## Elements of Natural Philosophy, Part 1 |

### From inside the book

Results 6-10 of 49

Page 5

... by different points of the string ; and these will , in general , be different curves .

But the following section shows that there is but one evolute . 22. Let AB be any

curve , PQ a

... by different points of the string ; and these will , in general , be different curves .

But the following section shows that there is but one evolute . 22. Let AB be any

curve , PQ a

**portion**of an involute , pP , qe positions of the free part of the string . Page 14

Hence the hodograph is a vertical straight line , whose distance from the origin is

the horizontal velocity , and which is described uniformly . 51. To prove

Hamilton's proposition ( $ 49 ) , let APB be a

focus .

Hence the hodograph is a vertical straight line , whose distance from the origin is

the horizontal velocity , and which is described uniformly . 51. To prove

Hamilton's proposition ( $ 49 ) , let APB be a

**portion**of a conic section and S onefocus .

Page 27

In the case of epochs equal , or differing by a multiple of T , the curve is a

of a parabola , and is gone over twice in opposite directions by the moving point

in each complete period . If the periods be not exactly as 1 : 2 the form of the path

...

In the case of epochs equal , or differing by a multiple of T , the curve is a

**portion**of a parabola , and is gone over twice in opposite directions by the moving point

in each complete period . If the periods be not exactly as 1 : 2 the form of the path

...

Page 33

The points A and B describe similar and equal cycloids , of which AQC and BS

are

S the new positions of A and B , QPS is of course a right angle . If , therefore , QR

...

The points A and B describe similar and equal cycloids , of which AQC and BS

are

**portions**. If POR be any subsequent position of the generating circle , Q andS the new positions of A and B , QPS is of course a right angle . If , therefore , QR

...

Page 37

As it is evident that all

cylinder , it is obvious that the thread of the screw , which corresponds to the

edge , DE , of the upper board , must be traced on the cylinder so as always to

make a ...

As it is evident that all

**portions**of AB will be equally inclined to the axis of thecylinder , it is obvious that the thread of the screw , which corresponds to the

edge , DE , of the upper board , must be traced on the cylinder so as always to

make a ...

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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