The first three sections of Newton's Principia; with copious notes and illustrations, and a great variety of deductions and problems. Designed for the use of students / By the Rev. John Carr.

  • Newton, Isaac, 1642-1727.
Date:
1826
Catalogue details

Licence: Public Domain Mark

Credit: The first three sections of Newton's Principia; with copious notes and illustrations, and a great variety of deductions and problems. Designed for the use of students / By the Rev. John Carr. Source: Wellcome Collection.

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    1G8 37. Let the Force act in the direction of the ordinates; to 1 find the curve when F cc —. 1J2. F oc — dx^ oc y /. — d^y a dx^ dy dx^ dif dx^ and — dy d^y a-r—, ^ a —- .JO y 2 y /. dy y oc and x a or the curve is the semicubical parabola. 38. Required the curve in which a body, revolving by a force which acts in lines to the axis, shall approach or leave the axis with a velocity always proportional to the or¬ dinate. dy ^ dy Here t; cc 3/ or dy oc 3/, — is constant, or — a dx^ y y dy and if M be a proper constant Q^, M. — = y which is the property of the logarithmic curve. 39. Compare the velocity at any point in a curve with that in a <D at the same distance when the A formed by the distance and tangent is a minimum, (Fig. 8.) Sin. Z S P Y = — = min. ydp—pdy = 0, y p dy = 2 curvature = y, V : vel. m O ^ y : ^y I* 1 : J. 40. If the force vary according to any law of the dis-