## Elements of Natural Philosophy |

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Page 4

The mathematical condition to be expressed in any case of it is simply that the

constant , however the line be bent . 17 . The use of a cord in mechanism

presents us ...

The mathematical condition to be expressed in any case of it is simply that the

**distance**measured along the line from any one point to any other , remainsconstant , however the line be bent . 17 . The use of a cord in mechanism

presents us ...

Page 11

( c ) If the components of the velocity parallel to each axis be equi . multiples of

the

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 equi . multiples 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 12

Also QA is known in direction , for AP bisects the angle , QAC , between the focal

whatever ( and however varying ) be its magnitude , is directed to a fixed point ,

the ...

Also QA is known in direction , for AP bisects the angle , QAC , between the focal

**distance**of a point and the diameter through it . 45 . When the acceleration ,whatever ( and however varying ) be its magnitude , is directed to a fixed point ,

the ...

Page 15

Hence the hodograph is a vertical straight line , whose

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

' s proposition ( $ 49 ) , let APB be a portion of a copic 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 copic section and S one focus .

Page 16

... to that perpendicular to a fixed line : and therefore the radius - vector of any

point is proportional to the

belonging exclusively to the conic sections referred to their focus and directrix .

53 .

... to that perpendicular to a fixed line : and therefore the radius - vector of any

point is proportional to the

**distance**' of that point from a fixed line - a propertybelonging exclusively to the conic sections referred to their focus and directrix .

53 .

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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 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 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