1Accelerate Motion of the Velocity of the Equable Motion (which defi
cient Moments are repreſented by the Parallels of the Triangle A G I)
is made up by the moments repreſented by the Parallels of the Triangle
I E F. It is manifeſt, therefore, that thoſe Spaces are equal which are
in the ſame Time by two Moveables, one whereof is moved with a Mo
tion uniformly Accelerated from Reſt, the other with a Motion Equable
according to the Moment ſubduple of that of the greateſt Velocity of the
Accelerated Motion: Which was to be demonſtrated.
cient Moments are repreſented by the Parallels of the Triangle A G I)
is made up by the moments repreſented by the Parallels of the Triangle
I E F. It is manifeſt, therefore, that thoſe Spaces are equal which are
in the ſame Time by two Moveables, one whereof is moved with a Mo
tion uniformly Accelerated from Reſt, the other with a Motion Equable
according to the Moment ſubduple of that of the greateſt Velocity of the
Accelerated Motion: Which was to be demonſtrated.
THEOR. II. PROP. II.
If a Moveable deſcend out of Reſt with a Moti
on uniformly Accelerate, the Spaces which it
paſſeth in any whatſoever Times are to each
other in a proportion Duplicate of the ſame
Times; that is, they are as the Squares of
them.
on uniformly Accelerate, the Spaces which it
paſſeth in any whatſoever Times are to each
other in a proportion Duplicate of the ſame
Times; that is, they are as the Squares of
them.
Let A B repreſent a length of Time beginning at the firſt Inſtant A;
and let A D and A E repreſent any two parts of the ſaid Time;
and let H I be a Line in which the Moveable out of H, (as the firſt
beginning of the Motion) deſcendeth uniformly accelerating; and let the
84[Figure 84]
Space H L be paſſed in the firſt Time A D; and let H M
be the Space that it ſhall deſcend in the Time A E. I ſay,
the Space M H is to the Space H L in duplicate propor
tion of that which the Time E A hath to the Time A D:
Or, if you will, that the Spaces M H and H L are to one
another in the ſame proportion as the Squares E A and
A D. Draw the Line A C at any Angle with A B, and
from the points D and E draw the Parallels D O and
P E: of which D O will repreſent the greateſt degree
of Velocity acquired in the Inſtant D of the Time A D;
and P the greateſt degree of Velocity acquired in the In
ſtant E of the Time A E. And becauſe we have de
monſtrated in the laſt Propoſition concerning Spaces, that
thoſe are equal to one another, of which two Moveables
have paſt in the ſame Time, the one by a Moveable out
of Reſt with a Motion uniformly Accelerate, and the
other by the ſame Moveable with an Equable Motion,
whoſe Velocity is ſubduple to the greateſt acquired by the
Accelerate Motion: Therefore M H and H L are the Spaces that two
Lquable Motions, whoſe Velocities ſhould be as the half of P E, and
and let A D and A E repreſent any two parts of the ſaid Time;
and let H I be a Line in which the Moveable out of H, (as the firſt
beginning of the Motion) deſcendeth uniformly accelerating; and let the
84[Figure 84]Space H L be paſſed in the firſt Time A D; and let H M
be the Space that it ſhall deſcend in the Time A E. I ſay,
the Space M H is to the Space H L in duplicate propor
tion of that which the Time E A hath to the Time A D:
Or, if you will, that the Spaces M H and H L are to one
another in the ſame proportion as the Squares E A and
A D. Draw the Line A C at any Angle with A B, and
from the points D and E draw the Parallels D O and
P E: of which D O will repreſent the greateſt degree
of Velocity acquired in the Inſtant D of the Time A D;
and P the greateſt degree of Velocity acquired in the In
ſtant E of the Time A E. And becauſe we have de
monſtrated in the laſt Propoſition concerning Spaces, that
thoſe are equal to one another, of which two Moveables
have paſt in the ſame Time, the one by a Moveable out
of Reſt with a Motion uniformly Accelerate, and the
other by the ſame Moveable with an Equable Motion,
whoſe Velocity is ſubduple to the greateſt acquired by the
Accelerate Motion: Therefore M H and H L are the Spaces that two
Lquable Motions, whoſe Velocities ſhould be as the half of P E, and