Solutions of the Problems and Riders Proposed in the Senate-house Examination for 1864Macmillan, 1864 - 212 sider |
Vanlige uttrykk og setninger
angular velocity arithmetical progression axes bisecting cardioid centre of force centre of gravity chord circle conic conjugate constant coordinates cos² cose cotb curvature curve cycloid cylinder described determination diameter distance drawn ecliptic ellipse equal equation equilibrium Find fixed point fluid foci focus formulæ given point Hence horizontal plane hyperbola inclination integral intersection Investigate length line joining locus maximum minimum motion orbit P₁ parabola parallel parallelogram particle pencil perpendicular placed position pressure prove quadric radii radius ratio rays refraction respectively right angles shew sides Similarly sin² sine singular solution sino sphere square string surface surface of revolution tangent lines tanr transverse axis triangle Trin tube vertex vertical weight whence x₁
Populære avsnitt
Side 177 - Triangles upon equal bases, and between the same parallels, are equal to one another.
Side 177 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Side 198 - Prove that a heavy particle, let fall from rest in a medium in which the resistance varies as the square of the velocity...
Side 177 - EUCLID'S ELEMENTS. PROPOSITION 36. THEOREM. If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the otlier touches it; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square on the line which touches it.
Side 177 - Describe a square which shall be equal to a given rectilineal figure.
Side 104 - Find the geometrical focus of a pencil of rays after direct refraction at a spherical surface.
Side 95 - Prove that the distance between the foot of the inclined plane and the focus of the parabola which the particle describes after leaving the plane is equal to the height of the plane.
Side 109 - ... y'/k, the equation to a conic section with the origin at the focus. Hence the path described by a particle under the action of a central force varying inversely as the square of the distance is a conic section whose focus is at the center of force. This is the case of planetary motion, the sun being at the center of force. The further discussion of this problem will be found in works on mathematical astronomy. 103. CONSTRAINED MOTION. — To a particle acted on by a force F in an assigned...
Side 177 - To erect a straight line at right angles to a given plane, from a point given in the plane. Let A be the point given in the plane.
Side 181 - Enunciate the principle of virtual velocities, and prove it in the case of a bent lever.