## Elements of Natural Philosophy, Volume 1 |

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Page 2

To exemplify this ,

OP , OQ , to the points of contact . The angle between the tangents is the change

of direction between P and l , and the rate of change is to be measured by the ...

To exemplify this ,

**suppose**two ' tangents PT , QU , drawn to a circle , and radiiOP , OQ , to the points of contact . The angle between the tangents is the change

of direction between P and l , and the rate of change is to be measured by the ...

Page 3

... of an arc of a plane curve , is the angle through which the tangent has turned

as we pass from one extremity to the other . The average curvature of any portion

is its whole curvature divided by its length .

... of an arc of a plane curve , is the angle through which the tangent has turned

as we pass from one extremity to the other . The average curvature of any portion

is its whole curvature divided by its length .

**Suppose**a line , drawn through any ... Page 4

... the inevitable friction ) it is a wheel , on part of whose circumference the cord is

wrapped . ( 1 )

inextensible cord ABP is wrapped , and

... the inevitable friction ) it is a wheel , on part of whose circumference the cord is

wrapped . ( 1 )

**Suppose**we have a single pulley B , about which the flexible andinextensible cord ABP is wrapped , and

**suppose**its free portions to be parallel . Page 6

We may

as to keep the train running for some time at a uniform velocity . This is the

velocity which the train had at the instant in question . Without supposing any

such ...

We may

**suppose**that , at any instant during the motion , the steam is so adjustedas to keep the train running for some time at a uniform velocity . This is the

velocity which the train had at the instant in question . Without supposing any

such ...

Page 26

... any periods , whose directions must of course be in one plane . Mechanical

methods of obtaining such combinations will be afterwards described , as well as

cases of their occurrence in Optics and Acoustics . We may

simplicity ...

... any periods , whose directions must of course be in one plane . Mechanical

methods of obtaining such combinations will be afterwards described , as well as

cases of their occurrence in Optics and Acoustics . We may

**suppose**, forsimplicity ...

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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.