## Elements of Natural Philosophy, Volume 1 |

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Page 5

Hence pP is

thus the evolute of PQ is B a definite curve , viz . the envelop of ( or line which is

touched by ) the normals drawn at every point of PQ , or , which is the same thing

...

Hence pP is

**normal**( or perpendicular to the tangent ) to the curve р PQ . Andthus the evolute of PQ is B a definite curve , viz . the envelop of ( or line which is

touched by ) the normals drawn at every point of PQ , or , which is the same thing

...

Page 38

... this point — the other body being fixed . This motion is what we call rolling , or

simple rolling , of the movable body on the fixed . On the other hand , let the

instantaneous axis of the moving body be the common

contact .

... this point — the other body being fixed . This motion is what we call rolling , or

simple rolling , of the movable body on the fixed . On the other hand , let the

instantaneous axis of the moving body be the common

**normal**at the point ofcontact .

Page 39

In the former case , the surface bends away from the tangent plane partly towards

one side of it , and partly towards the other , and has thus , in some of its

sections , curvatures oppositely directed to those in others . In the latter case ...

In the former case , the surface bends away from the tangent plane partly towards

one side of it , and partly towards the other , and has thus , in some of its

**normal**sections , curvatures oppositely directed to those in others . In the latter case ...

Page 40

In an anticlastic surface there is maximum curvature ( but in opposite directions )

in the two

which the surface cuts its tangent plane . On account of the difference of sign ...

In an anticlastic surface there is maximum curvature ( but in opposite directions )

in the two

**normal**sections whose planes bisect the angles between the lines inwhich the surface cuts its tangent plane . On account of the difference of sign ...

Page 50

For we may take the

of resolution . No displacement can be effected parallel to it : and the other two

displacements , at right angles to each other , in the tangent plane to the surface

...

For we may take the

**normal**to the surface as one of three rectangular directionsof resolution . No displacement can be effected parallel to it : and the other two

displacements , at right angles to each other , in the tangent plane to the surface

...

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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