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

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1had in the centre, ſucceſſively until it come to total extinction,
do carry the moveable in ſuch a time ſuch a certain ſpace, as it had
gone in ſuch a like quantity of time, by the acquiſt of velocity
from the total privation of it until it came to that its greateſt degree;
it ſeemeth very reaſonable, that if it ſhould move always with the
ſaid greateſt degree of velocity it would paſs, in ſuch another
quantity of time, both thoſe ſpaces: For if we do but in our
mind ſucceſſively divide thoſe velocities into riſing and falling
degrees, as v. g. theſe numbers in the margine; ſo that the
firſt ſort unto 10 be ſuppoſed the increaſing velocities, and the
others unto 1, be the decreaſing; and let thoſe of the time
of the deſcent, and the others of the time of the aſcent being
added all together, make as many, as if one of the two ſums of
them had been all of the greateſt degrees, and therefore the
whole ſpace paſſed by all the degrees of the increaſing
ties, and decreaſing, (which put together is the whole
ter) ought to be equal to the ſpace paſſed by the greateſt
cities, that are in number half the aggregate of the increaſing
and decreaſing velocities.
I know that I have but obſcurely
expreſſed my ſelf, and I wiſh I may be underſtood.
If the Terreſtrial
Globe were
rated, a grave
dy deſcending by
that bore, would
paß and aſcend as
far beyond the
tre, as it did
ſcend.
SAGR. I think I underſtand you very well; and alſo that I
can in a few words ſhew, that I do underſtand you.
a mind to ſay, that the motion begining from reſt, and all the
way increaſing the velocity with equal augmentations, ſuch as
are thoſe of continuate numbers begining at 1, rather at 0,
which repreſenteth the ſtate of reſt, diſpoſed as in the margine:
and continued at pleaſure, ſo as that the leaſt degree may be 0,
and the greateſt v. g. 5, all theſe degrees of velocity wherewith
the moveable is moved, make the ſum of 15; but if the
moveable ſhould move with as many degrees in number as
theſe are, and each of them equal to the biggeſt, which is 5, the
aggregate of all theſe laſt velocities would be double to the
others, namely 30. And therefore the moveable moving with
a like time, but with uniform velocity, which is that of the
higheſt degree 5, ought to paſs a ſpace double to that which it
paſſeth in the accelerate time, which beginneth at the ſtate of reſt.
SALV. According to your quick and piercing way of
hending things, you have explained the whole buſineſs with more
plainneſs than I my ſelf; and put me alſo in mind of adding
thing more: for in the accelerate motion, the augmentation
ing continual, you cannot divide the degrees of velocity, which
continually increaſe, into any determinate number, becauſe
ging every moment, they are evermore infinite.
Therefore we
ſhall be the better able to exemplifie our intentions by deſcribing
a Triangle, which let be this A B C, [in Fig. 8.] taking in the