Problems in the Different Branches of Philosophy: Adapted to the Course of Reading Pursued in the University of Cambridge

Whittaker, Treacher & Company, 1830 - Trigonometry - 374 pages

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Page 158 - If an object be placed between two plane reflectors inclined to each other at any angle, and the eyes of a spectator be in any point between the planes...
Page 291 - Things that are equal to the same thing are equal to one another," and the theorems of Euclid. The law that portions of matter attract each other with a force varying inversely as the square of the distance, does not seem to offer any explanation of the perturbations of Uranus, or the rising of a balloon.
Page 45 - The product of all the lines that can be drawn from one of the angles of a regular polygon of n sides inscribed in a circle •whose radius is a to all the other angular points is na"~'.
Page 19 - From the top of a tower, whose height is 108 feet, the angles of depression of the top and bottom of a vertical column standing in the horizontal plane are found to be 30° and 60° respectively; required the height of the column.
Page 318 - ... they should have been previously cut in the house, from the pattern given by one of the cards that had been mounted and cut in the instrument. In mounting the instrument in place, the points to attend to are, (1) that it shall be level as regards east and west, (2) that the axis of the ring shall be inclined to the horizon at an angle equal to the latitude of the place...
Page 352 - Upon comparing the observations with each other, it was discovered that in both the fore-mentioned stars, the apparent difference of declination from the maxima was always nearly proportional to the versed sine of the sun's distance from the equinoctial points. This was an inducement to think that the cause, whatever it was, had some relation to the sun's situation with respect to those points.
Page 303 - If the force vary according to any law of the distance ; shew that in any orbit, at the point where the centripetal and centrifugal forces are equal, the velocity towards the centre of force is a maximum. 19. Determine the nature of the curve by the revolution ' of which round its axis a solid will be generated, such that a corpuscle placed on its surface will be attracted towards the centre of gravity with a force varying as the distance ; the solid revolving round its axis in a given time, 20....
Page 293 - If a body revolve in an ellipse round the focus, prove that a progressive motion of the apse will be the effect of any continual addition of force in the direction of the radius vector during the progress of the body from the higher to the lower apse, and point out the effect on the excentricity.
Page 70 - ... inches, and the weight of a cubic foot of water being 1000 ounces.
Page 245 - A body is projected from a point near a centre of force which varies inversely as the square of the distance, in...