## Elements of Natural Philosophy, Volume 1 |

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Page 5

And thus the evolute of PQ is 2 . a definite curve , viz . the envelop of ( or line

which is touched by ) the normals drawn at every point of PQ , or , which is the

same thing , the locus of the

same ...

And thus the evolute of PQ is 2 . a definite curve , viz . the envelop of ( or line

which is touched by ) the normals drawn at every point of PQ , or , which is the

same thing , the locus of the

**centres**of the circles which have at each point thesame ...

Page 10

Since the velocity in ABD is constant , all the lines OP , OQ , etc . , will be equal (

to V ) , and therefore POS is a circle whose bB

acceleration at A is parallel to the tangent at P , that is , is perpendicular to OP , i .

e . to ...

Since the velocity in ABD is constant , all the lines OP , OQ , etc . , will be equal (

to V ) , and therefore POS is a circle whose bB

**centre**is O . The direction ofacceleration at A is parallel to the tangent at P , that is , is perpendicular to OP , i .

e . to ...

Page 11

... and the acceleration is directed to or from the

instant ( $ $ 66 , 78 ) . ( c ) If the components of the velocity parallel to each axis

be equimultiples of the distances from the other axis , the path is a straight line

passing ...

... and the acceleration is directed to or from the

**centre**of the curve at everyinstant ( $ $ 66 , 78 ) . ( c ) If the components of the velocity parallel to each axis

be equimultiples of the distances from the other axis , the path is a straight line

passing ...

Page 15

But we may also prove this important proposition as follows : Let A be the

of the circle , and 0 the hodographic origin . Join OA and draw the perpendiculars

PM to 0A and ON to PA . ` Then OP is the velocity in the orbit : and ON , being ...

But we may also prove this important proposition as follows : Let A be the

**centre**of the circle , and 0 the hodographic origin . Join OA and draw the perpendiculars

PM to 0A and ON to PA . ` Then OP is the velocity in the orbit : and ON , being ...

Page 16

The unit angular velocity is that of a point which describes , or would describe ,

unit angle about a fixed point in unit of time . The usual unit angle is ( as

explained in treatises on plane trigonometry ) that which subtends at the

a circle ...

The unit angular velocity is that of a point which describes , or would describe ,

unit angle about a fixed point in unit of time . The usual unit angle is ( as

explained in treatises on plane trigonometry ) that which subtends at the

**centre**ofa circle ...

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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.