1Impetus, and particular Velocity our Author hath not found any
way more commodious, than the making uſe of the Impetus which
the Moveable from time to time acquires in the Naturally-Accele
rate Motion, any acquired Moment of which being reduced into
an Equable Motion retaineth its Velocity preciſely limited, and
ſuch, that in ſuch another Time as that wherein it did Deſcend, it
paſſeth double the Space of the Height from whence it fell. But
becauſe this is the principal point in the buſineſs that we are upon,
it is good to make it to be perfectly underſtood by ſome particular
Example. Reaſſuming therefore the Velocity and Impetus acqui
red by the Cadent Moveable, as we ſaid before, from the height
of a Pike, of which Velocity we will make uſe for a Meaſure of
other Velocities and Impetuſſes upon other occaſions, and ſuppo
ſing, for example, that the Time of that Fall be four ſecond Mi
nutes of an hour, to find by this ſame Meaſure how great the Im
petus of the Moveable would be falling from any other height
greater, or leſſer, we ought not from the proportion that this other
height hath to the height of a Pike to argue and conclude the quan
tity of the Impetus acquired in this ſecond height, thinking, for
example, that the Moveable falling from quadruple the height
hath acquired quadruple Velocity, for that it is falſe: for that the
Velocity of the Naturally-Accelerate Motion doth not increaſe or
decreaſe according to the proportion of the Spaces, but according
to that of the Times, than which that of the Spaces is greater in a
duplicate proportion, as was heretofore demonſtrated. Therefore
when in a Right Line we have aſſigned a part for the Meaſure of
the Velocity, and alſo of the Time, and of the Space in that Time
paſſed (for that for brevity ſake all theſe three Magnitudes are
often repreſented by one ſole Line,) to find the quantity of the
Time, and the degree of Velocity that the ſame Moveable would
have acquired in another Diſtance we ſhall obtain the ſame, not
immediataly by this ſecond Diſtance, but by the Line which ſhall
be a Mean-proportional betwixt the two Diſtances. But I will
better declare my ſelf by an Example. In the Line A C Perpendi
cular to the Horizon let the part A B be underſtood to
be a Space paſſed by a Moveable naturally deſcending
151[Figure 151]
with an Accelerate Motion: the Time of which paſ
ſage, in regard I may repreſent it by any Line, I will, for
brevity, imagine it to be as much as the ſame Line A B
and likewiſe for a Meaſure of the Impetus and Velocity
acquired by that Motion, I again take the ſame Line
A B; ſo that of all the Spaces that are in the progreſs of
the Diſcourſe to be conſidered the part A B may be the
Meaſure. Having all our pleaſure eſtabliſhed under one
ſole Magnitude A B theſe three Meaſures of different kinds of
way more commodious, than the making uſe of the Impetus which
the Moveable from time to time acquires in the Naturally-Accele
rate Motion, any acquired Moment of which being reduced into
an Equable Motion retaineth its Velocity preciſely limited, and
ſuch, that in ſuch another Time as that wherein it did Deſcend, it
paſſeth double the Space of the Height from whence it fell. But
becauſe this is the principal point in the buſineſs that we are upon,
it is good to make it to be perfectly underſtood by ſome particular
Example. Reaſſuming therefore the Velocity and Impetus acqui
red by the Cadent Moveable, as we ſaid before, from the height
of a Pike, of which Velocity we will make uſe for a Meaſure of
other Velocities and Impetuſſes upon other occaſions, and ſuppo
ſing, for example, that the Time of that Fall be four ſecond Mi
nutes of an hour, to find by this ſame Meaſure how great the Im
petus of the Moveable would be falling from any other height
greater, or leſſer, we ought not from the proportion that this other
height hath to the height of a Pike to argue and conclude the quan
tity of the Impetus acquired in this ſecond height, thinking, for
example, that the Moveable falling from quadruple the height
hath acquired quadruple Velocity, for that it is falſe: for that the
Velocity of the Naturally-Accelerate Motion doth not increaſe or
decreaſe according to the proportion of the Spaces, but according
to that of the Times, than which that of the Spaces is greater in a
duplicate proportion, as was heretofore demonſtrated. Therefore
when in a Right Line we have aſſigned a part for the Meaſure of
the Velocity, and alſo of the Time, and of the Space in that Time
paſſed (for that for brevity ſake all theſe three Magnitudes are
often repreſented by one ſole Line,) to find the quantity of the
Time, and the degree of Velocity that the ſame Moveable would
have acquired in another Diſtance we ſhall obtain the ſame, not
immediataly by this ſecond Diſtance, but by the Line which ſhall
be a Mean-proportional betwixt the two Diſtances. But I will
better declare my ſelf by an Example. In the Line A C Perpendi
cular to the Horizon let the part A B be underſtood to
be a Space paſſed by a Moveable naturally deſcending
151[Figure 151]with an Accelerate Motion: the Time of which paſ
ſage, in regard I may repreſent it by any Line, I will, for
brevity, imagine it to be as much as the ſame Line A B
and likewiſe for a Meaſure of the Impetus and Velocity
acquired by that Motion, I again take the ſame Line
A B; ſo that of all the Spaces that are in the progreſs of
the Diſcourſe to be conſidered the part A B may be the
Meaſure. Having all our pleaſure eſtabliſhed under one
ſole Magnitude A B theſe three Meaſures of different kinds of