 | Charles William Hackley - Geometry - 1847 - 248 pages
...declination and in right ascension of a star, and various other useful relations of a similar kind. PROP. IV. The angle formed by two arcs of great circles is equal to the angle contained by the tangents drawn to these arcs at their point of intersection, and is measured by the... | |
 | Charles Davies - Trigonometry - 1849 - 372 pages
...pole with which a perpendicular to AM may be described passing through the point P. PROPOSITION VI. THEOREM. The angle formed by two arcs of great circles,...equal to the angle formed by the tangents of these, arcs at their point of intersection, and is measured by the arc described from this point of intersection,... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...radii; in which case, the centers and the point of contact lie in one straight line. PROPOSITION VII. THEOREM. The angle formed by two arcs of great circles, is equal to the angle formed by the tangents of those arcs at the point of their intersection ; and is measured by the arc of a great circle described... | |
 | George Roberts Perkins - Geometry - 1850 - 332 pages
...the centres and the point of contact lie in the same straight line. PROPOSITION XXI. THEOREM. Tlie angle formed by two arcs of great circles is equal to the angle formed by the tangents of these arcs at the point of intersection, and is therefore measured by the arc described from the point of... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...the point D, its extremity A will describe the arc of a great circle AMB. PROPOSITION IV. THEOEEM. The angle formed by two arcs of great circles, is equal to the angle formed by the tangents of these arcs at their point of intersection. The angle is measured by the arc of a great circle described from... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...point D, its extremity A will describe the arc of a great circle AMB. PROPOSITION IV. THEOREM. &»** The angle formed by two arcs of great circles, is equal to the angle formed by the tangents of these arcs at their point of intersection. The angle is measured by the arc of a great circle described from... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...radii ; in which case, the centers and the point of contact lie in one straight line. PROPOSITION VII. THEOREM. The angle formed by two arcs of great circles, is equal to the angle formed by the tangents of those arcs at the point of their intersection ; and is measured by the arc of a great circle described... | |
 | Charles Hutton - Mathematics - 1860 - 1020 pages
...XYZ, except Z, is without the sphere. Therefore, the plane XYZ is a tangent to the sphere. PROF. fr. The angle formed by two arcs of great circles, is equal to the angle connota b) the tangents drawn to these arcs at their point of intersection, taid и mese-t by the arc... | |
 | George Roberts Perkins - Geometry - 1860 - 472 pages
...same distance, describe the arc PM, which will be the perpendicular required. EIGHTH BOOK. THEOREM V. The angle formed by two arcs of great circles is equal to tho angle formed by the tangents of these arcs at the point of intersection, and is therefore measured... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...centres and the point of contact lie in the same straight line. PROPOSITION VII. — THEOREM. 534. The angle formed by two arcs of great circles is equal to the angle formed by the tangents of those arcs at BOOK IX. Let BAC be an angle formed by the two arcs AB, AC ; then will it be equal to... | |
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... this point of intersection, as a pole, and limited by the sides, produced if necessary. Let the angle BAC be formed by the two arcs AB, AC ; then it will be equal to the angle FAG formed by the tangents AF, AG, and be measured by the arc DE, described... 
