Elements of Plane Analytic Geometry, Volum 25Ginn, 1888 - 344 pàgines |
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a² b2 a²b² a²k² a²m² abscissa asymptotes auxiliary circle axes are oblique axis of X b2 a² b²h² becomes bisectors bisects By² centre chord of contact circle x² confocal conjugate diameters conjugate hyperbola constant coordinate axes corresponding cos² curve denote directrix drawn ellipse equal find the equation Find the length find the locus Find the points fixed point focal chord focal distance foci focus given circles given line imaginary latus-rectum loci locus major axis meet middle points opposite sides ordinate P(xy parabola y=4px parabola y² perpendicular point h point of intersection point P'(x'y point P(h point x'y points of tangency polar coordinates polar equation pole radical axis ratio rectangular axes required equation secant sin² subtangent system of conics tangent tangent and normal triangle trilinear coordinates Va² values vertex vertices
Passatges populars
Pàgina 137 - A conic section is the locus of a point which moves so that its distance from a fixed point, called the focus, is in a constant ratio to its distance from a fixed straight line, called the directrix.
Pàgina 344 - Many theorems are proved both by the method of rates and that of limits• and thus each is made to throw light upon the other. The chapter on differentiation is followed by one on direct integration and its more important applications. Throughout the work there are numerous practical problems in Geometry and Mechanics, which serve to exhibit the power and use of the science, and to excite and keep alive the interest of the student.
Pàgina 178 - Conic, is the locus of a point which moves so that its distance from a fixed point is in a constant ratio to its distance from a fixed straight line. The fixed point is called a focus, the fixed straight line is called a directrix, and the constant ratio is called the eccentricity.
Pàgina 176 - The locus of a point, the sum of the squares of whose distances from n fixed points is constant, is a circle.
Pàgina iii - TN this work, the author has had particularly in mind the needs of those students who can devote but a limited time to the subject, and yet must become quite familiar with at least its more elementary and fundamental part. For this reason, the earlier chapters are treated with somewhat more fulness than is usual. For some propositions, more than a single proof is given, and particular care has been taken to illustrate and enforce all parts of the subject by a large number of numerical applications....