Galilei, Galileo - The systems of the world

Galilei, Galileo, The systems of the world, 1661

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SALV. And have you no other conceit thereof than this?

SIMPL. This I think to be the proper definition of equal mo
tions.

Velocities are ſaid
to be equal, when
the ſpaces paſſed
are proportionate to
their time.

SAGR. We will add moreover this other: and call that equal
velocity, when the ſpaces paſſed have the ſame proportion, as the
times wherein they are paſt, and it is a more univerſal definition.

SALV. It is ſo: for it comprehendeth the equal ſpaces paſt in
equal times, and alſo the unequal paſt in times unequal, but pro
portionate to thoſe ſpaces. Take now the ſame Figure, and apply
ing the conceipt that you had of the more haſtie motion, tell me
why you think the velocity of the Cadent by C B, is greater
than the velocity of the Deſcendent by C A?

SIMPL. I think ſo; becauſe in the ſame time that the Cadent
ſhall paſs all C B, the Deſcendent ſhall paſs in C A, a part leſs
than C B.

SALV. True; and thus it is proved, that the moveable moves
more ſwiftly by the perpendicular, than by the inclination. Now
conſider, if in this ſame Figure one may any way evince the o
ther conceipt, and finde that the moveables were equally ſwift
by both the lines C A and C B.

SIMPL. I ſee no ſuch thing; nay rather it ſeems to contradict
what was ſaid before.

SALV. And what ſay you, Sagredus? I would not teach you
what you knew before, and that of which but juſt now you pro
duced me the definition.

SAGR. The definition I gave you, was, that moveables may
be called equally ſwift, when the ſpaces paſſed are proportional
to the times in which they paſſed; therefore to apply the defini
tion to the preſent caſe, it will be requiſite, that the time of de
ſcent by C A, to the time of falling by C B, ſhould have the
ſame proportion that the line C A hath to the line C B; but I
underſtand not how that can be, for that the motion by C B is
ſwifter than by C A.

SALV. And yet you muſt of neceſſity know it. Tell me a little,
do not theſe motions go continually accelerating?

SAGR. They do; but more in the perpendicular than in the
inclination.

SALV. But this acceleration in the perpendicular, is it yet not
withſtanding ſuch in compariſon of that of the inclined, that
two equal parts being taken in any place of the ſaid perpendicu
lar and inclining lines, the motion in the parts of the perpendicu
lar is alwaies more ſwift, than in the part of the inclination?

SAGR. I ſay not ſo: but I could take a ſpace in the inclinati
on, in which the velocity ſhall be far greater than in the like ſpace
taken in the perpendicular; and this ſhall be, if the ſpace in the

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