A Treatise on Analytical Geometry |
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Common terms and phrases
a² b² a² sin 2a abscissas angle formed asymptote b2 a² becomes centre chord passing circle co-ordinates x coefficients conjugate diameters consequently constant quantities Corollary corresponding curve deduced derive determined diametral plane distance ellipse equa equal to zero equation h formula geometrical loci given point hence hyperbola Let fig line in space line passing locus negative normal observed obtain ordinates origin P₁ P₂ parabola perpendicular perpendicular drawn plane passing plane XAY positive preceding equation preceding number principal plane PROPOSITION radius real value rectangular axes represented right angles Scholium second degree second member second order semi-axes square straight line substituting subtangent suppose supposition surface system of axes system of chords tangent termed tion transverse axis trigonometry x₁ y₁ ε²
Popular passages
Page xiii - ... of the squares of any two conjugate diameters is equal to the difference of the squares of the axes.
Page 3 - A is projected into an area which is equal to the given area multiplied by the cosine of the angle between the planes.
Page 39 - If two planes which cut each other are perpendicular to a third plane, their common intersection is also perpendicular to that plane. Let the planes BA, DA, be perpendicular to NM; then will their intersection AP be perpendicular to NM. For, at the point P, erect a perpendicular to the plane MN; that perpendicular must be at once in the plane AB and in the plane AD (P, 17, c.) ; therefore, it is their common intersection...
Page 81 - ... in which x", y", are the co-ordinates of the point of contact...
Page 125 - Find the equation of a straight line passing through the origin of the coordinates, and perpendicular to the line x — y=l.
Page iii - ... of co-ordinates, and geometrical loci on a plane ; the second of co-ordinates, and geometrical loci in space ; the third treats of lines of the second order ; and the fourth of surfaces of the same order.
Page 91 - F s = p and ss' — 2p ; that is, the double ordinate passing through the focus is equal to the parameter.
Page 94 - MTX = fnamely, the trigonometrical tangent of the angle which the tangent of the curve...
Page 203 - Л пу straight line can meet a surface of the second order in no more than two points.
Page 205 - Since from (e,) we have in which x , y , z are the co-ordinates of any point of mn ; substituting these values of a and a...