Galilei, Galileo
,
Mechanics
,
1665
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De æquiponder antium,
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there came into my thoughts a Rule which
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exquiſitely reſolveth our Queſtion; which Rule I believe to be
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the ſame that
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Archimedes
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made uſe of, ſeeing that beſides the
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uſe that is to be made of the Water, the exactneſs of the Work
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dependeth alſo upon certain Demonſtrations found by the ſaid
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Archimedes.
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>The way is by help of a Ballance, whoſe Conſtruction and Uſe
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ſhall be ſhewn by and by, after we ſhall have declared what is
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neceſſary for the knowledge thereof. </
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>You muſt know there
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fore, that the Solid Bodies that ſink in the Water weigh ſo much
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leſs in the Water than in the Air, as a Maſs of Water equal to
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the ſaid Solid doth weigh in the Air: which hath been demon
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ſtrated by
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Archimedes.
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But, in regard his Demonſtration is very
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mediate, becauſe I would not be over long, laying it aſide, I ſhall
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declare the ſame another way. </
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<
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>Let us conſider, therefore, that
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putting into the Water
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v. </
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<
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a Maſs of Gold, if that Maſs were
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of Water it would have no weight at all: For the Water moveth
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neither upwards, nor downwards in the Water: It remains,
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therefore, that the Maſs of Gold weigheth in the Water only ſo
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much as the Gravity of the Gold exceeds the Gravity of the Wa
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ter. </
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<
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>And the like is to be underſtood of other Metals. </
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<
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>And be
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cauſe the Metals are different from each other in Gravity, their
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Gravity in the Water ſhall diminiſh according to ſeveral proporti
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ons. </
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<
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>As for example: Let us ſuppoſe that Gold weigheth twenty
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times more than Water, it is manifeſt by that which hath been
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ſpoken, that the Gold will weigh leſs in the Water than in the
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Air by a twentieth part of its whole weight. </
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<
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>Now, let us ſuppoſe
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that Silver, as being leſs Grave than Gold, weigheth 12 times more
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than Water: this then, being weighed in the Water, ſhall di
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miniſh in Gravity the twelfth part of its whole weight. </
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<
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>Therefore
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the Gravity of Gold in the Water decreaſeth leſs than that of
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Silver; for that diminiſheth a twentieth part, and this a twelfth.
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>If therefore in an exquiſite Ballance we ſhall hang a Metal at the
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one Arm, and at the other a Counterpoiſe that weigheth equally
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with the ſaid Metal in the Water, leaving the Counterpoiſe in the
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Air, to the end that it may equivalate and compenſate the Me
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tal, it will be neceſſary to hang it nearer the Perpendicular or
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Cook. </
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<
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>As for example, Let the Ballance be A B, its Perpendicu
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lar C, and let a
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Maſs of ſome
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Metal be ſu
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ſpended at B,
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counterpoiſedby
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the Weight D: putting the Weight B into the Water, the
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Weight D in A would weigh more: therefore that they may </
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