The Elements of Coordinate Geometry: In Three Parts: 1. Cartesian Geometry; 2. Quaternions; 3. Modern Geometry, and an Appendix |
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a²b² algebraic angle asymptote Ax² axes axis of x B₁ b²x² bisects By² centre chord circle coefficients cone conic section constant coördinate planes coördinates cos² curve directrix distance ellipse equa equal equation becomes equation of condition Find the equation fixed point foci focus generatrix given line gives hence hyperbola hypocycloid imaginary infinite number intercept latus rectum length locus major axis medial middle point multiplying negative nß₁ ordinate origin parabola parallel perpendicular plane xy point of intersection polar equation pole positive preceding Article preceding equation principal vertex quadric Quaternions radius vector reference required equation right line secant sides Similarly sin² straight line Substituting the values subtangent surface tangent tion transferrence triangle unit vectors variables versor vertex y₁ zero
Popular passages
Page 178 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Page 139 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Page 286 - These equations may also be written in the form of proportions sin a : sin b : sin c = sin A : sin B : sin C. That is, the sines of the sides of a spherical triangle are proportional to the sines of the opposite angles.
Page 91 - From these values we have or, 7%e swm o/" the squares of any pair of conjugate diameters of an ellipse is constant (see Ex. 3, Art. 159). 174. In the hyperbola we must change the signs of i...
Page 73 - MRS^ at a point on the indifference curve we can do so by drawing tangent at the point on the indifference curve and then measuring the slope by estimating the value of the tangent of the angle which the tangent line makes with the X-axis.
Page 256 - Cor. 1. Hence, the line which bisects the vertical angle of an isosceles triangle, bisects the base.
Page 9 - P", in the 4th angle, we have x", and — y"; which, substituted in the formula, gives for P' in the 1st angle and P" in the 4th, D — \/(x — x'")*-{- (y + y" )"• THE EIGHT LINE IN A PLANE.
Page 139 - Show that the locus of a point whose distance from a fixed plane is always equal to its distance from a fixed line perpendicular to the plane is a quadric cone.
Page 139 - Given the base of a triangle and the sum of the squares on its sides: to find the locus of its vertex.
Page 206 - ... case the conditions mentioned under (2) are met with. 6. — Interference between the teeth themselves is a common cause of noisy gearing. To rightly understand this cause it is necessary to enter briefly into the theory of the shape of the involute tooth. The involute is commonly denned as a curve described by the end of a string as it is unwound from a cylinder, the string being kept taut, so that in every position it may be described as a tangent to the cylinder. In Fig. 3, A represents the...