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

Table of figures

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<archimedes>
<text>
<body>
<chap>
<p type="main">
<s>
of the Members and Muſcles, and as we uſe to ſay, by Force of
<lb/>
Armes, beſides the extern Weight, we are to lift up the Weight of
<lb/>
our own Armes, in which greater pains is required. </s>
<s>Conclude we,
<lb/>
therefore, that this upper Pulley doth not bring any Facility to the
<lb/>
Force ſimply conſidered, but onely to the manner of applying it:
<lb/>
but if we ſhall make uſe of the like Machine
<lb/>
<lb/>
in another manner, as we are now about to
<lb/>
declare; we may raiſe the Weight with di­
<lb/>
minution of Forces: For let the Pulley
<lb/>
B D C be voluble about the Center E placed
<lb/>
in it's Frame B L C, at which hang the
<lb/>
Grave G; and let the Rope A B D C F
<lb/>
paſſe about the Pulley; of which let the end
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A be faſtned to ſome fixed ſtay, and in the
<lb/>
other F let the Force be placed; which
<lb/>
moving to wards H ſhall raiſe the Machine
<lb/>
B L C, and conſequently the Weight G:
<lb/>
and in this operation I ſay, that the Force in
<lb/>
F is the half of the Weight ſuſtained by it.
<lb/>
</s>
<s>For the ſaid Weight being kept to Rights by the two ^{*} Ropes A B
<lb/>
<arrow.to.target n="marg1110"/>
<lb/>
and F C, it is manifeſt, that the Labour is equally ſhared betwixt
<lb/>
the Force F and the Fulciment A: and more ſubtilly examining the
<lb/>
nature of this Inſtrument, if we but continue forth the Diameter
<lb/>
B E C, we ſhall ſee a Leaver to be made, at the midſt of which, that
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is at the point E, the Grave doth hang, and the Fulciment cometh
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to be at the end B, and the Force in the Term C: whereupon, by
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what hath been above demonſtrated, the Force ſhall have the ſame
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proportion to the Weight, that the Diſtance E B hath to the Di­
<lb/>
ſtance; Therefore it ſhall be the half of the ſaid Weight: And
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becauſe the Force riſing towards A, the Pulley turneth round,
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therefore that Reſpect or Conſtitution which the Fulciment B and
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Center E, on which the Weight and Term C, in which the Force
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is employed do depend, ſhall not change all the while; but yet in
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the Circuinduction the Terms B and C happen to vary in number,
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but not in vertue, others and others continually ſucceeding in their
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place, whereby the Leaver B C cometh to be perpetuated. </s>
<s>And
<lb/>
here (as hath been done in the other Inſtruments, and ſhall be in
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thoſe that follow) we will not paſſe without conſidering how that
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the journey that the Force maketh, is double to the Moment of the
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Weight. </s>
<s>For in caſe the Weight ſhall be moved ſo far, till that
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the Line B C come to arrive with it's points B and C, at the points
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A and F, it is neceſſary that the two equal Ropes be diſtended in
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one ſole Line F H, and conſequently, when the Weight ſhall have
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aſcended along the Intervall B A, the Force ſhall have been moved
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twice as far, that is, from
<emph type="italics"/>
F
<emph.end type="italics"/>
unto H. </s>
<s>Then conſidering that the </s>
</p>
</chap>
</body>
</text>
</archimedes>