 | Charles Hutton - 1811 - 424 pages
...the quotient of the cube of the length of the arc divided by the square of the radius. PROBLEM VIII. It is required to Investigate a Theorem, by means...which, for the sake of brevity, we represent by a, /3, y, respectively : then, by , COS a — COS & . COS y euua. I chap, iv, we have cos A n - : —... | |
 | Charles Hutton - 1811 - 404 pages
...considering the Chords of the respective Arcs or Sides. bet a, b, c, be the sides, and А, в, с, the angles of a spherical triangle, on the surface of a sphere whose radius is r ; then then a similar triangle on the surface of a sphere whose radius = 1 , will have for its sides — ,... | |
 | Charles Hutton - 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...the surface of a sphere whose radius is r • then a siniilar triangle on the surface of a sphere whoseradius =3= 15 will have for its sides -, -, - ; which,... | |
 | Dionysius Lardner - 1828 - 434 pages
...case, 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 b ; and from the centre... | |
 | Euclid, Dionysius Lardner - 1828 - 542 pages
...sides, three times the sum of the squares of the sides is equal to four times that of the bisectors. Let A, B, C, be the sides and a, b, c the corresponding bisectors. The sum of the squares of B an'd C is equal twice the sum of the squares of... | |
 | 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 6; and from the centre... | |
 | Cambridge Philosophical Society - 1838 - 618 pages
...example, by one which I proposed in the Transactions of the Royal Society of Edinburgh, Vol. x. viz., Let a, b, c, be the sides, and A, B, C the opposite angles; a+b : ab = tan^(A+B) : tan^(AB), cos±(AB) : cos^(A + B) = a + b : C ; Also sin^(AB)... | |
 | Richard Abbatt - 1841 - 234 pages
...and 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... | |
 | 1856 - 410 pages
...[SECOND SOLUTION. Mr. Andrew Roy, Dundee Academy ; and similarly by Mr. Stephen Watson, Castleside.] Let a, b, c be the sides, and A, B, C the opposite angular points of the given triangle, and G the centre of the inscribed circle ; then if af... | |
 | Royal Military Academy, Woolwich - 1853 - 476 pages
...before. 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... | |
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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... 
