## Elements of Natural Philosophy, Volume 1 |

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Page 2

When a point moves from one position to another it must evidently describe a

continuous line , which may be curved or

curved and

of ...

When a point moves from one position to another it must evidently describe a

continuous line , which may be curved or

**straight**, or even made up of portions ofcurved and

**straight**lines meeting each other at any angles . If the motion be thatof ...

Page 3

curve , and if it be made up of portions of

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 aplane 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 7

The preceding definition of velocity is equally applicable whether the point move

in a

motion continually changes , the mere amount of the velocity is not sufficient ...

The preceding definition of velocity is equally applicable whether the point move

in a

**straight**or a curved line ; but , since , in the latter case , the direction ofmotion continually changes , the mere amount of the velocity is not sufficient ...

Page 11

( c ) If the components of the velocity parallel to each axis be equimultiples of the

distances from the other axis , the path is a

origin . ( d ) When the velocity is uniform , but in a direction revolving uniformly in

a ...

( c ) If the components of the velocity parallel to each axis be equimultiples of the

distances from the other axis , the path is a

**straight**line passing through theorigin . ( d ) When the velocity is uniform , but in a direction revolving uniformly in

a ...

Page 14

Hence the hodograph is a vertical

the horizontal velocity , and which is described uniformly . 51. To prove

Hamilton's proposition ( $ 49 ) , let APB be a portion of a conic section and S one

focus .

Hence the hodograph is a vertical

**straight**line , whose distance from the origin isthe horizontal velocity , and which is described uniformly . 51. To prove

Hamilton's proposition ( $ 49 ) , let APB be a portion of a conic section and S one

focus .

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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