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Page 29 - the definition. There remains then only the first case with this limitation, which is the proposition asserted. (B.) The greater angle of a spherical triangle is opposite to the greater side, and the sum of the angles of a spherical triangle is greater than two and less than six right angles.
Page 86 - AC. THE NORMAL. 126. The normal to any point of a curve is a straight line drawn through that point, and perpendicular to the tangent at that point. To find the equation to the normal P G. The equation to a straight line through the point P (x
Page 19 - y. Hence AD, and therefore AC and AB are found, and the triangle is determined. 18. To divide a straight line, so that the rectangle contained by the two parts may be equal to the square upon a given line 6. Let
Page 82 - it maybe proved that The rectangle QP, Q P' = The square on S M. 119. To find the length of the perpendicular from the focus on the tangent. Let S y, Hz, be the perpendiculars on the tangent PT. Taking the expression in (48.) we have
Page 101 - 165. Conversely, To find the locus of a point, the difference of whose distances from two fixed points S and H is constant or equal 2 a. Hence
Page 32 - y = 0, and the line passes through the origin ; also a or the tangent of the angle which the line makes with the axis of a?
Page xx - HP - SP = A A' .... 93 165. To find the locus of a point the difference of whose distances from two fixed points is constant ..........93
Page 21 - Sin. (A + B) = sin. A. cos. B + cos. A. sin. B sin, (a + ft) sin, a. cos, ft cos. a sin. ft a