## Elements of Natural Philosophy |

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Page 2

We devote to it , accordingly , the

were , the Geometry of the subject , embracing what can be observed or

concluded with regard to actual motions , as long as the cause is not sought . In

this category ...

We devote to it , accordingly , the

**whole**of this chapter ; which will form , as itwere , the Geometry of the subject , embracing what can be observed or

concluded with regard to actual motions , as long as the cause is not sought . In

this category ...

Page 3

The Integral Curvature , or

is the angle through which the tangent has turned as we pass from one extremity

to the other . The average curvature of any portion is its

The Integral Curvature , or

**whole**change of direction , of an arc of a plane curve ,is the angle through which the tangent has turned as we pass from one extremity

to the other . The average curvature of any portion is its

**whole**curvature divided ... Page 7

... and nearer approximations to the velocity an the beginning of the first second .

The

the simple question , " What is the rate at which the space described by a moving

...

... and nearer approximations to the velocity an the beginning of the first second .

The

**whole**foundation of Newton's differential calculus is , in fact , contained inthe simple question , " What is the rate at which the space described by a moving

...

Page 8

The velocity resolved in any direction is the sum of the resolved parts ( in that

direction ) of the three rectangular components of the

consider motion in one plane , this is still true , only we have but two rectangular

com ...

The velocity resolved in any direction is the sum of the resolved parts ( in that

direction ) of the three rectangular components of the

**whole**velocity . And'if weconsider motion in one plane , this is still true , only we have but two rectangular

com ...

Page 9

The average accelera . tion during any time is the

that time divided by the time . In Newton's notation v is used to express the

acceleration in the direction of motion ; and , if v = $ as in $ 28 , wehave a = j = $ .

" E 34.

The average accelera . tion during any time is the

**whole**velocity gained duringthat time divided by the time . In Newton's notation v is used to express the

acceleration in the direction of motion ; and , if v = $ as in $ 28 , wehave a = j = $ .

" E 34.

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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 expression figure fixed fluid force friction give given gravity harmonic Hence 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 produce projection proportional quantity radius reference relative remain remarkable resistance respectively rest resultant right angles rigid rotation round sides simple solid space spherical square straight strain stress suppose surface theory turned uniform unit velocity vertical weight whole wire