Galilei, Galileo
,
Mechanics
,
1665
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<
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>The preſent Speculation hath been attempted by
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Pappus Alex
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andrinus
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in
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Lib.
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8.
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de Collection. </
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<
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>Mathemat.
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but, if I be in the
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right, he hath not hit the mark, and was overſeen in the Aſſumpti
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on that he maketh, where he ſuppoſeth that the Weight ought to
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be moved along the Horizontal Line by a
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F
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orce given; which is
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falſe: there needing no ſenſible
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F
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orce (removing the Accidental
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Impediments, which in the Theory are not regarded) to move the
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given Weight along the Horizon, ſo that he goeth about in vain
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afterwards to ſeek with what
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F
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orce it is to be moved along the
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elevated Plane. </
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<
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>It will be therefore better, the
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F
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orce that moveth
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the Weight upwards perpendicularly, (which equalizeth the Gra
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vity of that Weight which is to be moved) being given, to
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ſeek the
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F
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orce that moveth it along the Elevated Plane: Which
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we will endeavour to do in a Method different from that of
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Pappus.
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<
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>Let us therefore ſuppoſe the Circle A I C, and in it the Diame
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ter A B C, and the Center B, and two Weights of equal Moment
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in the extreams B and C; ſo that the Line A C being a Leaver,
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or Ballance moveable about the Center B, the Weight C ſhall
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come to be ſuſtained by the Weight A. </
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<
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>But if we ſhall imagine
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the Arm of the Ballance B C to be inclined downwards according
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to the Line B F, but yet in ſuch a manner that the two Lines
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A B
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and
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B F
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do continue ſolidly conjoyned in the point
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B,
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in this caſe
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the Moment of the Weight C ſhall not be equal to the Moment
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of the Weight
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A,
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for that the Di
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ſtance of the point
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F
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from the Line
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of Direction, which goeth accord
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ing to B I, from the
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F
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ulciment B un
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to the Center of the Earth, is dimi
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niſhed: But if from the point
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F
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we
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erect a Perpendicular unto B C, as is
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F
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K, the Moment of the Weight in
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F
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ſhall be as if it did hang by the
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Line K
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F,
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and look how much the
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Diſtance K B is diminiſhed by the
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Diſtance B
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A,
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ſo much is the Moment of the Weight
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F
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diminiſhed
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by the Moment of the
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W
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eight
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A. A
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nd in this faſhion inclining
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the
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W
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eight more, as for inſtance, according to B L, its Moment ſhall
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ſtill diminiſh and ſhall be as if it did hang at the Diſtance
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B
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M, ac
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cording to the
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L
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ine M
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L,
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in which point
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L
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it ſhall be ſuſtained by
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a
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W
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eight placed in
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A,
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ſo much leſs than it ſelf, by how much the
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Diſtance B
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A
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is greater than the Diſtance
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B
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M. </
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<
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>See therefore that
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the
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W
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eight placed in the extream of the
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L
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eaver B C, in inclining
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downwards along the Circumference C
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F L
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I, cometh to diminiſh
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its Moment and
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Impetus
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of going downwards from time to time, </
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