## Elements of Natural Philosophy, Part 1 |

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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

( 6 ) If a point moves in a plane , and its component velocity parallel to each of

two rectangular axes is proportional to its

ellipse or hyperbola whose principal diameters coincide with those axes ...

( 6 ) If a point moves in a plane , and its component velocity parallel to each of

two rectangular axes is proportional to its

**distance**from that axis , the path is anellipse or hyperbola whose principal diameters coincide with those axes ...

Page 12

Also OA is known in direction , for AP bisects the angle , OAC , between the focal

directed to a fixed point , the path is in a plane passing through that point ; and in

...

Also OA is known in direction , for AP bisects the angle , OAC , between the focal

**distance**of a point and the diameter through it . 45. When the acceleration isdirected to a fixed point , the path is in a plane passing through that point ; and in

...

Page 14

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 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 .

Page 15

... 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 evidently experience 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 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