Galilei, Galileo, Mechanics, 1665

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and in the Velocity: which peradventure, might not have ſeemed
to ſome ſo true and manifeſt in the preſent Contemplation; nay,
rather it ſeems, that in this caſe the Force is multiplied without the
Movers moving a longer way than the Moveable: In regard, that
if we ſhall in the Triangle A B C ſuppoſe the Line A B to be the
Plane of the Horizon, A C the elevated Plane, whoſe Altitude is
meaſured by the Perpendicular C B, a Moveable placed upon the
Plane A C, and the Cord E D F tyed to it, and a Force or Weight
applyed in F that hath to the
Gravity of the Weight E the

Figure: /permanent/archimedes/galil_mecha_070_en_1665/figures/070.01.028.1.jpg not scanned
[Figure 25]

ſame proportion that the Line
B C hath to C A; by what
hath been demonſtrated, the
Weight F ſhall deſcend
downwards, drawing the
Moveable E along the eleva-
ted Plane; nor ſhall the Move-
able E meaſure a greater Space
when it ſhall have paſſed the
whole Line A C, than that which the ſaid Grave F meaſureth in its
deſcent downwards.
But here yet it muſt be advertiſed, that al-
though the Moveable E ſhall have paſſed the whole Line A C, in
the ſame Time that the other Grave F ſhall have been abaſed the
like Space, nevertheleſs the Grave E ſhall not have retired from the
common Center of things Grave more than the Space of the Per-
pendicular C B. but yet the Grave F deſcending Perpendicularly ſhall
be abaſed a Space equal to the whole Line A C. And becauſe Grave
Bodies make no Reſiſtance to Tranſverſal Motions, but only ſo
far as they happen to recede from the Center of the Earth; There-
fore the Moveable E in all the Motion A C being raiſed no more
than the length of the Line CB, but the other F being abaſed per-
pendicularly the quantity of all the Line A C: Therefore we may
deſervedly affirm that Way of the Force E maintaineth the ſame
proportion to the Force F that the Line A C hath to C B; that is,
the Weight E to the Weight F. It very much importeth, therefore,
to conſider by [or along] what Lines the Motions are made, eſpe-
cially in exanimate Grave Bodies, the Moments of which have their
total Vigour, and entire Reſiſtance in the Line Perpendicular to
the Horizon; and in the others tranſverſally Elevated and Inclined
they feel the more or leſs Vigour, Impetus, or Reſiſtance, the more
or leſs thoſe Inclinations approach unto the Perpendicular Inclina-
tion.

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