Spherical Trigonometry: For the Use of Colleges and SchoolsMacmillan and Company, 1863 - 132 σελίδες |
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Σελίδα 4
... preceding Article , the angle between the great circles CD and CE is the angle MON . In the figure to Art . 6 , since PO is perpen- dicular to the plane ACB , every plane which contains PO is at right angles to the plane ACB . Hence the ...
... preceding Article , the angle between the great circles CD and CE is the angle MON . In the figure to Art . 6 , since PO is perpen- dicular to the plane ACB , every plane which contains PO is at right angles to the plane ACB . Hence the ...
Σελίδα 5
... preceding Article . ) For suppose PA and PC to be quadrants , and O the centre of the sphere ; then since PA and PC are quadrants , the angles POC and POA are right angles . Hence PO is at right angles to the plane AOC , and P is a pole ...
... preceding Article . ) For suppose PA and PC to be quadrants , and O the centre of the sphere ; then since PA and PC are quadrants , the angles POC and POA are right angles . Hence PO is at right angles to the plane AOC , and P is a pole ...
Σελίδα 8
... preceding Article , the arc AB forms one side of the spherical triangle ABC , and the plane angle AOB is measured by the frac- arc AB ; and thus the arc AB is proportional to the angle tion radius OA AOB so long as we keep to the same ...
... preceding Article , the arc AB forms one side of the spherical triangle ABC , and the plane angle AOB is measured by the frac- arc AB ; and thus the arc AB is proportional to the angle tion radius OA AOB so long as we keep to the same ...
Σελίδα 9
... preceding Article it will follow that any angle of a spherical triangle is less than two right angles . For suppose a triangle formed by BC , CA , and BEDA , having the angle BCA greater than two right angles . Then suppose D to denote ...
... preceding Article it will follow that any angle of a spherical triangle is less than two right angles . For suppose a triangle formed by BC , CA , and BEDA , having the angle BCA greater than two right angles . Then suppose D to denote ...
Σελίδα 13
... preceding two Articles may be extended . Thus , if there be any polygon which has each of its angles less than two right angles , any one side is less than the sum of all the others . This may be proved by repeated use of Art . 29 ...
... preceding two Articles may be extended . Thus , if there be any polygon which has each of its angles less than two right angles , any one side is less than the sum of all the others . This may be proved by repeated use of Art . 29 ...
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a+b+c angular points approximately bisecting calculated centre circle described circular measure cos b cos cos² cos³ cosb cosines Crown 8vo deduce denote equal equation Fcap Fellow of St formed formulæ given greater Hence inscribed John's College late Fellow less Let ABC limp cloth lune M.A. Fellow middle point Napier's analogies Napier's Rules obtain perpendicular plane triangle Plane Trigonometry polar triangle pole polygon preceding article primitive triangle quadrant radius regular polyhedron respectively right angles right-angled triangles School Second Edition Sermons preached shew shewn Similarly sin b sin sin² sin³ sine small circle solid angle solution sphere spherical excess spherical triangle Spherical Trigonometry St John's College suppose surface tangent tetrahedron Third Edition Treatise triangle ABC Trinity College University of Cambridge values vols
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