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

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<archimedes>
<text>
<body>
<chap>
<p type="main">
<s>
as in the greater, the velocity is greater onely in the bigger wheel,
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<arrow.to.target n="marg384"/>
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for that its circumference is bigger; there is no man that thinketh
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that the cauſe of the extruſion in the great wheel will encreaſe
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cording to the proportion of the velocity of its circumference, to
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the velocity of the circumference of the other leſſer wheel; for that
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this is moſt falſe, as by a moſt expeditious experiment I ſhall thus
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groſly declare: We may ſling a ſtone with a ſtick of a yard long,
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farther than we can do with a ſtick ſix yards long, though
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the motion of the end of the long ſtick, that is of the ſtone placed
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in the ſlit thereof, were more than double as ſwift as the
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tion of the end of the other ſhorter ſtick, as it would be if
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the velocities were ſuch that the leſſer ſtick ſhould turn thrice
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round in the time whilſt the greater is making one onely
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verſion.</s>
</p>
<p type="margin">
<s>
<margin.target id="marg384"/>
<emph type="italics"/>
The cauſe of the
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projection
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eth not according
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to the proportion of
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the velocity,
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creaſed by making
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the wheel bigger.
<emph.end type="italics"/>
</s>
</p>
<p type="main">
<s>SAGR. </s>
<s>This which you tell me,
<emph type="italics"/>
Salviatus,
<emph.end type="italics"/>
muſt, I ſee, needs
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ſucceed in this very manner; but I do not ſo readily apprehend
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the cauſe why equal velocities ſhould not operate equally in
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extruding projects, but that of the leſſer wheel much more than
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the other of the greater wheel; therefore I intreat you to tell me
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how this cometh to paſs.</s>
</p>
<p type="main">
<s>SIMP. Herein,
<emph type="italics"/>
Sagredus,
<emph.end type="italics"/>
you ſeem to differ much from your
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ſelf, for that you were wont to penetrate all things in an inſtant,
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and now you have overlook'd a fallacy couched in the experiment
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of the ſtick, which I my ſelf have been able to diſcover: and this
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is the different manner of operating, in making the projection one
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while with the ſhort ſling and another while with the long one,
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for if you will have the ſtone fly out of the ſlit, you need not
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tinue its motion uniformly, but at ſuch time as it is at the ſwifteſt,
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you are to ſtay your arm, and ſtop the velocity of the ſtick;
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upon the ſtone which was in its ſwifteſt motion, flyeth out, and
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moveth with impetuoſity: but now that ſtop cannot be made in
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the great ſtick, which by reaſon of its length and flexibility, doth
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not entirely obey the check of the arm, but continueth to
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pany the ſtone for ſome ſpace, and holdeth it in with ſo much leſs
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force, and not as if you had with a ſtiff ſling ſent it going with a
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jerk: for if both the ſticks or ſlings ſhould be check'd by one and
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the ſame obſtacle, I do believe they would fly aſwell out of the
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one, as out of the other, howbeit their motions were equally
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ſwift.</s>
</p>
<p type="main">
<s>SAGR. </s>
<s>With the permiſſion of
<emph type="italics"/>
Salviatus,
<emph.end type="italics"/>
I will anſwer
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thing to
<emph type="italics"/>
Simplicius,
<emph.end type="italics"/>
in regard he hath addreſſed himſelf to me;
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and I ſay, that in his diſcourſe there is ſomewhat good
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and ſomewhat bad: good, becauſe it is almoſt all true;
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bad, becauſe it doth not agree with our caſe: Truth is, that when
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that which carrieth the ſtones with velocity, ſhall meet with a </s>
</p>
</chap>
</body>
</text>
</archimedes>