instruments is employed. 342. By a Table of Natural Sines. The sine of any arc is equal to half the chord of twice that arc, or to the chord of twice the number of degrees on a circle of half the radius. "We... | |
 | Nathaniel Bowditch - Nautical astronomy - 1888 - 704 pages
...bisecting a chord at right angles must pass through the centre, and consequently be a diameter. XX. The sine of any arc is equal to half the chord of twice that arc. Forain the last scheme) AD is the sine of the arc AF, and AF is equal to half the arc... | |
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The sine of any arc is equal to half the chord of double the arc. Let the arc PB be double of PA. Join OA, PB intersecting each other in E. 