## Elements of Natural Philosophy, Volume 1 |

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Page 3

As two successive positions of it contain the second side of the polygon above

mentioned , it is evident that the osculating plane

next by revolving about the tangent to the curve . 13. Thus , as we proceed along

...

As two successive positions of it contain the second side of the polygon above

mentioned , it is evident that the osculating plane

**passes**from one position to thenext by revolving about the tangent to the curve . 13. Thus , as we proceed along

...

Page 4

all the sides being produced each in the direction in which the moving point

describes it while

closed or not . If closed , then , as long as it is not crossed , this sum is four right

angles ...

all the sides being produced each in the direction in which the moving point

describes it while

**passing**round the figure . This is true whether the polygon beclosed or not . If closed , then , as long as it is not crossed , this sum is four right

angles ...

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 straight line

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 12

When the acceleration is directed to a fixed point , the path is in a plane

through that point ; and in this plane the areas traced out by the radius - vector

are proportional to the times employed . This includes the case of a satellite or ...

When the acceleration is directed to a fixed point , the path is in a plane

**passing**through that point ; and in this plane the areas traced out by the radius - vector

are proportional to the times employed . This includes the case of a satellite or ...

Page 13

... always

motion in which the acceleration is directed to a fixed point , and we thus prove

the second theorem of $ 45 , that in the case supposed the areas described by

the ...

... always

**passes**through the point , its moment vanishes . This is the case of amotion in which the acceleration is directed to a fixed point , and we thus prove

the second theorem of $ 45 , that in the case supposed the areas described by

the ...

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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