Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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ROBL. XVI.
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RO
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P.
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XXXVIII.</
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>Two Horizontal Planes cut by the Perpendicular
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being given, to find a ſublime point in the
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er
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pendicular, out of which Moveables falling
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and being reflected along the Horizontal
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lanes may in Times equal to the Times of
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the Deſcents along the ſaid Horizontal
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lanes,
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namely, along the upper and along the lower,
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paſſe Spaces that have to each other any given
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proportion of the leſſer to the greater.</
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LET the Planes C D and B E be interſected by the Perpendicular
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A C B, and let the given proportion of the leſſe to the greater be
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N to F G. </
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>It is required in the Perpendicular A B to find a point
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on high, out of which a Moveable falling, and reflected along C D may
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in a Time equal to the Time of its Fall, paſſe a Space, that ſhall have
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unto the Space paſſed by the other Moveable coming out of the ſame ſub
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lime point in a Time equal to the Time of its Fall with a Reflex Motion
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along the Plane B E the ſame proportion as the given Line N batb to
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F G. </
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>Let G H be
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made equal to the
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ſaid N; and as F H
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is to H G, ſo let
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B C be to C L. </
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>I ſay,
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L is the ſublime
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point required. </
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>For
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taking C M double
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to C L, draw L M
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meeting the Plane
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B E in O; B O
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ſhall be double to
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B L: And becauſe,
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as F H is to H G, ſo is B C to C L; therefore, by Compoſition and In
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verſion, as H G, that is, N is to G F, ſo is C L to L B, that is, C M to
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B O: But becauſe C M is double to L C; let the Space C M be that
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which by the Moveable coming from L after the Fall L C is paſſed along
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the Plane C D; and by the ſame reaſon B O is that which is paſſed after
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the Fall L B in a Time equal to the Time of the Fall along L B; foraſ
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much as B O is double to B L: Therefore the Propoſition is manifeſt.
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