Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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Accelerate Motion of the Velocity of the Equable Motion (which defi
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cient Moments are repreſented by the Parallels of the Triangle A
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G I)
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is made up by the moments repreſented by the Parallels of the Triangle
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I E F.
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It is manifeſt, therefore, that thoſe Spaces are equal which are
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in the ſame Time by two Moveables, one whereof is moved with a Mo
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tion uniformly Accelerated from Reſt, the other with a Motion Equable
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according to the Moment ſubduple of that of the greateſt Velocity of the
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Accelerated Motion: Which was to be demonſtrated.
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<
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>THEOR. II. PROP. II.</
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>If a
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M
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oveable deſcend out of Reſt with a
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M
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oti
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on uniformly Accelerate, the Spaces which it
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paſſeth in any whatſoever Times are to each
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other in a proportion Duplicate of the ſame
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Times; that is, they are as the Squares of
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them.</
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Let
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A B
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repreſent a length of Time beginning at the firſt Inſtant A;
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and let
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A D
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and
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A E
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repreſent any two parts of the ſaid Time;
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and let
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H I
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be a Line in which the Moveable out of H, (as the firſt
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beginning of the Motion) deſcendeth uniformly accelerating; and let the
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Space
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H L
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be paſſed in the firſt Time
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A D;
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and let
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H M
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be the Space that it ſhall deſcend in the Time
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A E.
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I ſay,
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the Space
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M H
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is to the Space
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H L
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in duplicate propor
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tion of that which the Time
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E A
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hath to the Time
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A D
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:
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Or, if you will, that the Spaces
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M H
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and
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H L
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are to one
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another in the ſame proportion as the Squares
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E A
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and
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A D.
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Draw the Line
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A C
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at any Angle with
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A B,
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and
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from the points D and E draw the Parallels
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D O
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and
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P E
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: of which
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D O
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will repreſent the greateſt degree
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of Velocity acquired in the Inſtant D of the Time
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A D;
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and
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P
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the greateſt degree of Velocity acquired in the In
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ſtant E of the Time
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A E.
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And becauſe we have de
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monſtrated in the laſt Propoſition concerning Spaces, that
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thoſe are equal to one another, of which two Moveables
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have paſt in the ſame Time, the one by a Moveable out
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of Reſt with a Motion uniformly Accelerate, and the
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other by the ſame Moveable with an Equable Motion,
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whoſe Velocity is ſubduple to the greateſt acquired by the
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Accelerate Motion: Therefore
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M H
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and
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H L
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are the Spaces that two
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Lquable Motions, whoſe Velocities ſhould be as the half of
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P E,
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and
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