## Elements of Natural Philosophy, Volume 1 |

### From inside the book

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Page 2

If the path be not straight the direction of motion changes from point to point , and

the rate of this change , per unit of length of the curve , is called the

exemplify this , suppose two tangents PT , QU , drawn to a circle , T and radii ...

If the path be not straight the direction of motion changes from point to point , and

the rate of this change , per unit of length of the curve , is called the

**Curvature**. Toexemplify this , suppose two tangents PT , QU , drawn to a circle , T and radii ...

Page 3

If the line do not lie in one plane , we have in one case what is called a curve of

double

...

If the line do not lie in one plane , we have in one case what is called a curve of

double

**curvature**, in the other a gauche polygon . The term ' curve of double**curvature**' is a very bad one , and , though in very general use , is , we hope , not...

Page 5

... 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 , the locus of the centres of the

circles which have at each point the same tangent and

.

... 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 , the locus of the centres of the

circles which have at each point the same tangent and

**curvature**as the curve PQ.

Page 10

... motion and equal to the acceleration of the velocity ; the other towards the

centre of

magnitude is proportional to the square of the velocity and also to the

the ...

... motion and equal to the acceleration of the velocity ; the other towards the

centre of

**curvature**( perpendicular therefore to the direction of motion ) , whosemagnitude is proportional to the square of the velocity and also to the

**curvature**ofthe ...

Page 17

Hence ( § 9 ) the

demonstration , reversed , proves that if the hodograph be a circle , and the

acceleration be towards a fixed point , the acceleration varies inversely as the

square of the ...

Hence ( § 9 ) the

**curvature**of PQ is constant , or PQ is a circle . Thisdemonstration , reversed , proves that if the hodograph be a circle , and the

acceleration be towards a fixed point , the acceleration varies inversely as the

square of the ...

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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