 | Charles Hutton - Mathematics - 1811 - 424 pages
...rules for Plane Trigonometry, without considering the Chords of the respective Arcs or Sides. " Let a, b, c, be the sides, and A, B, c, the angles of a spherical triangle, on the surface of a sphere whose radius is r ; then a similar triangle on the surface... | |
 | Charles Hutton - Mathematics - 1812 - 624 pages
...rules for Plane Trigonometry, without considering the Chords of the respective Arcs or Sides. Let a, A, c, be the sides, and A, B, c, the angles of a spherical triangle, on the surface of a sphere whose radius is r ; then a similar triangle on the surface... | |
 | Charles Hutton - Mathematics - 1822 - 680 pages
...Plane Trigonometry, without considering the Ghofds of the respective Arcs or Sides. , 81 Let 0, 5, c, be the sides, and A, B, c/ the angles of a spherical triangle, on the surface of a sphere whose radius is r • then a siniilar triangle on the... | |
 | Dionysius Lardner - Plane trigonometry - 1828 - 434 pages
...we shall establish it by geometrical construction, and subsequently derive all others from it. Let a, b, c, be the sides, and A, B, c, the angles of a spherical triangle, as usual. From the vertex of the angle c let tangents be drawn to the arcs a and... | |
 | Charles Hutton - Mathematics - 1831 - 656 pages
...the rules for plane trigonometry, without considering the chords of the respective arcs or sides. Let a, b, c, be the sides, and A, B, c, the angles of a sphe. rical triangle, on the surface of a sphere whose radius is r : then a similar triangle on the... | |
 | Encyclopedias and dictionaries - 1832 - 636 pages
...shall establish it by geometrical construction, and subsequently derive all others from it. Let a, 6, c, be the sides, and A, B, C, the angles of a spherical triangle, as usual. From the vortex of the angle C let tangents be drawn to the arcs a and... | |
 | Richard Abbatt - Spherical astronomy - 1841 - 234 pages
...the included side to find the other sides and the third angle. Take the polar triangle (81.) and let a', b', c', be the sides and A' B' C' the angles opposite : then since the sides and angles of the polar triangle are the supplements of the angles... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 476 pages
...or<j!> =49 8' 19" '7 2. Given A = 5T 30', C = 131 30', and b = 80 19', to find the other parts. Let a', b', c' , be the sides, and A', B', C', the angles, of the polar triangle, then a'= 180' -A = 128" 30', c' = 180 - C = 48' 30', B' = 180"- b = 99 41'. Whence... | |
 | Mathematics - 1865 - 132 pages
...produced to meet the circle in F ; prove that the rectangle AF . FE is constant ............ 110 1702. If a, b, c be the sides, and A, B, C the angles of a triangle, prove that tan' t A tan' IB + - - l - tan' IB tan' JO _— - - - (b — c) (c— a) (c— a) (a—... | |
 | Florian Cajori - Mathematics - 1893 - 476 pages
...To the four fundamental formulas already given by Ptolemy, he added a fifth, discovered by himself. If a, b, c, be the sides, and A, B, C, the angles of a spherical triangle, right-angled at A, then cos B = cosb sin C. This is frequently called " Geber's... | |
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PROBLEM VIII. It is required to Investigate a Theorem, by means of which, Spherical Triangles, whose Sides are Small compared with the radius, may be solved by the rules for Plane Trigonometry, without considering the Chords of the respective Arcs or... 
