Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667

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1as in the greater, the velocity is greater onely in the bigger wheel,

for that its circumference is bigger; there is no man that thinketh
that the cauſe of the extruſion in the great wheel will encreaſe
cording to the proportion of the velocity of its circumference, to
the velocity of the circumference of the other leſſer wheel; for that
this is moſt falſe, as by a moſt expeditious experiment I ſhall thus
groſly declare: We may ſling a ſtone with a ſtick of a yard long,
farther than we can do with a ſtick ſix yards long, though
the motion of the end of the long ſtick, that is of the ſtone placed
in the ſlit thereof, were more than double as ſwift as the
tion of the end of the other ſhorter ſtick, as it would be if
the velocities were ſuch that the leſſer ſtick ſhould turn thrice
round in the time whilſt the greater is making one onely
verſion.
The cauſe of the
projection
eth not according
to the proportion of
the velocity,
creaſed by making
the wheel bigger.
SAGR. This which you tell me, Salviatus, muſt, I ſee, needs
ſucceed in this very manner; but I do not ſo readily apprehend
the cauſe why equal velocities ſhould not operate equally in
extruding projects, but that of the leſſer wheel much more than
the other of the greater wheel; therefore I intreat you to tell me
how this cometh to paſs.
SIMP. Herein, Sagredus, you ſeem to differ much from your
ſelf, for that you were wont to penetrate all things in an inſtant,
and now you have overlook'd a fallacy couched in the experiment
of the ſtick, which I my ſelf have been able to diſcover: and this
is the different manner of operating, in making the projection one
while with the ſhort ſling and another while with the long one,
for if you will have the ſtone fly out of the ſlit, you need not
tinue its motion uniformly, but at ſuch time as it is at the ſwifteſt,
you are to ſtay your arm, and ſtop the velocity of the ſtick;
upon the ſtone which was in its ſwifteſt motion, flyeth out, and
moveth with impetuoſity: but now that ſtop cannot be made in
the great ſtick, which by reaſon of its length and flexibility, doth
not entirely obey the check of the arm, but continueth to
pany the ſtone for ſome ſpace, and holdeth it in with ſo much leſs
force, and not as if you had with a ſtiff ſling ſent it going with a
jerk: for if both the ſticks or ſlings ſhould be check'd by one and
the ſame obſtacle, I do believe they would fly aſwell out of the
one, as out of the other, howbeit their motions were equally
ſwift.
SAGR. With the permiſſion of Salviatus, I will anſwer
thing to Simplicius, in regard he hath addreſſed himſelf to me;
and I ſay, that in his diſcourſe there is ſomewhat good
and ſomewhat bad: good, becauſe it is almoſt all true;
bad, becauſe it doth not agree with our caſe: Truth is, that when
that which carrieth the ſtones with velocity, ſhall meet with a