## Elements of Natural Philosophy, Volume 1 |

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Page 8

When there are two velocities , or three velocities , in two or in three rectangular

directions , the resultant is the

cosines of its inclination to the given directions are the ratios of the components

to ...

When there are two velocities , or three velocities , in two or in three rectangular

directions , the resultant is the

**square**root of the sum of their squares ; and thecosines of its inclination to the given directions are the ratios of the components

to ...

Page 10

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

curvature ( perpendicular therefore to the direction of motion ) , whose magnitude

is proportional to the

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

curvature ( perpendicular therefore to the direction of motion ) , whose magnitude

is proportional to the

**square**of the velocity and also to the curvature of the path . Page 16

When a point moves uniformly in a straight line its angular velocity evidently

diminishes as it recedes from the point about which the angles are measured ,

and it may easily be shown that it varies inversely as the

from ...

When a point moves uniformly in a straight line its angular velocity evidently

diminishes as it recedes from the point about which the angles are measured ,

and it may easily be shown that it varies inversely as the

**square**of the distancefrom ...

Page 17

acceleration in the orbit , varies inversely as the

and therefore ( $ 59 ) directly as the angular velocity . Hence the arc of Pl ,

described in any time , is proportional to the corresponding angle - vector in the

orbit , i.e. ...

acceleration in the orbit , varies inversely as the

**square**of the radius - vector ;and therefore ( $ 59 ) directly as the angular velocity . Hence the arc of Pl ,

described in any time , is proportional to the corresponding angle - vector in the

orbit , i.e. ...

Page 35

... and the direction of its axis is found , as follows : — The

angular velocity is the sum of the squares of its components , and the ratios of the

three components to the resultant are the direction - cosines of the axis . Hence ...

... and the direction of its axis is found , as follows : — The

**square**of the resultantangular velocity is the sum of the squares of its components , and the ratios of the

three components to the resultant are the direction - cosines of the axis . Hence ...

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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