Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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ſuperficies A E, the Cylinder C F ſhall be leſſe than A E: For
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if they were equal, its Superficies, by the laſt Propoſition would
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be greater than the Superficies A E, and
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much the more, if the ſaid Cylinder C F
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were greater than A E. </
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>Let the Cylinder
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I D be ſuppoſed equal to A E: There
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fore, by the precedent Propoſition, the
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Superficies of the Cylinder I D ſhall be
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to the Superficies A E, as the height I F
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to the Mean-proportional betwixt I F &
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A B. </
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>But the Superficies A E being by
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Suppoſition equal to C F and I D, ha
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ving the ſame proportion to C F that the
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height I F hath to C D: Therefore
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C D is the Mean-Proportional between
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I F and A B. Moreover, the Cylinder
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I D being equal to the Cylinder A E,
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they ſhall both have the ſame proporti
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on to the Cylinder C F: But I D is to
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C F, as the height I F is to C D: Therefore the Cylinder A E
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ſhall have the ſame proportion to the Cylinder C F, that the line
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I F hath to C D; that is, that C D hath to A B: Which was to be
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demonſtrated.
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Of Corn-ſacks
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with a Board at
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the Bottom, made
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of the ſame Stuffe,
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but different in
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height, which are
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the more capa
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cious.
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>From hence is collected the Cauſe of an Accident, which the
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Vulgar do not hearken to without admiration; and it is, how it
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is poſſible that the ſame piece of ^{*}Cloth, being longer one way than
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another, if a Sack be made thereof to hold Corn, as the uſual
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manner is, with a Board at the bottom, will hold more, making
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uſe of the leſſer breadth of the Cloth, for the height of the Sack, </
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and with the other encompaſſing the Board at the bottom, than if
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it be made up the other way: As if for Example, the Cloth were
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one way ſix foot, and the other way twelve, it will hold more,
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when with the length of twelve one encompaſſeth the Board at the
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bottom, the Sack being ſix foot high, than if it encompaſſed a
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bottom of ſix foot, having twelve for its height. </
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>Now, by what
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hath been demonſtrated, there is added to the Knowledge in ge
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neral that it holds more that way than this, the Specifick, and
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particular Knowledge of how much it holdeth more: which is,
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That it will hold more in proportion as it is lower, and leſſer, as
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it is higher. </
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<
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>And thus in the meaſures afore taken, the Cloth be
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ing twice as long as broad, when it is ſewed the length-ways it will
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hold but half ſo much, as it will do the other way. </
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<
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>And likewiſe
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having a Mat to make a ^{*} Frale or Basket twenty five foot long,
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and ſuppoſe ſeven broad; made up the long-way it will hold but
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onely ſeven of thoſe meaſures, whereof the other way it will hold
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five and twenty.</
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