Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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deſcending groweth leſs & leſs in it, the nearer it is to the firſt term
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of its deſcent; that is, to the ſtate of reſt; as is manifeſt from that
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which you declare unto us, demonſtrating that the deſcending grave
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body departing from reſt, ought to paſſe thorow all the degrees of
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tardity comprehended between the ſaid reſt, & any aſſigned degree
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of velocity, the which grow leſs and leſs
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in infinitum.
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To which may
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be added, that the ſaid velocity and propenſion to motion, doth for
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another reaſon diminiſh to infinity; and it is becauſe the gravity of
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the ſaid moveable may infinitely diminiſh. </
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<
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>So that the cauſes which
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diminiſh the propenſion of aſcending, and conſequently favour
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the projection, are two; that is, the levity of the moveable, and its
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vicinity to the ſtate of reſt; both which are augmentable
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in infinit.
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and theſe two on the contrary being to contract but with one ſole
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cauſe of making the projection, I cannot conceive how it alone,
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though it alſo do admit of infinite augmentation, ſhould be able to
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remain invincible againſt the union & confederacy of the others, w^{ch}
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are two, and are in like manner capable of infinite augmentation.</
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<
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>SALV. </
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>This is a doubt worthy of
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Sagredus
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; and to explain it ſo as
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that we may more cleerly apprehend it, for that you ſay that you
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your ſelf have but a confuſed
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Idea
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of it, we will diſtinguiſh of the
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ſame by reducing it into figure; which may alſo perhaps afford us
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ſome caſe in reſolving the ſame. </
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<
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>Let us therefore [
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in Fig.
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4.] draw
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a perpendicular line towards the centre, and let it be AC, and to it
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at right angles let there be drawn the Horizontal line A
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B,
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upon
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which the motion of the projection ought to be made; now the
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ject would continue to move along the ſame with an even motion, if
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ſo be its gravity did not incline it downwards. </
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<
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>Let us ſuppoſe from
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the point A a right line to be drawn, that may make any angle at
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pleaſure with the line A B; which let be A E, and upon A
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B
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let us
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mark ſome equal ſpaces AF, FH, HK, and from them let us let fall
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the perpendiculars FG, HI, K L, as far as AE. </
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<
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>And becauſe, as al
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ready hath been ſaid, the deſcending grave body departing from reſt,
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goeth from time to time acquiring a greater degree of velocity,
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according as the ſaid time doth ſucceſſively encreaſe; we may
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ceive the ſpaces AF, FH, HK, to repreſent unto us equal times; and
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the perpendiculars FG, HI, KL, degrees of velocity acquired in the
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ſaid times; ſo that the degree of velocity acquired in the whole time
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A K, is as the line K L, in reſpect to the degree H I, acquired in the
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time AH, and the degree FG in the time AF; the which degrees KL,
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HI, FG, are (as is manifeſt) the ſame in proportion, as the times K A,
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HA, F A, and if other perpendiculars were drawn from the points
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marked at pleaſure in the line F A, one might ſucceſſively find
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grees leſſe and leſſe
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in infinitum,
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proceeding towards the point A,
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repreſenting the firſt inſtant of time, and the firſt ſtate of reſt. </
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<
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>And
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this retreat towards A, repreſenteth the firſt propenſion to the </
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