1Quantities, that is to ſay, of Spaces, of Times, and of Impetus's, let
it be required to determine in the aſſigned Space, and at the height
A C, how much the Time of the Fall of the Moveable from A to
C is to be, and what the Impetus is that ſhall be found to have been
acquired in the ſaid Term C, in relation to the Time and to the
Impetus meaſured by A B. Both theſe queſtions ſhall be reſolved
taking A D the Mean-proportional betwixt the two Lines A C
and A B; affirming the Time of the Fall along the whole Space
A C to be as the Time A D is in relation to A B, aſſigned in the
beginning for the Quantity of the Time in the Fall A B. And like
wiſe we will ſay that the Impetus, or degree of Velocity that the
Cadent Moveable ſhall obtain in the Term C, in relation to the
Impetus that it had in B, is as the ſame Line A D is in relation to
A B, being that the Velocity encreaſeth with the ſame proportion
as the Time doth: Which Concluſion although it was aſſumed as
a Poſtulatum, yet the Author was pleaſed to explain the Applicati
on thereof above in the third Propoſition.
it be required to determine in the aſſigned Space, and at the height
A C, how much the Time of the Fall of the Moveable from A to
C is to be, and what the Impetus is that ſhall be found to have been
acquired in the ſaid Term C, in relation to the Time and to the
Impetus meaſured by A B. Both theſe queſtions ſhall be reſolved
taking A D the Mean-proportional betwixt the two Lines A C
and A B; affirming the Time of the Fall along the whole Space
A C to be as the Time A D is in relation to A B, aſſigned in the
beginning for the Quantity of the Time in the Fall A B. And like
wiſe we will ſay that the Impetus, or degree of Velocity that the
Cadent Moveable ſhall obtain in the Term C, in relation to the
Impetus that it had in B, is as the ſame Line A D is in relation to
A B, being that the Velocity encreaſeth with the ſame proportion
as the Time doth: Which Concluſion although it was aſſumed as
a Poſtulatum, yet the Author was pleaſed to explain the Applicati
on thereof above in the third Propoſition.
This point being well underſtood and proved, we come to the
Conſideration of the Impetus derived from two compound Moti
ons: whereof let one be compounded of the Horizontal and alwaies
Equable, and of the Perpendicular unto the Horizon, and it alſo
Equable: but let the other be compounded of the Horizontal like
wiſe alwaies Equable, and of the Perpendicular Naturally-Accele
rate. If both ſhall be Equable, it hath been ſeen already that the
Impetus emerging from the compoſition of both is potentia equal to
both, as for more plainneſs we will thus Exemplifie. Let the Move
able deſcending along the Perpendicular A B be ſuppoſed to have,
for example, three degrees of Equable Impetus, but being tranſ
ported along A B towards C, let the ſaid Velocity and Impetus be
ſuppoſed four degrees, ſo that in the ſame Time that falling it would
paſs along the Perpendicular, v. gr. three yards,
152[Figure 152]
it would in the Horizontal paſs four, but in
that compounded of both the Velocities it
cometh in the ſame Timefrom the point A un
to the Term C, deſcending all the way along the Diagonal Line
A C, which is not ſeven yards long, as that ſhould be which is com
pounded of the two Lines A B, 3, and B C, 4, but is 5; which 5 is
potentia equal to the two others, 3 and 4: For having found the
Squares of 3 and 4, which are 9 and 16, and joyning theſe together,
they make 25 for the Square of A C, which is equal to the two
Squares of A B and B C: whereupon A C ſhall be as much as is the
Side, or, if you will, Root of the Square 25, which is 5. For a conſtant
and certain Rule therefore, when it is required to aſſign the
Quantity of the Impetus reſulting from two Impetus's given, the
one Horizontal, and the other Perpendicular, and both Equable,
Conſideration of the Impetus derived from two compound Moti
ons: whereof let one be compounded of the Horizontal and alwaies
Equable, and of the Perpendicular unto the Horizon, and it alſo
Equable: but let the other be compounded of the Horizontal like
wiſe alwaies Equable, and of the Perpendicular Naturally-Accele
rate. If both ſhall be Equable, it hath been ſeen already that the
Impetus emerging from the compoſition of both is potentia equal to
both, as for more plainneſs we will thus Exemplifie. Let the Move
able deſcending along the Perpendicular A B be ſuppoſed to have,
for example, three degrees of Equable Impetus, but being tranſ
ported along A B towards C, let the ſaid Velocity and Impetus be
ſuppoſed four degrees, ſo that in the ſame Time that falling it would
paſs along the Perpendicular, v. gr. three yards,
152[Figure 152]it would in the Horizontal paſs four, but in
that compounded of both the Velocities it
cometh in the ſame Timefrom the point A un
to the Term C, deſcending all the way along the Diagonal Line
A C, which is not ſeven yards long, as that ſhould be which is com
pounded of the two Lines A B, 3, and B C, 4, but is 5; which 5 is
potentia equal to the two others, 3 and 4: For having found the
Squares of 3 and 4, which are 9 and 16, and joyning theſe together,
they make 25 for the Square of A C, which is equal to the two
Squares of A B and B C: whereupon A C ſhall be as much as is the
Side, or, if you will, Root of the Square 25, which is 5. For a conſtant
and certain Rule therefore, when it is required to aſſign the
Quantity of the Impetus reſulting from two Impetus's given, the
one Horizontal, and the other Perpendicular, and both Equable,