1let C E be drawn parallel and equal to B D, and thus by the Points
B and E we ſhall deſcribe the Parabolick Line B E I. And becauſe
that in the Time A B with the Impetus A B the Horizontal Line B D
or C E is paſſed, double to A B, and in ſuch another Time the Per
pendicular B C is paſſed with an acquiſt of Impetus in C equal to
the ſaid Horizontal Line; therefore the Moveable in ſuch another
Time as A B ſhall be found to have paſſed from B to E along the
Parabola B E with an Impetus compounded of two, each equal to
the Impetus A B. And becauſe one of them is Horizontal, and the
other Perpendicular, the Impetus compound of them ſhall be equal
in Power to them both, that is
153[Figure 153]
double to one of them. So that
ſuppoſing B F equal to B A, and
drawing the Diagonal A F, the
Impetus or the Percuſſion in E
ſhall be greater than the Percuſ
ſion in B of the Moveable fal
ling from the Height A, or than
the Percuſſion of the Horizon
tal Impetus along B D, according
to the proportion of A F to
A B. But in caſe, ſtill retaining
B A for the Meaſure of the
Space of the Fall from Reſt in
A unto B, and for the Meaſure of the Time and of the Impetus of
the falling Moveable acquired in B, the Altitude B O ſhould not be
equal to, but greater than A B, taking B G to be a Mean-propor
tional betwixt the ſaid A B and B O, the ſaid B G would be the
Meaſure of the Time and of the Impetus in O, acquired in O by the
Fall from the height B O; and the Space along the Horizontal
Line, which being paſſed with the Impetus A B in the Time A B
would be double to A B, ſhall, in the whole duration of the Time
B G, be ſo much the greater, by how much in proportion B G is
greater than B A. Suppoſing therefore L B equal to B G, and draw
ing the Diagonal A L, it ſhall give us the quantity compounded of
the two Impetus's Horizontal and Perpendicular, by which the
Parabola is deſcribed; and of which the Horizontal and Equable is
that acquired in B by the fall of A B, and the other is that acquired
in O, or, if you will, in I by the Deſcent B O, whoſe Time, as alſo
the quantity of its Moment was B G. And in this Method we ſhall
inveſtigate the Impetus in the extream term of the Parabola, in caſe
its Altitude were leſſer than the Sublimity A B, taking the Mean
proportional betwixt them both: which being ſet off upon the Ho
rizontal Line in the place of B F, and the Diagonal drawn, as A F,
we ſhall hereby have the quantity of the Impetus in the extream
term of the Parabola.
B and E we ſhall deſcribe the Parabolick Line B E I. And becauſe
that in the Time A B with the Impetus A B the Horizontal Line B D
or C E is paſſed, double to A B, and in ſuch another Time the Per
pendicular B C is paſſed with an acquiſt of Impetus in C equal to
the ſaid Horizontal Line; therefore the Moveable in ſuch another
Time as A B ſhall be found to have paſſed from B to E along the
Parabola B E with an Impetus compounded of two, each equal to
the Impetus A B. And becauſe one of them is Horizontal, and the
other Perpendicular, the Impetus compound of them ſhall be equal
in Power to them both, that is
153[Figure 153]double to one of them. So that
ſuppoſing B F equal to B A, and
drawing the Diagonal A F, the
Impetus or the Percuſſion in E
ſhall be greater than the Percuſ
ſion in B of the Moveable fal
ling from the Height A, or than
the Percuſſion of the Horizon
tal Impetus along B D, according
to the proportion of A F to
A B. But in caſe, ſtill retaining
B A for the Meaſure of the
Space of the Fall from Reſt in
A unto B, and for the Meaſure of the Time and of the Impetus of
the falling Moveable acquired in B, the Altitude B O ſhould not be
equal to, but greater than A B, taking B G to be a Mean-propor
tional betwixt the ſaid A B and B O, the ſaid B G would be the
Meaſure of the Time and of the Impetus in O, acquired in O by the
Fall from the height B O; and the Space along the Horizontal
Line, which being paſſed with the Impetus A B in the Time A B
would be double to A B, ſhall, in the whole duration of the Time
B G, be ſo much the greater, by how much in proportion B G is
greater than B A. Suppoſing therefore L B equal to B G, and draw
ing the Diagonal A L, it ſhall give us the quantity compounded of
the two Impetus's Horizontal and Perpendicular, by which the
Parabola is deſcribed; and of which the Horizontal and Equable is
that acquired in B by the fall of A B, and the other is that acquired
in O, or, if you will, in I by the Deſcent B O, whoſe Time, as alſo
the quantity of its Moment was B G. And in this Method we ſhall
inveſtigate the Impetus in the extream term of the Parabola, in caſe
its Altitude were leſſer than the Sublimity A B, taking the Mean
proportional betwixt them both: which being ſet off upon the Ho
rizontal Line in the place of B F, and the Diagonal drawn, as A F,
we ſhall hereby have the quantity of the Impetus in the extream
term of the Parabola.
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