Principia: First Book. sections I, II, III

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Macmillan and Company, 1900 - 292 من الصفحات
 

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الصفحة v - Newton, by showing the extent to which they may be applied in the solution of problems ; he has also endeavoured to give assistance to the student who is engaged in the study of the higher branches of Mathematics, by representing in a geometrical form several of the processes employed in the Differential and Integral Calculus, and in the analytical investigations of Dynamics, FROST and WOLSTENHOLME.—k TREATISE ON SOLID GEOMETRY. ' By PERCIVAL FROST, MA, and the Rev.
الصفحة 232 - In a parabola, the velocity of a body at any distance from the focus is to the velocity of a body revolving in a circle, at the same distance...
الصفحة 33 - Ill) the former figure to the former sum, and the latter figure to the latter sum, are both in the ratio of equality. QED COR.
الصفحة 67 - LEMMA X. The spaces which a body describes [from rest] under the action of any finite force, whether that force be constant or else continually increase or continually diminish, are in the very beginning of the motion in the duplicate ratio of the times.
الصفحة 122 - The curve traced out by a point on the circumference of a circle, which rolls upon...
الصفحة 265 - The cubes of the mean distances of the planets from the sun are proportional to the squares of their times of revolution.
الصفحة 215 - Hence the particles describe elliptic orbits, the major axes of which are horizontal, and the motion in the ellipses is the same as in the case of a body describing an ellipse under the action of a force tending to the centre. The ratio of the minor to the major axis is that of 1 - e...
الصفحة 257 - If the velocity of the earth in its orbit were suddenly destroyed, find the time in which it would reach the sun. 3. A particle moves from any point in the directrix of a conic section, in a straight line towards a centre of force, which varies inversely as the square of the distance, in the corresponding focus. Prove that when it arrives at the conic section, if L be the latus /4u\9 rectum, the velocity will be \-~\ . LL 4.
الصفحة 49 - From the definition of an ellipse, as the locus of a point the sum of whose distances from two fixed points is constant, shew that ellipses are similar when the eccentricities are equal.

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