Galilei, Galileo - The systems of the world

Galilei, Galileo, The systems of the world, 1661

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ſhall be an eaſie task; for I reply, that the moveable paſſeth by
the aforeſaid degrees, but the paſſage is made without ſtaying in

The moveable de
parting from reſv
paſſeth thorow all
degrees of velocity
without ſtaying in
any.

SAGR. Hitherto I apprehend you; nevertheleſs it is very much
that that Ball ſhot from a Cannon (for ſuch I conceive the ca
dent moveable) which yet we ſee to fall with ſuch a precipice,
that in leſs than ten pulſes it will paſs two hundred yards of al
titude; ſhould in its motion be found conjoyned with ſo ſmall a
degree of velocity, that, ſhould it have continued to have moved
at that rate without farther acceleration, it would not have paſt
the ſame in a day.

SALV. You may ſay, nor yet in a year, nor in ten, no nor in a
thouſand; as I will endeavour to ſhew you, and alſo happily with
out your contradiction, to ſome ſufficiently ſimple queſtions that
I will propound to you. Therefore tell me if you make any que
ſtion of granting that, that that ball in deſcending goeth increa
ſing its impetus and velocity.

SAGR. I am moſt certain it doth.

SALV. And if I ſhould ſay that the impetus acquired in any
place of its motion, is ſo much, that it would ſuffice to re-carry
it to that place from which it came, would you grant it?

SAGR. I ſhould conſent to it without contradiction, provided al
waies, that it might imploy without impediment its whole impetus
in that ſole work of re-conducting it ſelf, or another equal toit, to

that ſelf-ſame height as it would do, in caſe the Earth were bored
thorow the centre, and the Bullet fell a thouſand yards from the
ſaid centre, for I verily believe it would paſs beyond the centre,
aſcending as much as it had deſcended; and this I ſee plainly in
the experiment of a plummet hanging at a line, which removed
from the perpendicular, which is its ſtate of reſt, and afterwards
let go, falleth towards the ſaid perpendicular, and goes as far be
yond it; or onely ſo much leſs, as the oppoſition of the air, and
line, or other accidents have hindred it. The like I ſee in the wa
ter, which deſcending thorow a pipe, re-mounts as much as it had
deſcended.

The ponderous mo
ver deſcending ac
quireth impetus
ſufficient to re
carry it to the like
height.

SALV. You argue very well. And for that I know you will not
ſcruple to grant that the acquiſt of the impetus is by means of the
receding from the term whence the moveable departed, and its ap
proach to the centre, whither its motion tendeth; will you ſtick
to yeeld, that two equal moveables, though deſcending by divers
lines, without any impediment, acquire equal impetus, provided
that the approaches to the centre be equal?

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