Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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<
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>SAGR. </
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<
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>You argue very well, and make no ſeruple at all of
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granting, that be the Force of the Mover never ſo ſmall it ſhall ſu
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perate any what ever great Reſiſtance at all times when that ſhall
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more exceed in Velocity than this doth in Force and Gravity.
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</
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<
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>Now come we to the caſe of the Rope. </
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<
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>And drawing a ſmall
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Scheme be pleaſed to underſtand for once that this Line A B, reſt
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ing upon the two fixed and ſtanding points A and B, to have hang
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ing at its ends, as you ſee, two immenſe Weights C and D, which
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drawing it with great Force make it to ſtand directly diſtended, it
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being a ſimple Line without any gravity. </
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<
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>And here I proceed, and
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tell you, that if at the midſt of that which is the point E, you ſhould
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hang any never ſo little a Weight, as is this H, the Line A B would
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yield, and inclining towards the point F, and by conſequence
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lengthening, will conſtrain the two great Weights C and D to
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aſcend upwards: which I demonſtrate to you in this manner:
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About the two points A and B as Centers I deſcribe two Quadrants
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E F G, and E L M, and in regard that the two Semidiameters AI
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and B L are equal to the two Semidiameters A E and E B, the exceſ
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ſes F I and F L ſhall be the quantity of the prolongations of the
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parts A F and F B, above A E and E B; and of conſequence ſhall
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<
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determine the Aſcents
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of the Weights C and
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D, in caſe that the
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Weight H had had a
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power to deſcend to F:
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which might then be
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in caſe the Line E F,
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which is the quantity
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of the Deſcent of the
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ſaid Weight H, had
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greater proportion to
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the Line F I which de
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termineth the Aſcent of
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the two Weights C &
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D, than the pondero
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ſity of both thoſe Weights hath to the ponderoſity of the Weight
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H. </
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<
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>But this will neceſſarily happen, be the ponderoſity of the
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Weights C and D never ſo great, and that of H never ſo ſmall; for
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the exceſs of the Weights C and D above the Weight His not ſo
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great, but that the exceſs of the Tangent E F above the part of the
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Secant F I may bear a greater proportion. </
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<
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>Which we will prove
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thus: Let there be a Circle whoſe Diameter is G A I; and look
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what proportion the ponderoſity of the Weights C and D have to
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the ponderoſity of H, let the Line B O have the ſame proportion to
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another, which let be C, than which let D be leſſer: So that B O </
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