## Elements of Natural Philosophy, Volume 1 |

### From inside the book

Results 1-5 of 40

Page 41

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 ' ( $ 125 ) . 129. Lift a square of

paper ...

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 ' ( $ 125 ) . 129. Lift a square of

paper ...

Page 49

... 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 54

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

, + v ) is equal to v , if be

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

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

, + v ) is equal to v , if be

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

Page 78

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 ...

Page 79

But if , when displaced infinitely little in any direction from a particular position of

equilibrium , and left to itself , it commences and continues vibrating , without ever

experiencing more than

But if , when displaced infinitely little in any direction from a particular position of

equilibrium , and left to itself , it commences and continues vibrating , without ever

experiencing more than

**infinitely small**deviation in any of its parts ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

### 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 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 remarkable 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