Solid Geometry, المجلد 1Macmillan, 1875 - 422 من الصفحات |
المحتوى
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طبعات أخرى - عرض جميع المقتطفات
عبارات ومصطلحات مألوفة
asymptotic ax² axes axis bisects by² central conicoid centre chord circular section cone confocal conical surface conjugate diameters constant corresponding cosines cubic curve of intersection cyclic sections cylinder cz² developable surface directing plane direction-cosines directrix drawn ellipse ellipsoid enveloping find the equation finite fixed plane fixed point focal conic given plane given point given straight line Hence hyperbola hyperbolic paraboloid hyperboloid infinite distance infinite number Let the equation line joining line of intersection locus normals obtain parabola parallel perpendicular plane containing plane of xy plane passing plane section position principal planes projection quadric ratio right angles satisfy the equation second degree semi-axes sheet shew similarly sphere sphero-conic surface tangent plane tetrahedral coordinates tetrahedron umbilical values vertex x² y²
مقاطع مشهورة
الصفحة 217 - Conic, is the locus of a point which moves so that its distance from a fixed point is in a constant ratio to its distance from a fixed straight line.
الصفحة 340 - Spirals contains demonstrations of the principal properties of the curve, now known as the Spiral of Archimedes, which is generated by the uniform motion of a point along a straight line revolving uniformly in one plane about one of its extremities. It appears from the introductory epistle to Dositheus that Archimedes had not been able to put these theorems in a satisfactory form without long-continued and repeated trials; and that Conon, to whom he had sent them as problems...
الصفحة 377 - R be the radii of curvature, torsion and spherical curvature of a curve at a point whose distance measured from a fixed point along the curve is s, prove that 8. When the polar surface of a curve is developed into a plane, prove that the curve itself degenerates into a point on the plane, and if r, p be the radius vector and perpendicular on the tangent to the developed edge of regression of the polar surface drawn from this point, prove that 9. Prove that the angle between the shortest distance...
الصفحة 289 - An annular surface is generated by the revolution of a circle about an axis in its own plane; prove that one of the principal radii of curvature, at any point of the surface, varies as the ratio of the distance of this point from the axis to its distance from the cylindrical surface described about the axis and passing through the centre of the circle.
الصفحة 18 - The orthogonal projection of a line upon a plane is the length of the line multiplied by the cosine of the angle of inclination of the line to the, plane.
الصفحة 410 - At any point of a geodesic on a central conicoid, the rectangle contained by the diameter parallel to the tangent at that point and the perpendicular from the centre on the tangent plane at the point is constant. The differential equations of a geodesic on the conicoid aa? + by* + cz3 = 1 are (Px d*y tfz d£==~di?=di? ax by cz ' *" y" z
الصفحة 110 - A conic section is by definition the locus of a point whose distance from a fixed point is in a constant ratio to its distance from a fixed straight line.
الصفحة 80 - To shew that the straight lines joining the middle points of opposite edges of a tetrahedron intersect and bisect each other.
الصفحة 26 - P, the opposite direction is defined by 7r+a, 7T+/3, 7T+7, and therefore these angles with an algebraical distance — PQ, equally determine the position of the point Q with reference to P. The distance of the point (x, y, z...