## Elements of Natural Philosophy, Volume 1 |

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Page 2

This is evident from the definition of the tangent to a

straight the direction of motion changes from point to point , and the rate of this

change , per unit of length of the

...

This is evident from the definition of the tangent to a

**curve**. 9 . If the path be notstraight the direction of motion changes from point to point , and the rate of this

change , per unit of length of the

**curve**, is called the Curvature . To exemplify this...

Page 3

plane polygon . If the line do not lie in one plane , we have in one case what is

called a

**curve**, and if it be made up of portions of straight or curved lines it is called aplane polygon . If the line do not lie in one plane , we have in one case what is

called a

**curve**of double curvature , in the other a gauche polygon . The term '**curve**of ... Page 5

In the mechanical tracing of

supposed . Thus , in drawing an ellipse , the focal property of the

that if we fix the ends of such a cord to the foci and keep it stretched by a pencil ,

the ...

In the mechanical tracing of

**curves**, a flexible and inextensible cord is oftensupposed . Thus , in drawing an ellipse , the focal property of the

**curve**shows usthat if we fix the ends of such a cord to the foci and keep it stretched by a pencil ,

the ...

Page 9

The points , P , Q , etc . , must form a continuous

change abruptly in direction . Now if Q be a point near to P , OP and OQ

represent two successive values of the velocity . Hence PQ is the whole change

of velocity ...

The points , P , Q , etc . , must form a continuous

**curve**, for ( § 7 ) OP cannotchange abruptly in direction . Now if Q be a point near to P , OP and OQ

represent two successive values of the velocity . Hence PQ is the whole change

of velocity ...

Page 10

In other words , if a point move in a

velocity , its change of direction is to be regarded as constituting an acceleration

towards the centre of curvature , equal in amount to the square of the velocity ...

In other words , if a point move in a

**curve**, whether with a uniform or a varyingvelocity , its change of direction is to be regarded as constituting an acceleration

towards the centre of curvature , equal in amount to the square of the velocity ...

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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.