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

#### Table of figures

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<archimedes>
<text>
<body>
<chap>
<p type="main">
<s>
and in the Velocity: which peradventure, might not have ſeemed
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to ſome ſo true and manifeſt in the preſent Contemplation; nay,
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rather it ſeems, that in this caſe the Force is multiplied without the
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Movers moving a longer way than the Moveable: In regard, that
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if we ſhall in the Triangle A B C ſuppoſe the Line A B to be the
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Plane of the Horizon, A C the elevated Plane, whoſe Altitude is
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meaſured by the Perpendicular C B, a Moveable placed upon the
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Plane A C, and the Cord E D
<emph type="italics"/>
F
<emph.end type="italics"/>
tyed to it, and a
<emph type="italics"/>
F
<emph.end type="italics"/>
orce or Weight
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applyed in
<emph type="italics"/>
F
<emph.end type="italics"/>
that hath to the
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Gravity of the Weight E the
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ſame proportion that the Line
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B C hath to C A; by what
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hath been demonſtrated, the
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Weight
<emph type="italics"/>
F
<emph.end type="italics"/>
ſhall deſcend
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downwards, drawing the
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Moveable E along the eleva­
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ted Plane; nor ſhall the Move­
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able E meaſure a greater Space
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when it ſhall have paſſed the
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whole Line A
<emph type="italics"/>
C,
<emph.end type="italics"/>
than that which the ſaid Grave
<emph type="italics"/>
F
<emph.end type="italics"/>
meaſureth in its
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deſcent downwards. </s>
<s>But here yet it muſt be advertiſed, that al­
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though the Moveable E ſhall have paſſed the whole Line A C, in
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the ſame Time that the other Grave
<emph type="italics"/>
F
<emph.end type="italics"/>
ſhall have been abaſed the
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like Space, nevertheleſs the Grave E ſhall not have retired from the
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common Center of things Grave more than the Space of the Per­
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pendicular
<emph type="italics"/>
C
<emph.end type="italics"/>
B. but yet the Grave
<emph type="italics"/>
F
<emph.end type="italics"/>
deſcending Perpendicularly ſhall
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be abaſed a Space equal to the whole Line A
<emph type="italics"/>
C.
<emph.end type="italics"/>
And becauſe Grave
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Bodies make no Reſiſtance to Tranſverſal Motions, but only ſo
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far as they happen to recede from the
<emph type="italics"/>
C
<emph.end type="italics"/>
enter of the Earth; There­
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fore the Moveable E in all the Motion A
<emph type="italics"/>
C
<emph.end type="italics"/>
being raiſed no more
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than the length of the Line
<emph type="italics"/>
C
<emph.end type="italics"/>
B, but the other
<emph type="italics"/>
F
<emph.end type="italics"/>
being abaſed per­
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pendicularly the quantity of all the Line A
<emph type="italics"/>
C
<emph.end type="italics"/>
: Therefore we may
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deſervedly affirm that Way of the
<emph type="italics"/>
F
<emph.end type="italics"/>
orce E maintaineth the ſame
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proportion to the
<emph type="italics"/>
F
<emph.end type="italics"/>
orce
<emph type="italics"/>
F
<emph.end type="italics"/>
that the
<emph type="italics"/>
L
<emph.end type="italics"/>
ine A
<emph type="italics"/>
C
<emph.end type="italics"/>
hath to
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C
<emph.end type="italics"/>
B; that is,
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the Weight E to the Weight
<emph type="italics"/>
F.
<emph.end type="italics"/>
It very much importeth, therefore,
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to conſider by [
<emph type="italics"/>
or along
<emph.end type="italics"/>
] what
<emph type="italics"/>
L
<emph.end type="italics"/>
ines the Motions are made, eſpe­
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cially in exanimate Grave Bodies, the Moments of which have their
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total Vigour, and entire Reſiſtance in the
<emph type="italics"/>
L
<emph.end type="italics"/>
ine Perpendicular to
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the Horizon; and in the others tranſverſally Elevated and Inclined
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they feel the more or leſs Vigour,
<emph type="italics"/>
Impetus,
<emph.end type="italics"/>
or Reſiſtance, the more
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or leſs thoſe Inclinations approach unto the Perpendicular Inclina­
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tion.</s>
</p>
</chap>
</body>
</text>
</archimedes>