Elements of Natural Philosophy, Part 1 |
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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 proportional to the square of the velocity and also to the curvature of the path .
... 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 proportional to its distance from that axis , the path is an
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 an
ellipse 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 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
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 ...
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 proportional to the velocity at P. Also | Proc .
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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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