## Elements of Natural Philosophy |

### 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 T two tangents , PT , QU , drawn to a circle , 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 T two tangents , PT , QU , drawn to a circle , and radii ...

Page 3

is called a plane polygon . If the line do not lie in one plane , we have in one case

what is called a curve of double

term ' curve of double

...

is called a plane polygon . 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 . Theterm ' curve of double

**curvature**' is a very bad one , and , though in very general...

Page 5

... same thing , the locus of the centres of the circles which have at each point the

same tangent and

an obyious result of the mode of tracing , that the arc qp is equal KINEMATICS . 5.

... same thing , the locus of the centres of the circles which have at each point the

same tangent and

**curvature**as the curve PQ . And we may merely mention , asan obyious result of the mode of tracing , that the arc qp is equal KINEMATICS . 5.

Page 10

When a point moves in a curve the whole acceleration may be resolved into two

parts , one in the direction of the motion and equal to the acceleration of the

velocity ; the other towards the centre of

...

When a point moves in a curve the whole acceleration may be resolved into two

parts , one in the direction of the motion and equal to the acceleration of the

velocity ; the other towards the centre of

**curvature**( perpendicular therefore to the...

Page 17

Hence ( 89 ) 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 ( 89 ) the

**curvature**of PQ is constant , or P.Q 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 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