Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667

Table of figures

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              <s>
                <pb xlink:href="040/01/1015.jpg" pagenum="321"/>
              I have thought good to omit this Conſideration, and in this manner
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              to ſingle out theſe others that I could explain without it: for
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              though there be no Motion but hath ſome Velocity, nevertheleſs
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              it is onely the Augmentations and Diminutions of this Velocity
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              that are conſiderable. </s>
              <s>And now that ſpeaking of the Motion of a
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              Body, we ſuppoſe that it is made according to the Velocity which
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              is moſt naturall to it, which is the ſame as if we did not conſider it
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              at all.</s>
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            <p type="main">
              <s>The other reaſon that may have hindred men from rightly un­
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              derſtanding my Principle is, that they have thought that they could
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              demonſtrate without it ſome of thoſe things which I demonſtrate
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              not without it: As, for example, touching the Pulley A B C, they
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              have thought that it was enough to know that the Nail in A did
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                <figure id="id.040.01.1015.1.jpg" xlink:href="040/01/1015/1.jpg" number="218"/>
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              ſuſtain the half of the Weight B; to conclude
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              that the Hand in C had need but of half ſo much
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              Force to ſuſtain or raiſe the Weight, thus wound
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              about the Pulley, as it would need for to ſuſtain
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              or raiſe it without it. </s>
              <s>But howbeit that this ex­
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              plaineth very well, how the application of the
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              Force at C is made unto a Weight double to that
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              which it could raiſe without a Pulley, and that I
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              my ſelf did make uſe thereof, yet I deny that
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              this is ſimply, becauſe that that the Nail A ſu­
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              ſtaineth one part of the Weight B, that the Force
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              in C, which ſuſtaineth it, might be leſs than if it
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              had been ſo ſuſtained. </s>
              <s>For if that had been true, the Rope C E be­
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              ing wound about the Pulley D, the Force in E might by the ſame
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              reaſon be leſs than the Force in C: for that the Nail A doth not
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              ſuſtain the Weight leſs than it did before, and that there is alſo
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              another Nail that ſuſtains it, to wit, that to wich the Pulley D is
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              faſtned. </s>
              <s>Thus therefore, that we may not be miſtaken in this, that
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              the Nail A ſuſtaineth the half of the Weight B, we ought to con­
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              clude no more but this, that by this application the one of the Di­
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              menſions of the Force that ought to be in C
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                <figure id="id.040.01.1015.2.jpg" xlink:href="040/01/1015/2.jpg" number="219"/>
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              to raiſe up this Weight is diminiſhed the one
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              half; and that the other, of conſequence, be­
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              cometh double, in ſuch ſort that if the Line
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              F G repreſent the Force that is required for
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              the ſuſtaining the Weight B in a point, with­
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              out the help of any Machine, and the
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              Quadrangle G H that which is required for
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              the raiſing of it to the height of a foot, the
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              ſupport of the Nail A diminiſheth the Di­
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              menſion which is repreſented by the Line F G the one half, and the
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              redoubling of the Rope A B C maketh the other Dimenſion to </s>
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