Elements of Trigonometry |
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a² b² a² y² abscissa algebraical asymptote axis major b₁ b² x x b²x² centre circle co-efficients co-ordinate planes conic section conjugate diameters cosec cosine cuts the axis determined directrix distance draw drawn ellipse equal find the equation formulas generatrix Geometry given line given point given straight line hyperbola intersection Latus Rectum line passing linear unit locus meets the curve negative oblique ordinate origin parabola parallel perpendicular polar equation positive quantities radius rectangle rectangular axes referred right angle second order sine solid angle square supplemental chords surface tangent transformation triangle trigonometrical values x₁ x¹² y₁ z₁
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Page 27 - 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 2 - 375. The position of a point referred to three co-ordinate planes . . . 197 376. 7, 8. The projection of a straight line on a plane is a straight line. If AB be the line, its projection on a plane or line is AB cos. 6
Page 80 - 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 17 - 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 76 - 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 95 - 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 30 - 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 xviii - 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
Page 201 - and the projection of AB on any line parallel to CD is of the same length as A' B'. 379. The projection of the diagonal of a parallelogram on any straight line is equal to the sum of the projections of the two sides upon the same straight line. B