1ſide A C, as many equal parts as we pleaſe, A D, D E, E F, F G,

and drawing by the points D, E, F, G, right lines parallel to the baſe

B C. Now let us imagine the parts marked in the line A C, to be

equal times, and let the parallels drawn by the points D, E, F, G,

repreſent unto us the degrees of velocity accelerated, and

ing equally in equal times; and let the point A be the ſtate of reſt,

from which the moveable departing, hath v. g. in the time A D,

acquired the degree of velocity D H, in the ſecond time we will

ſuppoſe, that it hath increaſed the velocity from D H, as far as to

E I, and ſo ſuppoſing it to have grown greater in the ſucceeding

times, according to the increaſe of the lines F K, G L, &c. but

becauſe the acceleration is made continually from moment to

ment, and not disjunctly from one certain part of time to another;

the point A being put for the loweſt moment of velocity, that is,

for the ſtate of reſt, and A D for the firſt inſtant of time

ing; it is manifeſt, that before the acquiſt of the degree of velocity

D H, made in the time A D, the moveable muſt have paſt by

infinite other leſſer and leſſer degrees gained in the infinite inſtants

that are in the time D A, anſwering the infinite points that are in

the line D A; therefore to repreſent unto us the infinite degrees

of velocity that precede the degree D H, it is neceſſary to imagine

infinite lines ſucceſſively leſſer and leſſer, which are ſuppoſed to

be drawn by the infinite points of the line D A, and parallels to

D H, the which infinite lines repreſent unto us the ſuperficies of

the Triangle A H D, and thus we may imagine any ſpace paſſed

by the moveable, with a motion which begining at reſt, goeth

formly accelerating, to have ſpent and made uſe of infinite degrees

of velocity, increaſing according to the infinite lines that

ing from the point A, are ſuppoſed to be drawn parallel to the

line H D, and to the reſt I E, K F, L G, the motion continuing as

far as one will.

and drawing by the points D, E, F, G, right lines parallel to the baſe

B C. Now let us imagine the parts marked in the line A C, to be

equal times, and let the parallels drawn by the points D, E, F, G,

repreſent unto us the degrees of velocity accelerated, and

ing equally in equal times; and let the point A be the ſtate of reſt,

from which the moveable departing, hath v. g. in the time A D,

acquired the degree of velocity D H, in the ſecond time we will

ſuppoſe, that it hath increaſed the velocity from D H, as far as to

E I, and ſo ſuppoſing it to have grown greater in the ſucceeding

times, according to the increaſe of the lines F K, G L, &c. but

becauſe the acceleration is made continually from moment to

ment, and not disjunctly from one certain part of time to another;

the point A being put for the loweſt moment of velocity, that is,

for the ſtate of reſt, and A D for the firſt inſtant of time

ing; it is manifeſt, that before the acquiſt of the degree of velocity

D H, made in the time A D, the moveable muſt have paſt by

infinite other leſſer and leſſer degrees gained in the infinite inſtants

that are in the time D A, anſwering the infinite points that are in

the line D A; therefore to repreſent unto us the infinite degrees

of velocity that precede the degree D H, it is neceſſary to imagine

infinite lines ſucceſſively leſſer and leſſer, which are ſuppoſed to

be drawn by the infinite points of the line D A, and parallels to

D H, the which infinite lines repreſent unto us the ſuperficies of

the Triangle A H D, and thus we may imagine any ſpace paſſed

by the moveable, with a motion which begining at reſt, goeth

formly accelerating, to have ſpent and made uſe of infinite degrees

of velocity, increaſing according to the infinite lines that

ing from the point A, are ſuppoſed to be drawn parallel to the

line H D, and to the reſt I E, K F, L G, the motion continuing as

far as one will.

The acceleration

of grave bodies

turally deſcendent,

increaſeth from

moment to moment.

of grave bodies

turally deſcendent,

increaſeth from

moment to moment.

Now let us compleat the whole Parallelogram A M B C, and let

us prolong as far as to the ſide thereof B M, not onely the Parallels

marked in the Triangle, but thoſe infinite others imagined to be

drawn from all the points of the ſide A C; and like as B C, was

the greateſt of thoſe infinite parallels of the Triangle,

ing unto us the greateſt degree of velocity acquired by the

able in the accelerate motion, and the whole ſuperficies of the ſaid

Triangle, was the maſs and ſum of the whole velocity, wherewith

in the time A C it paſſed ſuch a certain ſpace, ſo the parallelogram

is now a maſs and aggregate of a like number of degrees of

locity, but each equal to the greateſt B C, the which maſs of

locities will be double to the maſs of the increaſing velocities in

the Triangle, like as the ſaid Parallelogram is double to the

angle: and therefore if the moveable, that falling did make uſe

us prolong as far as to the ſide thereof B M, not onely the Parallels

marked in the Triangle, but thoſe infinite others imagined to be

drawn from all the points of the ſide A C; and like as B C, was

the greateſt of thoſe infinite parallels of the Triangle,

ing unto us the greateſt degree of velocity acquired by the

able in the accelerate motion, and the whole ſuperficies of the ſaid

Triangle, was the maſs and ſum of the whole velocity, wherewith

in the time A C it paſſed ſuch a certain ſpace, ſo the parallelogram

is now a maſs and aggregate of a like number of degrees of

locity, but each equal to the greateſt B C, the which maſs of

locities will be double to the maſs of the increaſing velocities in

the Triangle, like as the ſaid Parallelogram is double to the

angle: and therefore if the moveable, that falling did make uſe