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accelerating effect action angular velocity apse arcs described axes bisects body describes body moves central orbit centre of force centre of gravity centripetal force chord of curvature circle of curvature conic section conjugate constant curve curvilinear cycloid directrix distance drawn duplicate ratio eccentricity ellipse epicycloid equiangular spiral extremity fixed point focus force tending given point hence hodograph hyperbola indefinitely diminished inscribed intersect latus rectum Lemma length limit magnitude major axis orbit described ordinate parabola parallel parallelograms particle perp perpendicular plane polygon position PROP proportional proposition prove radii radius of curvature ratio of equality represented right angles sector shew similar space described square straight line string subtangent subtense tangent triangle ultimate ratio varies inversely vertex
Page 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.
Page 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.
Page 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.
Page 122 - The curve traced out by a point on the circumference of a circle, which rolls upon...
Page 265 - The cubes of the mean distances of the planets from the sun are proportional to the squares of their times of revolution.
Page 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...
Page 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.