## Elements of Natural Philosophy, Volume 1 |

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Page 4

The mathematical condition to be expressed in any case of it is simply that the

constant , however the line be bent . 17 . The use of a cord in mechanism

presents us ...

The mathematical condition to be expressed in any case of it is simply that the

**distance**measured along the line from any one point to any other , remainsconstant , however the line be bent . 17 . The use of a cord in mechanism

presents us ...

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

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

Also OA is known in direction , for AP bisects the angle , OAC , between the focal

directed to a fixed point , the path is in a plane passing through that point ; and in

...

Also OA is known in direction , for AP bisects the angle , OAC , between the focal

**distance**of a point and the diameter through it . 45 . When the acceleration isdirected to a fixed point , the path is in a plane passing through that point ; and in

...

Page 14

Hence the hodograph is a vertical straight line , whose

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 sone focus .

Hence the hodograph is a vertical straight line , whose

**distance**from the origin isthe horizontal velocity , and which is described uniformly . 51 . To prove Hamilton

' s proposition ( $ 49 ) , let APB be a portion of a conic section and sone focus .

Page 15

... to that perpendicular to a fixed line : and therefore the radius - vector of any

point is proportional to the

belonging exclusively to the conic sections referred to their focus and directrix .

53 .

... to that perpendicular to a fixed line : and therefore the radius - vector of any

point is proportional to the

**distance**of that point from a fixed line — a propertybelonging exclusively to the conic sections referred to their focus and directrix .

53 .

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acceleration according acting action amount angle angular applied attraction axes axis becomes body called centre centre of inertia circle cloth 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 period 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

### Popular passages

Page 161 - that every particle of matter in the universe attracts every other particle, with a force whose direction is that of the line joining the two, and whose magnitude is directly as the product of their masses, and inversely as the square of their distances from each other.

Page 9 - Persius. The Satires. With a Translation and Commentary. By John Conington, MA, late Corpus Professor of Latin in the University of Oxford. Edited by H. Nettleship, MA Second Edition.

Page 65 - Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it is compelled by force to change that state.

Page 10 - Crown 8vo. cloth, 7s. 6d. A Treatise on Electricity and Magnetism. By J. Clerk Maxwell, MA, FRS, Professor of Experimental Physics in the University of Cambridge.

Page 28 - Fourier's theorem is not only one of the most beautiful results of modern analysis, but may be said to furnish an indispensable instrument in the treatment of nearly every recondite question in modern physics.

Page 161 - Newton generalized the law of attraction into a statement that every particle of matter in the universe attracts every other particle with a force which varies directly as the product of their masses and inversely as the square of the distance between them; and he thence deduced the law of attraction for spherical shells of constant density.

Page 66 - Change of motion is proportional to the impressed force and takes place in the direction of the straight line in which the force acts.

Page 68 - To every action there is always an equal and contrary reaction; or, the mutual actions of any two bodies are always equal and oppositely directed in the same straight line.

Page 9 - An Elementary Treatise on Quaternions. By PG TAIT, MA, Professor of Natural Philosophy in the University of Edinburgh ; formerly Fellow of St Peter's College, Cambridge. Second Edition. Demy 8vo. 14*.

Page 130 - UNTIL we know thoroughly the nature of matter and the forces which produce its motions, it will be utterly impossible to submit to mathematical reasoning the exact conditions of any physical question.