Galilei, Galileo
,
Mechanics
,
1665
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the Weight to be at one extream, and the Force at the other, and
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the Fulciment placed in ſome point between the extreams: but we
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may make uſe of the Leaver another way, yet, placing, as we ſee,
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the Fulciment in the extream A, the Force in the other extream C,
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and ſuppoſing the Weight D to hang by ſome point in the midſt,
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as here we ſee by the point B, in
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this example it's manifeſt, that if
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the Weight did hang at a point
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Equi-diſtant from the two ex
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treams A and C, as at the point F,
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the labour of ſuſtaining it would
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be equally divided betwixt the
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two points A and C, ſo that half
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the Weight would be felt by the
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Force C, the other half being ſu
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ſtained by the Fulciment A: but if the Grave Body ſhall be hanged
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at another place, as at B, we ſhall ſhew that the Force in C is ſuffi
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cient to ſuſtain the Weight in B, as it hath the ſame proportion
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to it, that the Diſtance, A B hath to the Diſtance A C. </
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>For De
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monſtration of which, let us imagine the Line B A to be continued
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right out unto G, and let the Diſtance B A be equall to A G, and
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let the Weight hanging at G, be ſuppoſed equall to D: It is ma
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nifeſt, that by reaſon of the equality of the Weights D and E, and
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of the Diſtances G A and A B, the Moment of the Weight E
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ſhall equalize the Moment of the Weight D, and is ſufficient to
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ſuſtain it: Therefore whatever Force ſhall have Moment equall to
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that of the Weight E, and that ſhall be able to ſuſtain it, ſhall be
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ſufficient likewiſe to ſuſtain the Weight D: But for ſuſtaining the
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Weight E, let there be placed in the point C ſuch a Force, whoſe
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Moment hath that proportion to the Weight E, that the Diſtance
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G A hath to the Diſtance A C, it ſhall be ſufficient to ſuſtain it:
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Therefore the ſame Force ſhall likewiſe be able to ſuſtain the
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Weight D, whoſe Moment is equall to the of E: But look what
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Proportion the Line G A hath to the Line A C; and A B alſo hath
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the ſame to the ſaid A C, G A having been ſuppoſed equall to A B:
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And becauſe the Weights E and D are equall, each of them ſhall
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have the ſame proportion to the Force placed in C: Therefore the
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Force in C is concluded to equall the Moment of the Weight D,
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as often as it hath unto it the ſame proportion that the Diſtance B A
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hath to the Diſtance C A. </
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>And by moving the Weight, with the
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Leaver uſed in this manner, it is gathered in this alſo, as well as in
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the other Inſtruments, that what is gained in Force is loſt in Velo
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city: for the Force C raiſing the Leaver, and transferring it to A I,
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the Weight is moved the Space B H, which is as much leſſer than
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the Space C I paſſed by the Force, as the Diſtance A B is leſſer </
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