## Elements of Natural Philosophy |

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Results 1-5 of 53

Page 43

If these lines are infinite in number , and the angles of bending

but such that their sum may be finite , we have our plane surface bent into a

curved surface , which is of course * developable ' ( 9 * 125 ) . 129 . Lift a square

of ...

If these lines are infinite in number , and the angles of bending

**infinitely small**,but such that their sum may be finite , we have our plane surface bent into a

curved surface , which is of course * developable ' ( 9 * 125 ) . 129 . Lift a square

of ...

Page 51

... as we may call it , expresses that the rate of diminution of the density bears to

the density . at any instant , the same ratio as the rate of increase of the volume of

an

... as we may call it , expresses that the rate of diminution of the density bears to

the density . at any instant , the same ratio as the rate of increase of the volume of

an

**infinitely small**portion bears to the volume of this portion at the same instant . Page 53

The other four guiding points are the points , or

pivots on the Y ' s . ... Substitute for gravity a spring , or a screw and nut ( of not

planes ...

The other four guiding points are the points , or

**small**areas , of con . tact of thepivots on the Y ' s . ... Substitute for gravity a spring , or a screw and nut ( of not

**infinitely**rigid material ) , binding the stool to the rigid body to which these sixplanes ...

Page 58

Now M ( 0 , - v ) is the rate of change of momentum in the direction of motion , and

1 ( 0 , + v ) is equal to o , if a be

often convenient to use Newton ' s Fluxional notation for the rate of change of ...

Now M ( 0 , - v ) is the rate of change of momentum in the direction of motion , and

1 ( 0 , + v ) is equal to o , if a be

**infinitely small**. Hence the above statement . It isoften convenient to use Newton ' s Fluxional notation for the rate of change of ...

Page 83

If , therefore , in any such

energy uncompensated by work of the applied forces , constraint limiting the

freedom of the system to only this motion will bring us to the case in which we

have just ...

If , therefore , in any such

**infinitely small**motion , there is variation of potentialenergy uncompensated by work of the applied forces , constraint limiting the

freedom of the system to only this motion will bring us to the case in which we

have just ...

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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