## Elements of Natural Philosophy, Part 1 |

### From inside the book

Results 6-10 of 61

Page 24

In the first place , we see that any number of simple harmonic motions of one

period , and of the same phase , superimposed , produce a single simple

harmonic motion of the same phase . For , the displacement at any instant being ,

In the first place , we see that any number of simple harmonic motions of one

period , and of the same phase , superimposed , produce a single simple

harmonic motion of the same phase . For , the displacement at any instant being ,

**according**... Page 26

... directions and of any periods , may be effected by compounding ,

previously explained methods , their resolved parts in each of any three

rectangular directions , and then compounding the final resultants in these

directions .

... directions and of any periods , may be effected by compounding ,

**according**topreviously explained methods , their resolved parts in each of any three

rectangular directions , and then compounding the final resultants in these

directions .

Page 35

Hence rotations are to be compounded

and therefore the single angular velocity , equivalent to three co - existent

angular velocities about three mutually perpendicular axes , is determined in ...

Hence rotations are to be compounded

**according**to the same law as velocities ,and therefore the single angular velocity , equivalent to three co - existent

angular velocities about three mutually perpendicular axes , is determined in ...

Page 39

... the corresponding surface is concave . Hence the angular velocity of the rolling

curve is in this case equal to the product of the linear velocity of the point of

contact into the sum or difference of the curvatures ,

both ...

... the corresponding surface is concave . Hence the angular velocity of the rolling

curve is in this case equal to the product of the linear velocity of the point of

contact into the sum or difference of the curvatures ,

**according**as the curves areboth ...

Page 42

The surface must clearly , when complete (

consist of two sheets meeting in this edge of regression ( just as a cone consists

of two sheets meeting in the vertex ) , because each tangent may be produced ...

The surface must clearly , when complete (

**according**to mathematical ideas ) ,consist of two sheets meeting in this edge of regression ( just as a cone consists

of two sheets meeting in the vertex ) , because each tangent may be produced ...

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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