Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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demonſtrated, and the Motions thorow them ſhall be performed in equal
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Times ſeeing that they terminate in A unto the Circumference of the
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Circle A G O from the higheſt point of it A.
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>PROBL. XII. PROP.
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XXXIII.
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>A Perpendicular and Plane inclined to it being
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given, whoſe height is one and the ſame, as al
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ſo the higheſt term, to find a point in the Per
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pendicular above the common term, out of
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which if a Moveable be demitted that ſhall
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afterwards turn along the inclined Plane, the
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ſaid Plane may be paſt in the ſame Time in
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which the
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P
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erpendicular
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ex quiete
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would be
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paſſed.</
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Let the Perpendicular and inclined Plane, whoſe Altitude is the
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ſame, be A B and A C. </
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>It is required in the Perpendicular B A,
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continued out from the point A to find a Point out of which a
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Moveable deſcending may paſſe the Space A C in the ſame Time in
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which it will paſſe the ſaid Perpendicular A B out of Reſt in A. </
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>Draw
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D C E at Right-Angles to A C, and let C D be cut equal to A B, and
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draw a Line from A to D: The Angle A D C ſhall be greater than the
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Angles C A D: (for C A is greater than A B or C D:) Let the
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Angle D A E be equal to the Angle A D E; and to A E let E F an in
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clined Plane be Perpen-
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dicular, and let both be
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ing prolonged meet in F,
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and unto both A I and
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A G ſuppoſe C F to be
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equal, and by G draw
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G H equidiſtant to the
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Horizon. </
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>I ſay, that H
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is the point which is
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ſought. </
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>For ſuppoſing the
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Time of the Fall along
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the Perpendicular A B
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to be A B, the Time along
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A C ex quiete in A ſhall be the ſame A C. </
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>And becauſe in the Right
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angled Triangle A E F, from the Right Angle E unto the Baſe A F,
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E C is a Perpendicular, A E ſhall be a Mean-Proportional betwixt F A
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and A C, and C E a Mean betwixt A C and C F, that is, betwixt C A
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and A I: and foraſmuch as the Time of A C out of A is A C, A E
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