Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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<
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>PROP. VII. THE OR. VII.</
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The Right Portion of a Rightangled Conoid lighter
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than the Liquid, when it ſhall have its Axis greater
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than Seſquialter of the Semi-parameter, but leſſe
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than to be unto the ſaid Semi-parameter in proportion
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as fiſteen to fower, being demitted into the Liquid ſo
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as that its Baſe be wholly within the Liquid, it ſhall
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never ſtand ſo as that its Baſe do touch the Surface
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of the Liquid, but ſo, that it be wholly within the
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Liquid, and ſhall not in the leaſt touch its Surface.
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>Let there be a Portion as hath been ſaid; and let it be de
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mitted into the Liquid, as we have ſuppoſed, ſo as that its
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Baſe do touch the Surface in one Point only: It is to be de
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monſtrated that the ſame ſhall not ſo
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continue, but ſhall turn about in
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ſuch manner as that its Baſe do in no
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wiſe touch the Surface of the Liquid.
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>For let it be cut thorow its Axis by
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a Plane erect upon the Liquids Sur
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face: and let the Section be A P O L,
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the Section of a Rightangled
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Cone; the Section of the Liquids
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Surface S L; and the Axis of the
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Portion and Diameter of the Section P F: and let P F be cut in
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R, ſo, as that R P may be double to R F, and in
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ſo as that P F
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may be to R
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as fifteen to fower: and draw
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K at Right Angles </
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to P F:
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(a)
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R
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ſhall be leſſe than the Semi-parameter. </
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>There
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fore let R H be ſuppoſed equall to the Semi-parameter: and
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draw C O touching the Section in O and parallel unto S L; and
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let N O be parallel unto P F; and firſt let N O cut K
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in the Point
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I, as in the former Schemes: It ſhall be demonſtrated that N O is
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to O I either ſeſquialter, or greater than ſeſquialter. </
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<
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>Let O I be
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leſſe than double to I N; and let O B be double to B N: and let
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them be diſpoſed like as before. </
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<
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>We might likewiſe demonſtrate
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that if a Line be drawn thorow R and T it will make Right Angles
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with the Line C O, and with the Surface of the Liquid: Where
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fore Lines being drawn from the Points B and G parallels unto
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R T, they alſo ſhall be Perpendiculars to the Surface of the Liquid:
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The Portion therefore which is above the Liquid ſhall move </
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