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

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1round upon their centres with equal velocities, ſo as that two
veables, which ſuppoſe for example to be two ſtones placed in the
points B and C, come to be carried along the circumferences B G
and C E, with equal velocities; ſo that in the ſame time that the
ſtone B ſhall have run the arch B G, the ſtone C will have paſt the
arch C E.
I ſay now, that the whirl or vertigo of the leſſer wheel
is much more potent to make the projection of the ſtone B, than
the vertigo of the bigger wheel to make that of the ſtone C.
Therefore the projection, as we have already declared, being to be
made along the tangent, when the ſtones B and C are to ſeparate
from their wheels, and to begin the motion of projection from the
points B and C, then ſhall they be extruded by the impetus
ceived from the vertigo by (or along) the tangents B F and C D.
The two ſtones therefore have equal impetuoſities of running
long the tangents B F and C D, and would run along the ſame, if
they were not turn'd aſide by ſome other force: is it not ſo
gredus?
SAGR. In my opinion the buſineſſe is as you ſay.
SALV. But what force, think you, ſhould that be which averts
the ſtones from moving by the tangents, along which they are
tainly driven by the impetus of the vertigo.
SAGR. It is either their own gravity, or elſe ſome glutinous
matter that holdeth them faſt and cloſe to the wheels.
SALV. But for the diverting of a moveable from the motion
to which nature inciteth it, is there not required greater or leſſer
force, according as the deviation is intended to be greater or
ſer?
that is, according as the ſaid moveable in its deviation hath a
greater or leſſer ſpace to move in the ſame time?
SAGR. Yes certainly: for it was concluded even now, that to
make a moveable to move; the movent vertue muſt be increaſed
in proportion to the velocity wherewith it is to move.
SALV. Now conſider, that for the deviating the ſtone upon
the leſſe wheel from the motion of projection, which it would
make by the tangent B F, and for the holding of it faſt to the
wheel, it is required, that its own gravity draw it back the whole
length of the ſecant F G, or of the perpendicular raiſed from the
point G, to the line B F, whereas in the greater wheel the
on needs to be no more than the ſecant D E, or the
lar let fall from the tangent D G to the point E, leſſe by much
than F G, and alwayes leſſer and leſſer according as the wheel is
made bigger.
And foraſmuch as theſe retractions (as I may call
them) are required to be made in equal times, that is, whil'ſt the
wheels paſſe the two equal arches B G and C E, that of the ſtone
B, that is, the retraction F G ought to be more ſwift than the
ther D E; and therefore much greater force will be required for