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
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the aforeſaid degrees, but the paſſage is made without ſtaying in </
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any of them; ſo that the paſſage requiring but one ſole inſtant
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of time, and every ſmall time containing infinite inſtants, we ſhall
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not want enough of them to aſſign its own to each of the infinite
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degrees of tardity; although the time were never ſo ſhort.</
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The moveable
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parting from reſv
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paſſeth thorow all
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degrees of velocity
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without ſtaying in
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any.
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<
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>SAGR. </
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<
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>Hitherto I apprehend you; nevertheleſs it is very much
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that that Ball ſhot from a Cannon (for ſuch I conceive the
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dent moveable) which yet we ſee to fall with ſuch a precipice,
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that in leſs than ten pulſes it will paſs two hundred yards of
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titude; ſhould in its motion be found conjoyned with ſo ſmall a
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degree of velocity, that, ſhould it have continued to have moved
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at that rate without farther acceleration, it would not have paſt
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the ſame in a day.</
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<
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>SALV. </
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<
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>You may ſay, nor yet in a year, nor in ten, no nor in a
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thouſand; as I will endeavour to ſhew you, and alſo happily
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out your contradiction, to ſome ſufficiently ſimple queſtions that
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I will propound to you. </
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<
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>Therefore tell me if you make any
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ſtion of granting that, that that ball in deſcending goeth
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ſing its
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impetus
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and velocity.</
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<
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>SAGR. </
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<
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>I am moſt certain it doth.</
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<
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>SALV. </
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<
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>And if I ſhould ſay that the
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impetus
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acquired in any
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place of its motion, is ſo much, that it would ſuffice to re-carry
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it to that place from which it came, would you grant it?</
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<
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>SAGR. </
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<
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>I ſhould conſent to it without contradiction, provided
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waies, that it might imploy without impediment its whole
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impetus
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in that ſole work of re-conducting it ſelf, or another equal toit, to
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that ſelf-ſame height as it would do, in caſe the Earth were bored
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thorow the centre, and the Bullet fell a thouſand yards from the
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ſaid centre, for I verily believe it would paſs beyond the centre,
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aſcending as much as it had deſcended; and this I ſee plainly in
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the experiment of a plummet hanging at a line, which removed
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from the perpendicular, which is its ſtate of reſt, and afterwards
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let go, falleth towards the ſaid perpendicular, and goes as far
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yond it; or onely ſo much leſs, as the oppoſition of the air, and
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line, or other accidents have hindred it. </
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<
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>The like I ſee in the
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ter, which deſcending thorow a pipe, re-mounts as much as it had
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deſcended.</
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The ponderous
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ver deſcending
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quireth
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impetus
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ſufficient to
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carry it to the like
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height.
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</
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</
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<
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<
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>SALV. </
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<
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>You argue very well. </
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<
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>And for that I know you will not
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ſcruple to grant that the acquiſt of the
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impetus
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is by means of the
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receding from the term whence the moveable departed, and its
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proach to the centre, whither its motion tendeth; will you ſtick
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to yeeld, that two equal moveables, though deſcending by divers
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lines, without any impediment, acquire equal
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impetus,
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provided
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that the approaches to the centre be equal?</
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