## Elements of Natural Philosophy, Volume 1 |

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Page 7

In fact , if v be the velocity at either beginning or end , or at any instant , of an

interval t , and s the space actually described in that interval ; the

which expresses the definition of the average velocity , § 26 ) is more and more

nearly ...

In fact , if v be the velocity at either beginning or end , or at any instant , of an

interval t , and s the space actually described in that interval ; the

**equation**vs . (which expresses the definition of the average velocity , § 26 ) is more and more

nearly ...

Page 12

If there be no initial velocity our

course the preceding formulae apply to a constant retardation , as in the case of a

projectile moving vertically upwards , by simply giving a a negative sign . 44 .

If there be no initial velocity our

**equations**become ú = at , x = žat ” , { vé = ax . Ofcourse the preceding formulae apply to a constant retardation , as in the case of a

projectile moving vertically upwards , by simply giving a a negative sign . 44 .

Page 49

This idea , when expressed in a perfectly comprehensive manner for every

portion of a fluid in motion , constitutes what is commonly called the

continuity . 163 . Two ways of proceeding to express this idea present themselves

...

This idea , when expressed in a perfectly comprehensive manner for every

portion of a fluid in motion , constitutes what is commonly called the

**equation**ofcontinuity . 163 . Two ways of proceeding to express this idea present themselves

...

Page 53

If the density be not uniform , the

density ; or , as it is usually called , the Mean density , of the body . It is worthy of

particular notice that , in this definition , Newton says , if there be anything which ...

If the density be not uniform , the

**equation**M = Vp gives the Average ( § 26 )density ; or , as it is usually called , the Mean density , of the body . It is worthy of

particular notice that , in this definition , Newton says , if there be anything which ...

Page 70

As it is usual to investigate the general

treatises on Analytical Dynamics , before entering in detail on the kinetic branch

of the subject , this principle is found practically most useful in showing how we ...

As it is usual to investigate the general

**equations**or conditions of equilibrium , intreatises on Analytical Dynamics , before entering in detail on the kinetic branch

of the subject , this principle is found practically most useful in showing how we ...

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### Common terms and phrases

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.