## Elements of Natural Philosophy |

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Page 5

Hence PP is

thus the evolute of PQ is a 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 P . O . Andthus the evolute of PQ is a 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 40

On the other hand , let the instantaneous axis of the moving body be the common

point of contact . Let it move , so that the instantaneous axis , still passing ...

On the other hand , let the instantaneous axis of the moving body be the common

**normal**at the point of contact . This is . pure spinning , and does not change thepoint of contact . Let it move , so that the instantaneous axis , still passing ...

Page 41

In the latter case , the sur . face on every side of the point bends away from the

same side of its tangent plane , and the curvatures of all

similarly directed . Thus we may divide curved surfaces into Anticlastic and

Synclastic .

In the latter case , the sur . face on every side of the point bends away from the

same side of its tangent plane , and the curvatures of all

**normal**sections aresimilarly directed . Thus we may divide curved surfaces into Anticlastic and

Synclastic .

Page 42

If and be the maximum and minimum curvatures at any point the curvature of a

is - cosoe + sino e , which includes the above statements as particular cases .

If and be the maximum and minimum curvatures at any point the curvature of a

**normal**section making an angle 0 with the**normal**section of maximum curvatureis - cosoe + sino e , which includes the above statements as particular cases .

Page 52

... one degree of constraint is introduced , or there are left but two degrees of

freedom . For we may take the

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

other ...

... one degree of constraint is introduced , or there are left but two degrees of

freedom . For we may take the

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

other ...

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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 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 produce projection proportional quantity radius reference relative remain remarkable resistance respectively rest resultant right angles rigid rotation round sides simple solid space spherical square straight strain stress suppose surface theory turned uniform unit velocity vertical weight whole wire