Galilei, Galileo
,
The systems of the world
,
1661
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may have erred in rehearſing his Argument, and to avoid running
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into the ſame miſtakes for the future, I could wiſh I had his
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Book; and if you had any body to ſend for it, I would take it
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for a great favour.</
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<
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>SAGR. </
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<
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>You ſhall not want a Lacquey that will runne for it
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with all ſpeed: and he ſhall do it preſently, without loſing any
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time; in the mean time
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Salviatus
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may pleaſe to oblige us with his
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computation.</
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<
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>SIMP. </
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>If he go, he ſhall finde it lie open upon my Desk,
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together with that of the other Author, who alſo argueth
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gainſt
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Copernicus.
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<
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>SAGR. </
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<
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>We will make him bring that alſo for the more
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tainty: and in the interim
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Salviatus
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ſhall make his calculation: I
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have diſpatch't away a meſſenger.</
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<
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>SALV. </
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>Above all things it muſt be conſidered, that the motion
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of deſcending grave bodies is not uniform, but departing from
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reſt they go continually accelerating: An effect known and
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ſerved by all men, unleſſe it be by the forementioned modern
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thour, who not ſpeaking of acceleration, maketh it even and
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niforme. </
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<
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>But this general notion is of no avail, if it be not known
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according to what proportion this increaſe of velocity is made; a
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concluſion that hath been until our times unknown to all
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phers
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; and was firſt found out & demonſtrated by the ^{*}
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Academick,
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our common friend, who in ſome of his ^{*} writings not yet
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ed, but in familiarity ſhewn to me, and ſome others of his
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quaintance he proveth, how that the acceleration of the right
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tion of grave bodies, is made according to the numbers uneven
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beginning
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ab unitate,
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that is, any number of equal times being
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ſigned, if in the firſt time the moveable departing from reſt ſhall
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have paſſed ſuch a certain ſpace, as for example, an ell, in the
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cond time it ſhall have paſſed three ells, in the third five, in the
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fourth ſeven, and ſo progreſſively, according to the following odd
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numbers; which in ſhort is the ſame, as if I ſhould ſay, that the
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ſpaces paſſed by the moveable departing from its reſt, are unto
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each other in proportion double to the proportion of the times,
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in which thoſe ſpaces are meaſured; or we will ſay, that the
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ſpaces paſſed are to each other, as the ſquares of their times.</
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An exact
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pute of the time of
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the fall of the
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non bullet from the
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Moons concave to
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the Earths centre.
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* The Author.</
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* By theſe
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tings,
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he every
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where meanes his
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Dialogues,
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De
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tu,
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which I promiſe
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to give you in my
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ſecond Volume.</
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Acceleration of
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the natural motion
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of grave bodies is
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made according to
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the odde numbers
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beginning at unity.
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The ſpaces paſt
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by the falling
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grave body are as
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the ſquares of their
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times.
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<
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>SAGR. </
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<
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>This is truly admirable: and do you ſay that there is
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a Mathematical demonſtration for it?</
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>SALV. Yes, purely Mathematical; and not onely for this, but
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for many other very admirable paſſions, pertaining to natural
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tions, and to projects alſo, all invented, and demonſtrated by
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Our
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Friend,
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and I have ſeen and conſidered them all to my very great
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content and admiration, ſeeing a new compleat Doctrine to ſpring
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up touching a ſubject, upon which have been written hundreds of </
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