An Introduction to the Ancient and Modern Geometry of Conics: Being a Geometrical Treatise on the Conic Sections with a Collection of Problems and Historical Notes and ProlegomenaDeighton, Bell and Company, 1881 - 384 páginas |
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Otras ediciones - Ver todas
An Introduction to the Ancient and Modern Geometry of Conics: Being a ... Charles Taylor Sin vista previa disponible - 2017 |
Términos y frases comunes
ABCD abscissa asymptotes auxiliary circle axes bisects CA² central conic centre Chasles chord of contact circumscribed cone confocal Conic Sections conjugate axis conjugate diameters conjugate hyperbolas constant ratio Corollary cross ratio deduced Desargues described determine diagonals drawn eccentricity ellipse envelope equal angles equilateral hyperbola extremities fixed point fixed straight line focal chord focal distances focal perpendicular foci four points geometry given conic given point harmonically Hence homographic inscribed intercept intersection involution latus rectum lemma line at infinity line joining locus mean proportional meet the curve meet the directrix meet the tangent middle point Newton nine-point circle normal ordinate parabola parallelogram plane point of concourse points at infinity points of contact polar Porismes projection Prop PROPOSITION quadrilateral radius rectangular hyperbola respect right angles Scholium segments shew shewn supplementary angles tangents theorem triangle vertex vertices
Pasajes populares
Página 78 - Every central conic has a second focm and directrix ; and the sum of the focal distances of any point on the curve...
Página 46 - To draw that diameter of a given circle which shall pass at a given distance from a given point. 9. Find the locus of the middle points of any system of parallel chords in a circle.
Página xxxv - ... 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.
Página xxi - 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.
Página 40 - 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.
Página xliii - ... 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...
Página 223 - 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.
Página 209 - If a point move in a plane in such a way that the sum or difference of its distances from two fixed points...
Página 210 - 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.
Página 353 - In like manner it may be shewn that the two pairs of opposite sides of a quadrilateral inscribed in a conic make intercepts on either minor directrix which subtend supplementary angles at the centre.