Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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your incredulity; but for the knowledge of this, expect it at
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ſome other time, namely, when you ſhall ſee the matters
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ning local motion demonſtrated by our
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Academick
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; at which
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time you ſhall find it proved, that in the time that the one
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ble falls all the ſpace C B, the other deſcendeth by C A as far
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as the point T, in which falls the perpendicular drawn from the
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point B: and to find where the ſame Cadent by the
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cular would be when the other arriveth at the point A, draw from
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A the perpendicular unto C A, continuing it, and C B unto the
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interfection, and that ſhall be the point ſought. </
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>Whereby you
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ſee how it is true, that the motion by C B is ſwifter than by the
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inclination C A (ſuppoſing the term C for the beginning of the
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motions compared) becauſe the line C B is greater than C T,
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and the other from C unto the interſection of the perpendicular
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drawn from A, unto the line C A, is greater than C A, and
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therefore the motion by it is ſwifter than by C A But when we
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compare the motion made by all C A, not with all the motion
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made in the ſame time by the perpendicular continued, but with
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that made in part of the time, by the ſole part C B, it hinders
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not, that the motion by C A, continuing to deſcend beyond, may
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arrive to A in ſuch a time as is in proportion to the other time,
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as the line C A is to the line C B. </
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>Now returning to our firſt
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purpoſe; which was to ſhew, that the grave moveable leaving
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its quieſcence, paſſeth defcending by all the degrees of tardity,
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precedent to any whatſoever degree of velocity that it aequireth,
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re-aſſuming the ſame Figure which we uſed before, let us
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ber that we did agree, that the Deſcendent by the inclination C
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A, and the Cadent by the perpendicular C B, were found to have
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acquired equal degrees of velocity in the terms B and A: now to
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proceed, I ſuppoſe you will not ſcruple to grant, that upon
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ther plane leſs ſteep than A C; as for example, A D [in
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Fig.
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5.]
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the motion of the deſcendent would be yet more ſlow than in the
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plane A C. </
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>So that it is not any whit dubitable, but that there
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may be planes ſo little elevated above the Horizon A B, that the
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moveable, namely the ſame ball, in any the longeſt time may
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reach the point A, which being to move by the plane A B, an
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nite time would not ſuffice: and the motion is made always more
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ſlowly, by how much the declination is leſs. </
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>It muſt be therefore
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confeſt, that there may be a point taken upon the term B, ſo near
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to the ſaid B, that drawing from thence to the point A a plane,
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the ball would not paſs it in a whole year. </
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<
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>It is requiſite next
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for you to know, that the
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impetus,
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namely the degree of
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city the ball is found to have acquired when it arriveth at the
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point A, is ſuch, that ſhould it continue to move with this ſelf-ſame
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degree uniformly, that is to ſay, without accelerating or retarding; </
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