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arcs be drawn arcs drawn asymptotes axis bisects chords circle co-ordinate axes co-ordinate planes coefficients coincide cone conic section conical surface conjugate diameters consecutive constant contain cuts cyclic arc cyclic plane cylinder denote determine developable surface differential directrix distance ellipse ellipsoid envelope equa equal angles find the equation fixed arcs fixed planes fixed point focal line foci focus given line given point Hence hyperbola hyperboloid latus rectum lines of curvature locus meet oblique ordinate origin osculating plane parabola paraboloid perpendicular plane of xy plane parallel plane passing point of concourse point of intersection points of contact polar positive principal sections projection properties radii rectangular represents respectively right angles second degree second order sides similarly sphere spherical angle spherical conic straight line surface of revolution tangent arcs tangent plane theorems tion touching trace values vertex vertices
Página 138 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Página 81 - To find the locus of a point, the difference of whose distances from two fixed points is always equal to a given quantity 2 a.
Página 84 - Then the areas must be multiplied respectively by the expressions cos a cos a' + cos ß cos /3' + cos y cos y
Página 96 - Application to the tangent and to its construction. The rectangle of the parts of a secant, comprised between a point of the curve and the asymptotes, is equal to the square of half of the diameter to which the secant is parallel. Form of the equation of the hyperbola referred to its asymptotes. Of the parabola. Axis of the parabola.
Página 242 - Shew that the locus of the focus of an ellipse rolling along a straight line is a curve such that if it...
Página 76 - Pappus, the locus of a point whose distance from a given point is in a given ratio to its distance from a fixed...
Página 62 - The length of the projection of a limited line upon a plane, is equal to the length of the line multiplied by the cosine of the acute angle which it forms with the plane.
Página 89 - Unes drawn from the centre of the sphere, upon the tangent plane at о then ом and ON will be projected into rectilinear co-ordinates to the projection of P. The equation of a great circle is of the first degree, or of the form ax + by + c= 0, and an equation of the nth degree...