Galilei, Galileo
,
The systems of the world
,
1661
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<
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>SALV. </
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<
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>And have you no other conceit thereof than this?</
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<
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>SIMPL. </
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<
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>This I think to be the proper definition of equal
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tions.</
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Velocities are ſaid
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to be equal, when
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the ſpaces paſſed
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are proportionate to
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their time.
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<
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>SAGR. </
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<
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>We will add moreover this other: and call that equal
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velocity, when the ſpaces paſſed have the ſame proportion, as the
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times wherein they are paſt, and it is a more univerſal definition.</
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<
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>SALV. </
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<
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>It is ſo: for it comprehendeth the equal ſpaces paſt in
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equal times, and alſo the unequal paſt in times unequal, but
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portionate to thoſe ſpaces. </
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<
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>Take now the ſame Figure, and
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ing the conceipt that you had of the more haſtie motion, tell me
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why you think the velocity of the Cadent by C B, is greater
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than the velocity of the Deſcendent by C A?</
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<
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>SIMPL. </
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<
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>I think ſo; becauſe in the ſame time that the Cadent
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ſhall paſs all C B, the Deſcendent ſhall paſs in C A, a part leſs
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than C B.</
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<
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>SALV. True; and thus it is proved, that the moveable moves
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more ſwiftly by the perpendicular, than by the inclination. </
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<
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>Now
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conſider, if in this ſame Figure one may any way evince the
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ther conceipt, and finde that the moveables were equally ſwift
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by both the lines C A and C B.</
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<
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>SIMPL. </
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<
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>I ſee no ſuch thing; nay rather it ſeems to contradict
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what was ſaid before.</
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</
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<
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<
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>SALV. </
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<
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>And what ſay you,
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Sagredus
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? </
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<
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>I would not teach you
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what you knew before, and that of which but juſt now you
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duced me the definition.</
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</
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<
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<
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>SAGR. </
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>
<
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>The definition I gave you, was, that moveables may
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be called equally ſwift, when the ſpaces paſſed are proportional
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to the times in which they paſſed; therefore to apply the
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tion to the preſent caſe, it will be requiſite, that the time of
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ſcent by C A, to the time of falling by C B, ſhould have the
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ſame proportion that the line C A hath to the line C B; but I
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underſtand not how that can be, for that the motion by C B is
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ſwifter than by C A.</
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<
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>SALV. </
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<
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>And yet you muſt of neceſſity know it. </
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>
<
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>Tell me a little,
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do not theſe motions go continually accelerating?</
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>
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<
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>SAGR. </
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>
<
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>They do; but more in the perpendicular than in the
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inclination.</
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</
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<
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<
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>SALV. </
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>
<
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>But this acceleration in the perpendicular, is it yet
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withſtanding ſuch in compariſon of that of the inclined, that
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two equal parts being taken in any place of the ſaid
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lar and inclining lines, the motion in the parts of the
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lar is alwaies more ſwift, than in the part of the inclination?</
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>
</
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<
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<
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>SAGR. </
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>
<
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>I ſay not ſo: but I could take a ſpace in the
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on, in which the velocity ſhall be far greater than in the like ſpace
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taken in the perpendicular; and this ſhall be, if the ſpace in the </
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>
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</
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