## Elements of Natural Philosophy |

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Page 5

And 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 PC or , which is the

same thing , the locus of the

same ...

And 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 PC or , which is the

same thing , the locus of the

**centres**of the circles which have at each point thesame ...

Page 10

Since the velocity in ABD is constant , all the lines OP , OC , etc. , will be equal (

to V ) , and there fore POS is a circle whose

acceleration at A is parallel to S the tangent at P , that is , is perpendicular to OP ,

i.e. to AQ ...

Since the velocity in ABD is constant , all the lines OP , OC , etc. , will be equal (

to V ) , and there fore POS is a circle whose

**centre**is O. The direction ofacceleration at A is parallel to S the tangent at P , that is , is perpendicular to OP ,

i.e. to AQ ...

Page 11

... axes is proportional to its distance from that axis , the path is an ellipse or

hyperbola whose principal diameters coincide with those axes ; and the

acceleration is directed to or from the

78 ) .

... axes is proportional to its distance from that axis , the path is an ellipse or

hyperbola whose principal diameters coincide with those axes ; and the

acceleration is directed to or from the

**centre**of the curve at every instant ( S $ 66 ,78 ) .

Page 15

But we may also prove this important proposition as follows : Let A be the

of the circle , and the hodographic origin . Join OA and draw the perpendiculars

PM to OA and ON to PA . Then OP is the velocity in the orbit : and ON , being ...

But we may also prove this important proposition as follows : Let A be the

**centre**of the circle , and the hodographic origin . Join OA and draw the perpendiculars

PM to OA and ON to PA . Then OP is the velocity in the orbit : and ON , being ...

Page 16

The usual unit angle is ( as explained in treatises on plane trigonometry ) that

which subtends at the

radius ; being an angle of = 57 ° 29578 ... = 57 ° 17'44 " : 8 nearly 56. The angular

...

The usual unit angle is ( as explained in treatises on plane trigonometry ) that

which subtends at the

**centre**of a circle an arc whose length is equal 180 ° to theradius ; being an angle of = 57 ° 29578 ... = 57 ° 17'44 " : 8 nearly 56. The angular

...

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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 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