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An Introduction to the Ancient and Modern Geometry of Conics: Being a ...
No preview available - 2017
ABCD asymptotes axes axis becomes bisects called centre chord circle circumscribed common cone conic conjugate conjugate diameters constant construction contained conversely Corollary corresponding curvature curve deduce Desargues described determine diagonals diameter direction directrix distances divided double draw drawn ellipse envelope equal equilateral hyperbola evident extremities figure fixed point focal chord foci focus follows four points geometry given point harmonically Hence hyperbola infinity inscribed intercept intersection involution joining latter length locus mean meet method middle point normal opposite ordinate pair parabola parallel passes perpendicular plane points of contact polar pole position projection Prop proportional PROPOSITION proved quadrilateral radius ratio reciprocal rectangular rectum regarded relation respect right angles segments shew shewn sides similar sphere square straight line subtends taken tangents theorem third touch transversal triangle varies vertex vertices
Page 80 - Every central conic has a second focm and directrix ; and the sum of the focal distances of any point on the curve...
Page xxxvii - ... solidity of the pyramid will still be equal to one third of the product of the base multiplied by the altitude, whatever be the number of sides of the polygon which forms its base- • hence, the solidity of the cone is equal to one third of the product of its base multiplied by its altitude.
Page xxiii - The angles at the base of an isosceles triangle are equal to one another; and if the equal sides be produced, the angles -upon the other side of the base shall be equal.
Page 42 - The triangle whose angular points are the focus of a conic and the intersections of the tangent and the diameter at any point with the axis and the directrix respectively has its orthocentre at the point in which the tangent meets the directrix.
Page xlv - ... or scalenous, if the axis does not form a right angle with the base. If a cone is cut parallel with its base, the section, of course, is a circle : if, however, the section is made obliquely, that is, nearer to the base at one...
Page 225 - The radius of curvature at any point of a parabola is double of the portion of the normal intercepted between the curve and the directrix.
Page 211 - If a point move in a plane in such a way that the sum or difference of its distances from two fixed points...
Page 212 - Two circles have double internal contact with an ellipse,! and a third circle passes through the four points of contact. If t, ft T be the tangents from any point on the ellipse to these three circles, prove that T* = #'. 579.