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.

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.

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. You had

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.

can in a few words ſhew, that I do underſtand you. You had

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

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