1the Line A B) is much leſſer than the Line S O, which ſheweth
how much it mounteth in the Time that the Force opperates along
the Line B C.
how much it mounteth in the Time that the Force opperates along
the Line B C.
And to meaſure exactly what his Force ought to be in each Point
of the curved Line A B C D E, it is requiſite to know that it ope
rates there juſt in the ſame manner as if it drew the Weight along
a Plane Circularly Inclined, and that the Inclination of each of the
Points of this circular Plane were to be meaſured by that of the
right Line that toucheth the Circle in this Point. As for example,
when the Force is at the Point B, for to find the proportion that it
ought to have with the ponderoſity of the Weight which is at that
time at the Point G, it is neceſſary to draw the Contingent Line
G M, and to account that the ponderoſity of the Weight is to the
Force which is required to draw it along this Plane, and conſe
quently to raiſe it, according to the Circle F G H, as the Line G M
is to SM Again, for as much as B O is triple of O G, the Force
in B needs to be to the Weight in G but as the third part of the
Line SM is unto the whole Line G M. In the ſelf ſame manner,
when the Force is at the Point D, to know how much the Weight
weigheth at I, it is neceſſary to draw the Contingent Line betwixt
I and P, and the right Line I N perpendicular upon the Horizon,
and from the Point P taken at diſcretion in the Line I P, provided
that it be below the Point I, you muſt draw P N parallel to the
ſame Horizon, to the end you may have the proportion that is be
twixt the Line I P and the third part of the Line I N, for that which
betwixt the ponderoſity of the Weight, and the Force that ought to
be at the Point D for the moving of it: and ſo of others. Where,
nevertheleſs, you muſt except the Point H, at which the Contin
gent Line being perpendicular upon the Horizon, the Weight can
be no other than triple the Force which ought to be in C for the
moving of it: in the Points F and K, at which the Contingent
Line being parallel unto the Horizon it ſelf, the leaſt Force that
one can aſſign is ſufficient to move the Weight. Moreover, that you
may be perfectly exact, you muſt obſerve that the Lines S G and
P N ought to be parts of a Circle that have for their Center that
of the Earth; and GM and I P parts of Spirals drawn between two
ſuch Circles; and, laſtly, that the right Lines S M and I N both
tending towards the Center of the Earth are not exactly Paral
lels: and furthermore, that the Point H where I ſuppoſe the
Contingent Line to be perpendicular unto the Horizon ought
to be ſome ſmall matter nearer to the Point F than to K, at the
which F and K the Contingent Lines are Parallels unto the ſaid
Horizon.
of the curved Line A B C D E, it is requiſite to know that it ope
rates there juſt in the ſame manner as if it drew the Weight along
a Plane Circularly Inclined, and that the Inclination of each of the
Points of this circular Plane were to be meaſured by that of the
right Line that toucheth the Circle in this Point. As for example,
when the Force is at the Point B, for to find the proportion that it
ought to have with the ponderoſity of the Weight which is at that
time at the Point G, it is neceſſary to draw the Contingent Line
G M, and to account that the ponderoſity of the Weight is to the
Force which is required to draw it along this Plane, and conſe
quently to raiſe it, according to the Circle F G H, as the Line G M
is to SM Again, for as much as B O is triple of O G, the Force
in B needs to be to the Weight in G but as the third part of the
Line SM is unto the whole Line G M. In the ſelf ſame manner,
when the Force is at the Point D, to know how much the Weight
weigheth at I, it is neceſſary to draw the Contingent Line betwixt
I and P, and the right Line I N perpendicular upon the Horizon,
and from the Point P taken at diſcretion in the Line I P, provided
that it be below the Point I, you muſt draw P N parallel to the
ſame Horizon, to the end you may have the proportion that is be
twixt the Line I P and the third part of the Line I N, for that which
betwixt the ponderoſity of the Weight, and the Force that ought to
be at the Point D for the moving of it: and ſo of others. Where,
nevertheleſs, you muſt except the Point H, at which the Contin
gent Line being perpendicular upon the Horizon, the Weight can
be no other than triple the Force which ought to be in C for the
moving of it: in the Points F and K, at which the Contingent
Line being parallel unto the Horizon it ſelf, the leaſt Force that
one can aſſign is ſufficient to move the Weight. Moreover, that you
may be perfectly exact, you muſt obſerve that the Lines S G and
P N ought to be parts of a Circle that have for their Center that
of the Earth; and GM and I P parts of Spirals drawn between two
ſuch Circles; and, laſtly, that the right Lines S M and I N both
tending towards the Center of the Earth are not exactly Paral
lels: and furthermore, that the Point H where I ſuppoſe the
Contingent Line to be perpendicular unto the Horizon ought
to be ſome ſmall matter nearer to the Point F than to K, at the
which F and K the Contingent Lines are Parallels unto the ſaid
Horizon.
This done, we may eaſily reſolve all the difficulties of the Ba
lance, and ſhew, That then when it is moſt exact, and for inſtance,
lance, and ſhew, That then when it is moſt exact, and for inſtance,