Newton's Principia, First Book, Sections I., II., III.: With Notes and Illustrations, and a Collection of Problems Principally Intended as Examples of Newton's MethodsMacmillan, 1878 - 292 עמודים |
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מהדורות אחרות - הצג הכל
Newton's Principia, First Book, Sections I., II., III: With Notes and ... <span dir=ltr>Isaac Newton</span> אין תצוגה מקדימה זמינה - 2018 |
מונחים וביטויים נפוצים
accelerating effect action angular velocity apse arcs described bisects body describes body moves central orbit centre of force centre of gravity centripetal force chord of curvature circle of curvature conic section constant curve cycloid diameter of curvature directrix distance duplicate ratio eccentricity ellipse epicycloid equiangular spiral extremity fixed point focus force tending given point hence hyperbola indefinitely diminished inscribed intersect latus rectum Lemma length magnitude major axis orbit described ordinate oscillation parabola parallel parallelograms particle perp perpendicular plane polygon portions position PROP proportional proposition prove radius of curvature ratio of equality revolve right angles SCHOLIUM sector shew sides similar space described square straight line string subtangent subtense tangent triangle ultimate ratio vanishing quantities varies inversely vertex
קטעים בולטים
עמוד 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.
עמוד 58 - The tangent\ of an arc is a straight line drawn from one extremity of the arc, perpendicular to the...
עמוד 122 - The path traced out by a point on the circumference of a circle which rolls...
עמוד 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.
עמוד 263 - The cubes of the mean distances of the planets from the sun are proportional to the squares of their times of revolution.
עמוד 247 - A particle is describing an ellipse under the action of a force tending to the focus ; if, on arriving at the extremity of the minor axis, the force has its law changed, so that it varies as the distance, the magnitude at that point remaining...
עמוד 231 - ... distances, the velocity of a body in a conic section will be to the velocity in a circle at the same distance as a mean proportional between that common distance and half the latus rectum to the perpendicular from the focus on the tangent.
עמוד 245 - When a body revolves in an ellipse under the action of a force tending to the focus, find the velocity at any point of its orbit, and the periodic time. If on arriving at the extremity of the minor axis, the force has its law changed, so that it varies as the distance, the magnitude at that point remaining the same, the periodic time will be unaltered, and the sum of the new axes is...
עמוד 213 - We get (e"* + e"*) sin (mx - nt), r)= — (e"" - e"") cos (mx-nt) (33). 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...
עמוד 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.