Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667

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              <s>
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              but that the diminution of the ſame velocity, dependent on the
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              diminution of the gravity of the moveable (which vvas the ſecond
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              cauſe) doth alſo obſerve the ſame proportion, doth not ſo plainly
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              appear, And vvho ſhall aſſure us that it doth not proceed
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              ding to the proportion of the lines intercepted between the ſecant,
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              and the circumference; or vvhether vvith a greater proportion?</s>
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              <s>SALV. </s>
              <s>I have aſſumed for a truth, that the velocities of
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              bles deſcending naturally, vvill follovv the proportion of their
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              vities, with the favour of
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              Simplicius,
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              and of
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              Ariſtotle,
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              who doth
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              in many places affirm the ſame, as a propoſition manifeſt: You,
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              in favour of my adverſary, bring the ſame into queſtion, and ſay
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              that its poſſible that the velocity increaſeth with greater
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              tion, yea and greater
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              in infinitum
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              than that of the gravity; ſo that
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              all that hath been ſaid falleth to the ground: For maintaining
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              whereof, I ſay, that the proportion of the velocities is much leſſe
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              than that of the gravities; and thereby I do not onely ſupport
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              but confirme the premiſes. </s>
              <s>And for proof of this I appeal unto
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              experience, which will ſhew us, that a grave body, howbeit thirty
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              or fourty times bigger then another; as for example, a ball of
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              lead, and another of ſugar, will not move much more than twice
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              as faſt. </s>
              <s>Now if the projection would not be made, albeit the
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              locity of the cadent body ſhould diminiſh according to the
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              portion of the gravity, much leſſe would it be made ſo long as the
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              velocity is but little diminiſhed, by abating much from the
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              ty. </s>
              <s>But yet ſuppoſing that the velocity diminiſheth with a
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              tion much greater than that wherewith the gravity decreaſeth, nay
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              though it were the ſelf-ſame wherewith thoſe parallels conteined
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              between the tangent and circumference do decreaſe, yet cannot I
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              ſee any neceſſity why I ſhould grant the projection of matters of
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              never ſo great levity; yea I farther averre, that there could no ſuch
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              projection follow, meaning alwayes of matters not properly and
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              abſolutely light, that is, void of all gravity, and that of their own
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              natures move upwards, but that deſcend very ſlowly, and
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              have very ſmall gravity. </s>
              <s>And that which moveth me ſo to think
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              is, that the diminution of gravity, made according to the
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              tion of the parallels between the tangent and the circumference,
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              hath for its ultimate and higheſt term the nullity of weight, as thoſe
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              parallels have for their laſt term of their diminution the contact it
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              ſelf, which is an indiviſible point: Now gravity never diminiſheth
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              ſo far as to its laſt term, for then the moveable would ceaſe to be
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              grave; but yet the ſpace of the reverſion of the project to the
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              circumference is reduced to the ultimate minuity, which is when
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              the moveable reſteth upon the circumference in the very point of
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              contact; ſo as that to return thither it hath no need of ſpace:
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              and therefore let the propenſion to the motion of deſcent be </s>
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          </chap>
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    </archimedes>
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