Galilei, Galileo - Mechanics

Galilei, Galileo, Mechanics, 1665

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

Moveable be diminiſhed by the total Impetus which it hath in its
Perpendicular D C E, according to the proportion of the Line K B
to the Line B C, and B F, being by the Solicitude of the Triangles
K B F and K F H the ſame proportion betwixt the Lines K F and
F H, as betwixt the ſaid K B and B F, we will conclude that the
proportion of the entire and abſolute Moment, that the Moveable
hath in the Perpendicular to the Horizon to that which it hath up-
on the Inclined Plane H F, hath the ſame proportion that the
Line H F hath to the Line F K; that is, that the Length of the
Inclined Plane hath to the Perpendicular which ſhall fall from it
unto the Horizon. So that paſſing to a more diſtinct Figure, ſuch
as this here preſent, the Moment of Deſcending which the Move

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