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abscissa algebraical asymptote axis major bisecting called centre co-efficients co-ordinate planes cone conic section conjugate diameters cosec cosine cuts the axis cutting plane cycloid determined directrix distance draw drawn ellipse equal figure find the equation focus formulae generatrix geometrical given line given point hyperbola intersection Latus Rectum line passing linear unit loci locus meet the curve negative oblique ordinate origin parabola parallel parallelogram parallelopiped perpendicular polar equation positive quantities radius rectangle rectangular axes referred right angle roots sides sine solid angle spherical triangle square Substituting supplemental chords surface tangent trace trigonometrical trigonometrical functions values vertex
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