## Elements of Natural Philosophy, Part 1 |

### From inside the book

Results 1-5 of 56

Page 10

... and equal to the acceleration of the velocity ; the other towards the centre of

curvature ( perpendicular therefore to the direction of motion ) , whose magnitude

is

... and equal to the acceleration of the velocity ; the other towards the centre of

curvature ( perpendicular therefore to the direction of motion ) , whose magnitude

is

**proportional**to the square of the velocity and also to the curvature of the path . Page 11

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

two rectangular axes is

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

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

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

This is the case of a 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 radius - vector are

This is the case of a 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 radius - vector are

**proportional**to the times ; for , as we ... Page 14

Produce YS to cut the circle again in Z. Then YS SZ is constant , and therefore SZ

is inversely as SY , that is , SZ is

R. S. 1865 . U SZ is perpendicular to the direction of motion PY , 14

PRELIMINARY ...

Produce YS to cut the circle again in Z. Then YS SZ is constant , and therefore SZ

is inversely as SY , that is , SZ is

**proportional**to the velocity at P. Also | Proc .R. S. 1865 . U SZ is perpendicular to the direction of motion PY , 14

PRELIMINARY ...

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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 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