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

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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.
The acceleration
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