## Elements of Natural Philosophy |

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Page 36

... subject only to the condition that one of its points remains fixed , there is always

( without exception ) one line of it through this point common to the body in any

two positions . Consider a spherical

...

... subject only to the condition that one of its points remains fixed , there is always

( without exception ) one line of it through this point common to the body in any

two positions . Consider a spherical

**surface**within the body , with its centre at the...

Page 37

Thus we see that if a spherical polygon turns about its angular points in

succession , always keeping on the spherical

which it turns about each point is twice the supplement of the angle of the

polygon , or ...

Thus we see that if a spherical polygon turns about its angular points in

succession , always keeping on the spherical

**surface**, and if the angle throughwhich it turns about each point is twice the supplement of the angle of the

polygon , or ...

Page 38

The method of $ 100 also applies to the case of $ 106 ; and it is thus easy to

show that the most general motion of a spherical figure on a fixed spherical

the ...

The method of $ 100 also applies to the case of $ 106 ; and it is thus easy to

show that the most general motion of a spherical figure on a fixed spherical

**surface**is obtained by the rolling of a curye fixed in the figure on a curve fixed onthe ...

Page 39

Now , if both planes be bent so as to form portions . of the

right - cylinder , the motion of DF parallel to AC will become a rotation about the

axis of the cylinder , and the necessary accompaniment of vertical motion will

remain ...

Now , if both planes be bent so as to form portions . of the

**surface**of a verticalright - cylinder , the motion of DF parallel to AC will become a rotation about the

axis of the cylinder , and the necessary accompaniment of vertical motion will

remain ...

Page 40

... plane perpendicular to ON , and radius NP , which , as this radius revolves with

angular velocity w , is w . NP . Hence Q . QP = w . NP , or w : 0 : : QP : NP . 118 .

Suppose a rigid body bounded by any curved

...

... plane perpendicular to ON , and radius NP , which , as this radius revolves with

angular velocity w , is w . NP . Hence Q . QP = w . NP , or w : 0 : : QP : NP . 118 .

Suppose a rigid body bounded by any curved

**surface**to be touched at any point...

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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 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 period perpendicular plane portion position potential practical pressure principle produce projection proportional quantity radius reference relative remain remarkable resistance respectively rest resultant right angles rigid rotation round sides simple solid space spherical square straight strain stress suppose surface theory turned uniform unit velocity vertical weight whole wire