1an Horizontal Line, and parallel to C D. And if the Amplitude C D
be equal to the whole Altitude D A, B I ſhall be equal to B A and B D.
And if the Time of the Fall along A B, and the Moment of Velocity
acquired in B along the Deſcent A B ex quiete in A be ſuppoſed to be
meaſured by the ſaid A B, then D C (that is twice B I) ſhall be the
Space which ſhall be paſſed by the Impetus A B turned along the Hori
zontal Line in the ſame Time: But in the ſame Time falling along B D
out of Reſt in B, it ſhall paſs the Altitude B D: Therefore the Movea
ble falling out of Reſt in A along A B,
being converted with the Impetus A B
150[Figure 150]
along the Horizontal Parallel ſhall
paſs a Space equal to D C. And the
Fall along B D ſupervening, it paſſeth
the Altitude B D, and deſcribes the
Parabola B C; whoſe Impetus in the
Term C is compounded of the Equable
Tranſverſal whoſe Moment is as A B,
and of another Moment acquired in the
Fall B D in the Term D or C; which
Moments are Equal. If therefore we
ſuppoſe A B to be the Meaſure of one of them, as ſuppoſe of the Equa
ble Tranſverſal; and B I, which is equal to B D, to be the Meaſure of
the Impetus acquired in D or C; then the Subtenſe I A ſhall be the
quantity of the Moment compound of them both: Therefore it ſhall be
the quantity or Meaſure of the whole Moment which the Project deſcend
ing along the Parabola B C ſhall acquire of Impetus in C. This pre
miſed, take in the Parabola any point E, in which we are to determine
of the Impetus of the Project. Draw the Horizontal Parallel E F,
and let B G be a Mean-proportional between B D and B F. And foraſ
much as A B or B D is ſuppoſed to be the Meaſure of the Time, and of
the Moment of the Velocity in the Fall B D ex quiete in B: B G ſhall
be the Time, or the Meaſure of the Time, and of the Impetus in F, coming
out of B. If therefore B O be ſuppoſed equal to B G, the Diagonal
drawn from A to O ſhall be the quantity of the Impetus in E; for
A B hath been ſuppoſed the determinator of the Time, and of the Impe
tus in B, which turned along the Horizontal Parallel doth alwaies
continue the ſame: And B O determineth the Impetus in F or in E
along the Deſcent ex quiete in B in the Altitude B F: But theſe two
A B and B O are potentia equal to the Power A O. Therefore that is
manifeſt which was ſought.
be equal to the whole Altitude D A, B I ſhall be equal to B A and B D.
And if the Time of the Fall along A B, and the Moment of Velocity
acquired in B along the Deſcent A B ex quiete in A be ſuppoſed to be
meaſured by the ſaid A B, then D C (that is twice B I) ſhall be the
Space which ſhall be paſſed by the Impetus A B turned along the Hori
zontal Line in the ſame Time: But in the ſame Time falling along B D
out of Reſt in B, it ſhall paſs the Altitude B D: Therefore the Movea
ble falling out of Reſt in A along A B,
being converted with the Impetus A B
150[Figure 150]along the Horizontal Parallel ſhall
paſs a Space equal to D C. And the
Fall along B D ſupervening, it paſſeth
the Altitude B D, and deſcribes the
Parabola B C; whoſe Impetus in the
Term C is compounded of the Equable
Tranſverſal whoſe Moment is as A B,
and of another Moment acquired in the
Fall B D in the Term D or C; which
Moments are Equal. If therefore we
ſuppoſe A B to be the Meaſure of one of them, as ſuppoſe of the Equa
ble Tranſverſal; and B I, which is equal to B D, to be the Meaſure of
the Impetus acquired in D or C; then the Subtenſe I A ſhall be the
quantity of the Moment compound of them both: Therefore it ſhall be
the quantity or Meaſure of the whole Moment which the Project deſcend
ing along the Parabola B C ſhall acquire of Impetus in C. This pre
miſed, take in the Parabola any point E, in which we are to determine
of the Impetus of the Project. Draw the Horizontal Parallel E F,
and let B G be a Mean-proportional between B D and B F. And foraſ
much as A B or B D is ſuppoſed to be the Meaſure of the Time, and of
the Moment of the Velocity in the Fall B D ex quiete in B: B G ſhall
be the Time, or the Meaſure of the Time, and of the Impetus in F, coming
out of B. If therefore B O be ſuppoſed equal to B G, the Diagonal
drawn from A to O ſhall be the quantity of the Impetus in E; for
A B hath been ſuppoſed the determinator of the Time, and of the Impe
tus in B, which turned along the Horizontal Parallel doth alwaies
continue the ſame: And B O determineth the Impetus in F or in E
along the Deſcent ex quiete in B in the Altitude B F: But theſe two
A B and B O are potentia equal to the Power A O. Therefore that is
manifeſt which was ſought.