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

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1but that the diminution of the ſame velocity, dependent on the
diminution of the gravity of the moveable (which vvas the ſecond
cauſe) doth alſo obſerve the ſame proportion, doth not ſo plainly
appear, And vvho ſhall aſſure us that it doth not proceed
ding to the proportion of the lines intercepted between the ſecant,
and the circumference; or vvhether vvith a greater proportion?
SALV. I have aſſumed for a truth, that the velocities of
bles deſcending naturally, vvill follovv the proportion of their
vities, with the favour of Simplicius, and of Ariſtotle, who doth
in many places affirm the ſame, as a propoſition manifeſt: You,
in favour of my adverſary, bring the ſame into queſtion, and ſay
that its poſſible that the velocity increaſeth with greater
tion, yea and greater in infinitum than that of the gravity; ſo that
all that hath been ſaid falleth to the ground: For maintaining
whereof, I ſay, that the proportion of the velocities is much leſſe
than that of the gravities; and thereby I do not onely ſupport
but confirme the premiſes.
And for proof of this I appeal unto
experience, which will ſhew us, that a grave body, howbeit thirty
or fourty times bigger then another; as for example, a ball of
lead, and another of ſugar, will not move much more than twice
as faſt.
Now if the projection would not be made, albeit the
locity of the cadent body ſhould diminiſh according to the
portion of the gravity, much leſſe would it be made ſo long as the
velocity is but little diminiſhed, by abating much from the
ty.
But yet ſuppoſing that the velocity diminiſheth with a
tion much greater than that wherewith the gravity decreaſeth, nay
though it were the ſelf-ſame wherewith thoſe parallels conteined
between the tangent and circumference do decreaſe, yet cannot I
ſee any neceſſity why I ſhould grant the projection of matters of
never ſo great levity; yea I farther averre, that there could no ſuch
projection follow, meaning alwayes of matters not properly and
abſolutely light, that is, void of all gravity, and that of their own
natures move upwards, but that deſcend very ſlowly, and
have very ſmall gravity.
And that which moveth me ſo to think
is, that the diminution of gravity, made according to the
tion of the parallels between the tangent and the circumference,
hath for its ultimate and higheſt term the nullity of weight, as thoſe
parallels have for their laſt term of their diminution the contact it
ſelf, which is an indiviſible point: Now gravity never diminiſheth
ſo far as to its laſt term, for then the moveable would ceaſe to be
grave; but yet the ſpace of the reverſion of the project to the
circumference is reduced to the ultimate minuity, which is when
the moveable reſteth upon the circumference in the very point of
contact; ſo as that to return thither it hath no need of ſpace:
and therefore let the propenſion to the motion of deſcent be