Newton's Principia, First book Sections I, Ii, Iii, With Notes And Illustrations And a Collection of Problems, Principally Intended As Examples of Newton's Methods

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The measure of the accelerating effect of the force is Written ■^^, where fx the constant part of this measure is an algebraical symbol of w + 1 dimensions in linear space. If the imlt of space = a, -^ is the measure of the accelerating effect of the force on a body at an unit of distance, and /* is called the Absolute Force^ being the measure of the accelerating effect of the force at an unit of distance x the nth. power of that unit.
The absolute force is not the measure of the accelerating e
...ffect of any force, unless the symbols be treated numerically, in which case fjb is twice the number of units of space through which a constant force, equal to the force at pn unit of distance, would draw a body from rest in an unit of time.
Law of Force in a Circular Orbit 190. The law of force may be expressed in terms of the distance 8P^ for SD^ Sd being the greatest and least distances of the body from /S, SD.Sd= SP.SVj see figure, page 188.
.-. SP.PV=8P'±SD.Sd, + or — according as 8 is within or without the circle j 2Ji',A V\8P '' {8P''±8I).8dy' If 8 be on the circumference 8d = 0, therefore F= — =^-^v— * ' 8P'' If 8 be exterior to the circle, 8D.8d= 8B\ and the lower ,, , , .1 c IT ^h^AV\8P sign must be taken ; therefore j?


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