## Elements of Natural Philosophy, Volume 1 |

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Page 10

The whole acceleration in any direction is the sum of the components in that

direction ) of the accelerations parallel to any three rectangular

component acceleration being found by the same rule as component velocities ,

that is , by ...

The whole acceleration in any direction is the sum of the components in that

direction ) of the accelerations parallel to any three rectangular

**axes**- eachcomponent acceleration being found by the same rule as component velocities ,

that is , by ...

Page 11

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

two rectangular

ellipse or hyperbola whose principal diameters coincide with those

( 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 there is uniform acceleration in a constant direction , the path described is

a parabola , whose

moving in vacuo . For the velocity ( V ) in the original direction of motion ...

When there is uniform acceleration in a constant direction , the path described is

a parabola , whose

**axis**is parallel to that direction . This is the case of a projectilemoving in vacuo . For the velocity ( V ) in the original direction of motion ...

Page 24

The horizontal line is the

left of each being the

through one complete period , in the second it goes through two periods . 1 : 2 2 :

3 ...

The horizontal line is the

**axis**of abscissae of the curves ; the vertical line to theleft of each being the

**axis**of ordinates . In the first case the slower motion goesthrough one complete period , in the second it goes through two periods . 1 : 2 2 :

3 ...

Page 26

proved ( § 82 ) to be motion in an ellipse of which the ranges of the component

motions are conjugate

radius - vector from the centre in equal times . Hence the proposition of 8o . 84.

proved ( § 82 ) to be motion in an ellipse of which the ranges of the component

motions are conjugate

**axes**, and in which equal areas are described by theradius - vector from the centre in equal times . Hence the proposition of 8o . 84.

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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 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