## Elements of Natural Philosophy, Part 1 |

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Page 13

This is the case of a motion in which the acceleration is directed to a

and we thus prove the second theorem of $ 45 , that in the case supposed the

areas described by the radius - vector are proportional to the times ; for , as we ...

This is the case of a motion in which the acceleration is directed to a

**fixed**point ,and we thus prove the second theorem of $ 45 , that in the case supposed the

areas described by the radius - vector are proportional to the times ; for , as we ...

Page 14

For the product of this perpendicular and the velocity at any instant gives double

the area described in one second about the

shown to be a constant quantity . Other examples of these principles will be met

with ...

For the product of this perpendicular and the velocity at any instant gives double

the area described in one second about the

**fixed**point , which has just beenshown to be a constant quantity . Other examples of these principles will be met

with ...

Page 15

A reversal of the demonstration of § 51 shows that , if the acceleration be towards

a

of which the

A reversal of the demonstration of § 51 shows that , if the acceleration be towards

a

**fixed**point , and if the hodograph be a circle , the orbit must be a conic sectionof which the

**fixed**point is a focus . Bi we may also prove this important ... Page 16

We may also speak of the angular velocity of a moving plane with respect to a

their line of intersection remain

somewhat ...

We may also speak of the angular velocity of a moving plane with respect to a

**fixed**one , as the rate of increase of the angle contained by them ; but unlesstheir line of intersection remain

**fixed**, or at all events parallel to itself , asomewhat ...

Page 17

This demonstration , reversed , proves that if the hodograph be a circle , and the

acceleration be towards a

square of the distance of the moving point from the

52 ...

This demonstration , reversed , proves that if the hodograph be a circle , and the

acceleration be towards a

**fixed**point , the acceleration varies inversely as thesquare of the distance of the moving point from the

**fixed**point . 62. From $$ 61 ,52 ...

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### Common terms and phrases

acceleration according acting action amount angle angular applied attraction axes axis body called centre centre of inertia circle component condition consider constant corresponding couple course curvature curve denote density described determined direction displacement distance divided effect elastic elements energy equal equations equilibrium evidently experience expression figure fixed fluid force friction give given gravity harmonic Hence important increase infinitely small instant interval kinetic length less mass matter mean measured method motion moving natural normal observation opposite parallel particle passing path perpendicular plane portion position potential practical pressure principle problem produce projection proportional quantity radius reference relative remain respectively rest resultant right angles rigid rotation round sides simple solid space spherical square straight strain stress suppose surface theory turned uniform unit velocity weight whole wire