Solutions of the Problems and Riders Proposed in the Senate-house Examination for 1864 |
Common terms and phrases
action angular velocity axes axis base body centre chord circle common condition conic constant coordinates corresponding cose curve cylinder described determination diameter direction distance Draw drawn ellipse equal equation equilibrium figure Find fixed point fluid focus force function given greater greatest Hence horizontal inclination integral intersection joining length less locus maximum meet motion move normal orbit origin parallel parallelogram particle passes perpendicular placed plane position pressure produced prove quantity radius ratio rays respectively rest result right angles sides Similarly sine smooth sphere square straight lines string suppose surface taking tangent touches triangle Trin tube uniform varies vertical weight whence whole
Popular passages
Page 177 - Triangles upon equal bases, and between the same parallels, are equal to one another.
Page 177 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Page 198 - Prove that a heavy particle, let fall from rest in a medium in which the resistance varies as the square of the velocity...
Page 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.
Page 177 - Describe a square which shall be equal to a given rectilineal figure.
Page 104 - Find the geometrical focus of a pencil of rays after direct refraction at a spherical surface.
Page 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.
Page 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...
Page 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.
Page 181 - Enunciate the principle of virtual velocities, and prove it in the case of a bent lever.