Elements of Natural Philosophy, Volume 1 |
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Page 2
This is evident from the definition of the tangent to a curve . 9. 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 . To exemplify this
...
This is evident from the definition of the tangent to a curve . 9. 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 . To exemplify this
...
Page 3
curve , and if it be made up of portions of straight or curved lines it 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 . The term '
curve of ...
curve , and if it be made up of portions of straight or curved lines it 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 . The term '
curve of ...
Page 5
In the mechanical tracing of curves , a flexible and inextensible cord is often
supposed . Thus , in drawing an ellipse , the focal property of the curve shows us
that if we fix the ends of such a cord to the foci and keep it stretched by a pencil ,
the ...
In the mechanical tracing of curves , a flexible and inextensible cord is often
supposed . Thus , in drawing an ellipse , the focal property of the curve shows us
that if we fix the ends of such a cord to the foci and keep it stretched by a pencil ,
the ...
Page 9
The points , P , Q , etc. , must form a continuous curve , for ( $ 7 ) OP cannot
change abruptly in direction . Now if ( be a point near to P , OP and OQ represent
two successive values of the velocity . Hence PQ is the whole change of velocity
...
The points , P , Q , etc. , must form a continuous curve , for ( $ 7 ) OP cannot
change abruptly in direction . Now if ( be a point near to P , OP and OQ represent
two successive values of the velocity . Hence PQ is the whole change of velocity
...
Page 10
In other words , if a point move in a curve , whether with a uniform or a varying
velocity , its change of direction is to be regarded as constituting an acceleration
towards the centre of curvature , equal in amount to the square of the velocity ...
In other words , if a point move in a curve , whether with a uniform or a varying
velocity , its change of direction is to be regarded as constituting an acceleration
towards the centre of curvature , equal in amount to the square of the velocity ...
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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