Galilei, Galileo - Mechanics

Galilei, Galileo, Mechanics, 1665

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hitherto diſcourſed upon it, have ſaid any thing that hits the mark;
which we may take for a certain Sign and Argument of the Obſcu-
rity and difficulty of this S peculation. For Ariſtotle, or others,
who would reduce the cauſe of this admirable Effect unto the
length of the Manubrium, or Handle, may, in my judgement, be
made to ſee their miſtake in the effect of thoſe Inſtruments, which
having no Handle, yet percuſs, either in falling from on high
downwards, or by being thrown with Velocity ſidewaies. There-
fore it is requiſite, that we have recourſe to ſome other Principle, if
we would find out the truth of this buſineſs; the cauſe of which,
although it be of its own nature ſomewhat obſcure, and of diffi-
cult conſideration, yet nevertheleſs we will attempt with the grea-
teſt perſpicuity poſſible to render it clear and obvious, ſhewing, for
a cloſe of all, that the Principle and Original of this Effect is deri-
ved from no other Fountain than this, from which the reaſons of all
other Mechanick Effects do proceed: and this we will do, by ſetting
before your eyes that very thing which is ſeen to befall in every
other Mechanick Operation, ſcilicet, That the Force, the Reſiſtance,
and the Space by which the Motion is made, do go alternately
with ſuch proportion operating, and with ſuch a rate anſwering to
each other, that a Reſiſtance, equal to the Force, ſhall be moved by
the ſaid Force along an equal Space, with Velocity equal to that
with which it is moved. Likewiſe, That a Force that is leſs by half
than a Reſiſtance ſhall be able to move it, ſo that it be moved
with double Velocity, or, if you will, for a Diſtance twice as great
as that which the moved Reſiſtance ſhall paſs: and, in a word, it
hath been ſeen in all the other Inſtruments, that any, never ſo great,
Reſiſtance may be moved by every ſmall Force given, provided,
that the Space, along which the Reſiſtance ſhall move, have the
ſame proportion that is found to be betwixt the ſaid great Reſi-
ſtance and the Force: and that this is according to the neceſſary
Order and Conſtitution of Nature: So that inverting the Diſcourſe,
and Arguing the contrary way, what wonder ſhall it be, if that
Power that ſhall move a ſmall Reſiſtance a great way, ſhall carry
one an hundred times bigger an hundredth part of that Diſtance?
Certainly none at all: nay, it would be abſurd, yea, impoſſible
that it ſhould be otherwiſe. Let us therefore conſider, what the
Reſiſtance of the Beetle unto Motion may be in that point where
it is to ſtrike, and how far, if it do not ſtrike, it would be carryed
by the received Force beyond that point: and again, what Reſi-
ſtance to Motion there is in him who ſtriketh, and how much by
that ſame Percuſſion he is moved: and, having found that this
great Reſiſtance goeth forwards by a percuſſion ſo much leſs than
the Beetle driven by the Impetus of him that moveth it would do,
by how much that ſame great Reſiſtance is greater than that of

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