Of Newton's Principia

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                                Next the Motion of bodies in given surfaces is considered 
as likewise the Oscillatory motion of pendules, where is 
shewn how to make a pendulam vibrate alway in equall line,
tho the center or point of tendency be never so near, to which 
the demonstration of Mr Hugens de Cycloide is but a Corollary.
and in another proposition is shewn the Velocity in each point 
and the time spent in each parte of the Arch described by the 
Vibrating body. After this the effects of two or more bodies 
towards each of which there is a tendency is considered, and he made 
out that two bodies so drawing or attracting each other describe 
about the common center of gravity Curve lines, like to those 
they seem to describe about one another. And of three bodies 
attracting each other reciprocally as the square of the distance 
<s>from <\s> between their centers, <s>he proved that the differences from the Elliptick 
motion is less than if the <\s> the various consequences are considered 
and laid down in severall Corollarys of great use in explicating 
the phenomena of the Moons Motions, the Flux and reflux 
of the sea, the precession of the Equinox and the like.
This done our Author with his usuall acuteness proceeds to 
examine into the causes of this tendency or centripetall force 
which from endoubled arguments is shewn to be in all the great 
bodies of the Universes here he finds that if a <s>body <\s> sphere be composed 
of an infinity of Atoms, each of which have a conatus accedend 
ad invicem, which decreases in <s>the<\s> duplicate proportion of the distance 
between them, Then the whole congeries shall have the like tenden 
cy towards its center, decreasing, in spaces without it in duplicate 
                            
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Manuscript details

Author
Edmond Halley
Reference
CLP/21/13
Series
Cl.P
Date
1687
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Of Newton's Principia , 1687. From The Royal Society, CLP/21/13

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