## Elements of Natural Philosophy, Volume 1 |

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Results 1-5 of 45

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

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

and ( v , + v ) is equal to v , if be

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

...

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

and ( v , + v ) is equal to v , if be

**infinitely small**. Hence the above statement . It isoften convenient 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

... through this point . 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

...

... through this point . 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...

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### Common terms and phrases

acceleration according acting action amount angle angular applied attraction axes axis becomes body called centre centre of inertia circle cloth 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 period 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

### Popular passages

Page 161 - that every particle of matter in the universe attracts every other particle, with a force whose direction is that of the line joining the two, and whose magnitude is directly as the product of their masses, and inversely as the square of their distances from each other.

Page 9 - Persius. The Satires. With a Translation and Commentary. By John Conington, MA, late Corpus Professor of Latin in the University of Oxford. Edited by H. Nettleship, MA Second Edition.

Page 65 - Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it is compelled by force to change that state.

Page 10 - Crown 8vo. cloth, 7s. 6d. A Treatise on Electricity and Magnetism. By J. Clerk Maxwell, MA, FRS, Professor of Experimental Physics in the University of Cambridge.

Page 28 - Fourier's theorem is not only one of the most beautiful results of modern analysis, but may be said to furnish an indispensable instrument in the treatment of nearly every recondite question in modern physics.

Page 161 - Newton generalized the law of attraction into a statement that every particle of matter in the universe attracts every other particle with a force which varies directly as the product of their masses and inversely as the square of the distance between them; and he thence deduced the law of attraction for spherical shells of constant density.

Page 66 - Change of motion is proportional to the impressed force and takes place in the direction of the straight line in which the force acts.

Page 68 - To every action there is always an equal and contrary reaction; or, the mutual actions of any two bodies are always equal and oppositely directed in the same straight line.

Page 9 - An Elementary Treatise on Quaternions. By PG TAIT, MA, Professor of Natural Philosophy in the University of Edinburgh ; formerly Fellow of St Peter's College, Cambridge. Second Edition. Demy 8vo. 14*.

Page 130 - UNTIL we know thoroughly the nature of matter and the forces which produce its motions, it will be utterly impossible to submit to mathematical reasoning the exact conditions of any physical question.