Newton's Principia: Sections I. II. III.Macmillan and Company, 1863 - 288 עמודים |
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מהדורות אחרות - הצג הכל
מונחים וביטויים נפוצים
AB² accelerating effect action angular velocity apse area described axes bisect body describes body moves catenary center of force center of gravity central orbit centripetal force chord of curvature circle of curvature conic section constant curve curvilinear limit cycloid direction drawn duplicate ratio eccentricity ellipse epicycloid equiangular spiral extremity fixed point focus force tending force varying given point hence hyperbola impulse indefinitely diminished intersection latus rectum Lemma locus magnitude major axis motion orbit described ordinate parabola parallel parallelograms particle perpendicular plane polygon position PROP proposition prove quantities radii radius of curvature ratio of equality represented right angles SCHOLIUM shew similar space described square straight line string subtangent subtense tangent triangle ultimate ratio uniform velocity vanishes varies inversely vertex
קטעים בולטים
עמוד 253 - The curve traced out by a point on the circumference of a circle, which rolls upon that of a fixed circle, is called an Epicycloid if the rolling circle be on the exterior of the fixed circle, a Hypocycloid, if it be on the interior of the fixed circle.
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 219 - In the parabola, the velocity of the body at any distance from the focus is to the velocity of a body revolving in a circle at the same distance...
עמוד 120 - ... by radii drawn to the fixed centre of force, are in one fixed plane, and are proportional to the times of describing them. Let the time be divided into equal parts, and in the first interval let the body describe the straight line AB with uniform velocity, being acted on by no force. In the second interval it would, if no force acted, proceed to c in AB produced, describing Be equal to AB ; so that the equal areas ASB, BSc described by radii AS, BS, cS drawn to the centre S, would be completed...
עמוד 75 - 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 35 - For as the parallelograms in the one are severally to the parallelograms in the other, so (by composition) is the sum of all in the one to the sum of all in the other; and so is the one figure to the other; because (by Lem. 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.
עמוד 144 - The centripetal forces on equal bodies, which describe different circles with uniform velocity, tend to the centres of the circles, and are to each other as the squares of arcs described in the same time, divided by the radii of the circles.
עמוד 149 - ... that is (if the species of the polygon be given), as the length described in that given time, and increased or diminished in the ratio of the same length to the radius of the circle; that is, as the square of that length applied to the radius...
עמוד 95 - ... velocity with which the body arrives at its last place, and with which the motion ceases. And in like manner, by the ultimate ratio of evanescent quantities is to be understood the ratio of the quantities not before they vanish, nor afterwards, but with which they vanish.
עמוד 121 - EF, &c., they will all lie in the same plane; and the triangle SCD will be equal to the triangle SBC, and SDE to SCD, and SEF to SDE.