The General Laws of Nature and Motion: With Their Application to Mechanicks. Also the Doctrine of the Centripetal Forces, and Velocities of Bodies, Describing Any of the Conick Sections. Being a Part of the Great Mr. Newton's Principles. The Whole Illustrated with Variety of Useful Theorems and Problems, and Accommodated to the Use of the Younger Mathematicians

Richard Mount, 1709 - 232 pages

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Page 214 - If a body revolves in an ellipse (including the special case of a circle), it is required to find the law of the centripetal force tending to the focus of the ellipse.
Page 221 - And therefore the velocity in a conic section, at its greatest or least distance from the focus, is to the velocity in a circle, at the same distance from the centre, in the subduplicate ratio of the principal latus rectum to the double of that distance.
Page 163 - The spaces, described from rest by a body acted on by any finite force, are in the beginning of the motion as the squares of the times, in which they are described.
Page 220 - Orbs are in the Ratio compounded of the duplicate Ratio of the Velocities, and the duplicate Ratio of the Perpendiculars from the Focus to the Tangents.
Page 133 - ... of forces. PROPOSITION III. THEOREM III. Every body that by a radius drawn to the centre of another body, howsoever moved, describes areas about that centre proportional to the times is urged by a force compounded out of the centripetal force tending to that other body, and of all the accelerative force by which that other body is impelled.
Page 131 - Force acting upon it, by the firft Law of Motion. And that Force by which the Body is- made to...
Page 82 - Or, as our Great Authour exprefles it, when the Force by which the Wedge urges the two Sides of the cleft Bodies is to the Force of the Mallet upon the Wedge, as the Progrefs of the Wedge according to the Determination of the Force imprefs'd upon it, to the Velocity with which the Parts of the Body give way to the Wedge in Lines perpendicular to the Sides of the...
Page 85 - THE Quantity of Motion, that is gathered by taking the Sum of the Motions made towards the fame Part, and the Difference of thofe made towards the contrary Parts ^ is not altered by the Action of Bodies among/I themselves.
Page 129 - AreJs are not proportional to the Times, the Forces do not tend to the common Goncourfe of the Rays.

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