Galilei, Galileo - Mechanics

Galilei, Galileo, Mechanics, 1665

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D hath the ſame proportion to the Reſiſtance made by the Weight
A, in the point C: as the Diſtance B C hath to the Diſtance C D,
whereby it's clear, that the nearer the Fulciment E ſhall approach
to the Term B, encreaſing the proportion of the Diſtance D C to
the Diſtance C B, the more may one diminiſh the Force in D which
is to raiſe the Weight A. And here it is to be noted, which I ſhall
alſo in its place remember you of, that the benefit drawn from all
Mechanical Inſtruments, is not that which the vulgar Mechanitians
do perſwade us, to wit, ſuch, that there by Nature is overcome, and
in a certain manner deluded, a ſmall Force over-powring a very
great Reſiſtance with help of the Leaver; for we ſhall demonſtrate,
that without the help of the length of the Leaver, the ſame Force,
in the ſame Time, ſhall work the ſame effect. For taking the ſame
Leaver B C D, whoſe reſt or Fulci-
ment is in C, let the Diſtance C D

[Figure 6]

be ſuppoſed, for example, to be
in quintuple proportion to the
Diſtance C B, & the ſaid Leaver to
be moved till it come to I C G: In
the Time that the Force ſhall have
paſſed the Space D I, the Weight
ſhall have been moved from B
to G: and becauſe the Diſtance
D C, was ſuppoſed quintuple to the other C B, it is manifeſt from
the things demonſtrated, that the Weight placed in B may be five
times greater then the moving Force ſuppoſed to be in D: but now,

if on the contrary, we take notice of the ^{*} Way paſſed by
the Force from D unto I, whilſt the Weight is moved from B unto
G, we ſhall find likewiſe the Way D I, to be quintuple to the Space
B G. Moreover if we take the Diſtance C L, equal to the Diſtance
C B, and place the ſame Force that was in D, in the point L, and
in the point B the fifth part onely of the Weight that was put there
at firſt, there is no queſtion, but that the Force in L being now
equal to this Weight in B, and the Diſtances L C and C B being
equall, the ſaid Force ſhall be able, being moved along the Space LM
to transfer the Weight equall to it ſelf, thorow the other equall
Space B G: which five times reiterating this ſame action, ſhall tranſ-
port all the parts of the ſaid Weight to the ſame Term G: But
the repeating of the Space L M, is certainly nothing more nor leſſe
then the onely once meaſuring the Space D I, quintuple to the
ſaid L M. Therefore the transferring of the Weight from B to G,
requireth no leſſe Force, nor leſſe Time, nor a ſhorter Way if it
wee placed in D, than it would need if the ſame were applied
in L: And, in ſhort, the benefit that is derived from the length of
the Leaver C D, is no other, ſave the enabling us to move that

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