The Elements of Coördinate Geometry: In Three Parts and an AppendixJ. Wiley, 1890 - 642 páginas |
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The Elements of Coordinate Geometry: In Three Parts and an Appendix De Volson Wood No hay ninguna vista previa disponible - 2015 |
Términos y frases comunes
a²b² algebraic angle asymptote Ax² axis of x B₁ bisects By² centre chord circle coefficients coincide cone conic section constant construction coördinate planes coördinates cos² curve directrix distance drawn ellipse equa equal equation becomes equations of condition Find the equation fixed point foci focus generatrix given line gives hence hyperbola hypocycloid imaginary intercept latus rectum length line passing locus major axis medial middle point Multiplying negative normal nß₁ ordinate origin parabola parallel perpendicular plane xy point of intersection polar equation pole positive preceding equation principal vertex Quadric Quaternions radius vector reference required equation right line secant sides Similarly sin² Substituting the values subtangent surface tangent tion transferrence triangle unit vectors variables versor vertex y₁ zero
Pasajes populares
Página 139 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Página 236 - ... sides parallel. 13. Two quadrilaterals are equivalent when their diagonals are respectively equal, and form equal angles. 14. Lines joining the middle points of the opposite sides of any quadrilateral, bisect each other. 15. Is there a point in every triangle, such that any straight line through it divides the triangle into equivalent parts? 16. To construct a parallelogram having the diagonals and one side given. 17. The diagonal and side of a square have no common measure, nor common multiple.
Página 21 - ... in which a' and V are undetermined. The two right lines will be parallel, if they make the same angle with the axis of abscissas. Hence, if we make a' = a the second line will be parallel to the first ; and its equation will be y = ax + V, in which equation V is undetermined, as it should be, since an infinite number of lines may be drawn parallel to a given line. Scholium. If it be further required that the parallel shall pass through a given point, the position of the line will be entirely...
Página 37 - The two fixed points F and F' are called the foci of the ellipse. The point C midway between the foci is called the focal centre, or simply the centre.
Página 252 - Cor. 1 . Hence, the line which bisects the vertical angle of an isosceles triangle, bisects the base.
Página 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.
Página 139 - Given the base of a triangle and the sum of the squares on its sides: to find the locus of its vertex.
Página 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.
Página 155 - Y' + cos. Z cos. Z' = 0 ^ cos. X cos. X" -f- cos. Y cos. Y
Página 204 - ... 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...