## Elements of Natural Philosophy |

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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

moving point describes it while

polygon be closed or not . If closed , then , as long as it is not crossed , this sum is

four right angles , -an extension of the result in Euclid , where all reëntrant ...

moving point describes it while

**passing**round the figure . This is true whether thepolygon be closed or not . If closed , then , as long as it is not crossed , this sum is

four right angles , -an extension of the result in Euclid , where all reëntrant ...

Page 11

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 right ...

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 right ...

Page 12

... 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 path is in a plane ?

PRELIMINARY .

... 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 path is in a plane ?

**passing**through that point ; and in this planePRELIMINARY .

Page 13

vector are proportional to the times employed . Evidently there is no acceleration

perpendicular to the plane containing the fixed point and the line of motion of the

...

**passing**through that point ; and in this plane the areas traced out by the radius -vector are proportional to the times employed . Evidently there is no acceleration

perpendicular to the plane containing the fixed point and the line of motion of the

...

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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 expression figure fixed fluid force friction give given gravity harmonic Hence 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