The motion of bodies
Date
10 December 1684
Creator
Unknown, Artist
Object type
Archive reference number
Manuscript page number
p221
Material
Dimensions
height (page): 367mm
width (page): 232mm
width (page): 232mm
Subject
Description
Diagram in a copy of one of Newton's earliest drafts (now presumed lost) 'on motion' (1684), which became Book 1 of Principia mathematica philosophiae naturalis (1687).
Diagram for theorem 3: 'if a body P in orbiting around the centre S shall describe any curved line APQ, and if the straight line PR touches that curve at any point P and to this tangent from any point Q of the curve there be drawn QR parallel to the distance SP, and if QT be let fall perpendicular to this distance SP, I assert that the centripetal force is reciprocally as the 'solid' (SP2 x QT2)/QR, provided that the ultimate quantity of that solid when the points P and Q come to coincide is always taken.' See Principia (1687), proposition 6, theorem 5.
Diagram for problem 1: A body orbits in the circumference of a circle: the law of centripetal force tending to some point in its circumference is sought. Compare Principia (1687), proposition 7, problem 2.
Diagram for theorem 3: 'if a body P in orbiting around the centre S shall describe any curved line APQ, and if the straight line PR touches that curve at any point P and to this tangent from any point Q of the curve there be drawn QR parallel to the distance SP, and if QT be let fall perpendicular to this distance SP, I assert that the centripetal force is reciprocally as the 'solid' (SP2 x QT2)/QR, provided that the ultimate quantity of that solid when the points P and Q come to coincide is always taken.' See Principia (1687), proposition 6, theorem 5.
Diagram for problem 1: A body orbits in the circumference of a circle: the law of centripetal force tending to some point in its circumference is sought. Compare Principia (1687), proposition 7, problem 2.
Object history
At the meeting of the Royal Society on 10 December 1684, 'Mr. Halley gave an account, that he had lately seen Mr. Newton at Cambridge, who had shewed him a curious treatise, De Motu; which upon Mr. Halley's desire, was, he said, promised to be sent to the Society to be entered upon their register. Mr. Halley was desired to put Mr. Newton in mind of his promise for the securing his invention to himself till such time as he could be at leisure to publish it. Mr. Paget was desired to join with Mr. Halley' (Birch 4:347).
This is a copy of the tract sent via Edward Paget to Halley, which contained Newton's demonstration that an elliptical orbit entails an inverse-square force to one focus. From these insights, Newton went on to develop his Principia mathematica philosophiae naturalis. The original draft is presumed lost.
This is a copy of the tract sent via Edward Paget to Halley, which contained Newton's demonstration that an elliptical orbit entails an inverse-square force to one focus. From these insights, Newton went on to develop his Principia mathematica philosophiae naturalis. The original draft is presumed lost.
Related fellows
Isaac Newton (1642 - 1727, British) , Natural philosopher
Edmond Halley (1656 - 1742, British) , Astronomer
Edmond Halley (1656 - 1742, British) , Astronomer
Associated place