## Elements of Natural Philosophy, Volume 1 |

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Page 2

To exemplify this ,

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

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

the ...

To exemplify this ,

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

change of direction between P and , 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

( 1 )

inextensible cord ABP . is wrapped , and IP

parallel . If ( A being fixed ) a point P of the cord P be moved to P , it is evident that

each of the ...

( 1 )

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

**suppose**its free portions to beparallel . If ( A being fixed ) a point P of the cord P be moved to P , it is evident that

each of the ...

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 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