Galilei, Galileo
,
Mechanics
,
1665
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more and leſs, as it is more or leſs ſuſtained by the Lines B F and
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B L: But the conſidering that this Grave deſcending, and ſuſtained
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by the Semidiameters B F and B L is one while leſs, and another
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while more conſtrained to paſs along the Circumference C F L, is
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no other, than if we ſhould imagine the ſame Circumference
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C F L I to be a Superſicies ſo curved, and put under the ſame
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Moveable: ſo that bearing it ſelf thereon it were conſtrained to
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deſcend along thereby; for if in the one and other manner the
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Moveable deſcribeth the ſame Courſe or Way, it will nothing im
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port whether, if ſuſpended at the Center B, it is ſuſtained by the
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Semidiameter of the Circle, or elſe, whether that Fulciment being
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taken away, it proceed along the Circumference C F L I: So that
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we may confidently affirm, that the Grave deſcending downwards
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from the point C along the Circumference C F L I, its Moment
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of Deſcent in the point C is total and entire, becauſe it is not in
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any part ſuſtained by the Circumference: And there is not in that
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firſt point C, any indiſpoſition to Motion different from that, which
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being at liberty, it would make along the Perpendicular and Con
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tingent Line D C E: But if the Moveable ſhall be placed in the
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point F, then its Gravity is in part ſuſtained, and its Moment of
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Deſcent is diminiſhed by the Circular Path or Way that is placed
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under it, in that proportion wherewith the
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L
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ine
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B
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K is overcome
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by
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B
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C: But if when the Moveable is in F, at the firſt inſtant of
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ſuch its Motion, it be as if it were in the Plane elevated according
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to the Contingent
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L
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ine G F H, for that reaſon the inclination of the
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Circumference in the point F differeth not from the inclination of
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the Contingent
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L
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ine F G any more ſave the inſenſible Angle of
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the Contact. </
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>And in the ſame manner we ſhall find the Moment
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of the ſaid Moveable to diminiſh in the point
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L,
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as the
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L
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ine BM
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is diminiſhed by B C; ſo that in the Plane contingent to the Circle
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in the point
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L,
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as for inſtance, according to the
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L
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ine N
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L
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O, the
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Moment of Deſcent diminiſheth in the Moveable with the ſame
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proportion. </
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<
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>If therefore ^{*} upon the Plane HG the Moment of the
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Moveable be diminiſhed by the total
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Impetus
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which it hath in its
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Perpendicular D C E, according to the proportion of the
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L
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ine K B
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to the
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L
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ine B C, and B F, being by the Solicitude of the Triangles
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K B F and K F H the ſame proportion betwixt the
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L
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ines K F and
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F H, as betwixt the ſaid K B and
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B
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F, we will conclude that the
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proportion of the entire and abſolute Moment, that the Moveable
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hath in the Perpendicular to the Horizon to that which it hath up
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on the Inclined Plane H F, hath the ſame proportion that the
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L
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ine H F hath to the
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L
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ine F K; that is, that the
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L
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ength of the
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Inclined Plane hath to the Perpendicular which ſhall fall from it
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unto the Horizon. </
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<
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>So that paſſing to a more diſtinct Figure, ſuch
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as this here preſent, the Moment of Deſcending which the Move</
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