 | Euclid, Dionysius Lardner - 1828 - 542 sider
...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... | |
 | Charles Hutton - 1831 - 656 sider
...by 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... | |
 | 1832 - 636 sider
...foundation of the whole structure of spherical trigonometry. This formula, therefore, may be regarded in spherical trigonometry in the same point of view...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... | |
 | Cambridge Philosophical Society - 1838 - 618 sider
...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 sider
...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 sider
...[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 sider
...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... | |
 | 1865 - 128 sider
...= mi. p. 107, line 20, read (bC)-t- (Be)-', p. 110, Quest. 1702, line 1, before "prove," insert "If a, b, c be the sides, and A, B, C the angles of a triangle." p. Ill, line 1, the number of this Question should be 1668, instead of 1679. MATHEMATICAL... | |
 | 1865 - 132 sider
...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—... | |
 | Seth Thayer Stewart - 1893 - 262 sider
...and the common intersection are together one-third of the squares of the sides of the triangle. I. Let A, B, C, be the sides, and a, b, c, the medians, x, y, and z being the segments between the Z s and the common point of intersection. 2. x,... | |
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Let a, b, c, be the sides, and A, B, c, the angles of a spherical triangle, as usual. 