 | Francis Joseph Grund - Geometry, Plane - 1830 - 274 pages
...arc stands on the greater chord, and the greater chord subtends the greater arc. GEOMETRY. 175 13. The angles at the centre of a circle are to each other in the same ratio, as the arcs of the circumference intercepted by their legs. 14. If two angles at... | |
 | Francis Joseph Grund - Geometry, Plane - 1834 - 204 pages
...12. The greater arc stands on the greater chord, and the greater chord subtends the greater arc. 13. The angles at the centre of a circle are to each other in the same ratio, as the arcs of the circumference intercepted by their legs. 14. If two angles at... | |
 | James Hann - Plane trigonometry - 1854 - 138 pages
...arc equal to the radius of the circle, then, since by the 33rd Proposition of the 6th Book of Euclid, the angles at the centre of a circle / are to each other as the arcs on which they stand, i Angle AC В : four right angles :: arc AB : cir- \ cumference, but... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...°, ', " ; thus, to represent 1 6 degrees, 9 minutes, 23.5 seconds, we write 16° 9' 23".5. 40. Since angles at the centre of a circle are to each other as the arcs of the circumference intercepted between their sides (Geom., Prop. XVII. Bk. III.), these... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...°, ', "; thus, to represent 16 degrees, 9 minutes, 23.5 seconds, we write 16° 9' 23".5. 40. Since angles at the centre of a circle are to each other as the arcs of the circumference intercepted between their sides (Geom., Prop. XVII. Bk. III.), these... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...°, ', " ; thus, to represent 1 6 degrees, 9 minutes, 23.5 seconds, we write 16° 9' 23".5. 40. Since angles at the centre of a circle are to each other as the arcs of the circumference intercepted between their sides (Geom., Prop. XVII. Bk. III.), these... | |
 | James Smith - Mathematics - 1869 - 492 pages
...times radius = 6 x 57° 36- = 345° 36= perimeter of a regular inscribed hexagon to a circle of 360° ; But further : The angles at the centre of a circle...measure of an angle of 14" 24- to a circle of radius I = & ^~~^ = -25 = arc ACB ; therefore, 12-5 (arc ACB) =^ I2-5 x -25 =1 3-I25 = semi-circumference of... | |
 | James Smith - Circle-squaring - 1869 - 459 pages
...radius = 6 x 57? 36' = 345° 36' = perimeter of a regular inscribed hexagon to a circle of 360° ; But further : The angles at the centre of a circle...measure of an angle of 14° 24' to a circle of radius i = 8J^L5^5 = -25 - arc AC B ; therefore, 12-5 (arc ACB) — I2-5 x -25 = 3-125 ••= semi-circumference... | |
 | Benjamin Greenleaf - Trigonometry - 1876 - 204 pages
...°, ', " ; thus, to represent 1 6 degrees, 9 minutes, 23.5 seconds, we write 16° 9' 23".6. 40. Since angles at the centre of a circle are to each other as the arcs of the circumference intercepted between their sides (Geom., Prop. XVII. Bk. III.), these... | |
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... 23".5. 40. Since angles at the centre of a circle are to each other as the arcs of the circumference intercepted between their sides (Geom., Prop. XVII. Bk. III.), these arcs may be regarded as the measures of the angles, and the number of units of... 