The preſent Speculation hath been attempted by Pappus Alex
andrinus in Lib. 8. de Collection. Mathemat. but, if I be in the
right, he hath not hit the mark, and was overſeen in the Aſſumpti
on that he maketh, where he ſuppoſeth that the Weight ought to
be moved along the Horizontal Line by a Force given; which is
falſe: there needing no ſenſible Force (removing the Accidental
Impediments, which in the Theory are not regarded) to move the
given Weight along the Horizon, ſo that he goeth about in vain
afterwards to ſeek with what Force it is to be moved along the
elevated Plane. It will be therefore better, the Force that moveth
the Weight upwards perpendicularly, (which equalizeth the Gra
vity of that Weight which is to be moved) being given, to
ſeek the Force that moveth it along the Elevated Plane: Which
we will endeavour to do in a Method different from that of
Pappus.
andrinus in Lib. 8. de Collection. Mathemat. but, if I be in the
right, he hath not hit the mark, and was overſeen in the Aſſumpti
on that he maketh, where he ſuppoſeth that the Weight ought to
be moved along the Horizontal Line by a Force given; which is
falſe: there needing no ſenſible Force (removing the Accidental
Impediments, which in the Theory are not regarded) to move the
given Weight along the Horizon, ſo that he goeth about in vain
afterwards to ſeek with what Force it is to be moved along the
elevated Plane. It will be therefore better, the Force that moveth
the Weight upwards perpendicularly, (which equalizeth the Gra
vity of that Weight which is to be moved) being given, to
ſeek the Force that moveth it along the Elevated Plane: Which
we will endeavour to do in a Method different from that of
Pappus.
Let us therefore ſuppoſe the Circle A I C, and in it the Diame
ter A B C, and the Center B, and two Weights of equal Moment
in the extreams B and C; ſo that the Line A C being a Leaver,
or Ballance moveable about the Center B, the Weight C ſhall
come to be ſuſtained by the Weight A. But if we ſhall imagine
the Arm of the Ballance B C to be inclined downwards according
to the Line B F, but yet in ſuch a manner that the two Lines A B
and B F do continue ſolidly conjoyned in the point B, in this caſe
the Moment of the Weight C ſhall not be equal to the Moment
200[Figure 200]
of the Weight A, for that the Di
ſtance of the point F from the Line
of Direction, which goeth accord
ing to B I, from the Fulciment B un
to the Center of the Earth, is dimi
niſhed: But if from the point F we
erect a Perpendicular unto B C, as is
F K, the Moment of the Weight in
F ſhall be as if it did hang by the
Line K F, and look how much the
Diſtance K B is diminiſhed by the
Diſtance B A, ſo much is the Moment of the Weight F diminiſhed
by the Moment of the Weight A. And in this faſhion inclining
the Weight more, as for inſtance, according to B L, its Moment ſhall
ſtill diminiſh and ſhall be as if it did hang at the Diſtance B M, ac
cording to the Line M L, in which point L it ſhall be ſuſtained by
a Weight placed in A, ſo much leſs than it ſelf, by how much the
Diſtance B A is greater than the Diſtance B M. See therefore that
the Weight placed in the extream of the Leaver B C, in inclining
downwards along the Circumference C F L I, cometh to diminiſh
its Moment and Impetus of going downwards from time to time,
ter A B C, and the Center B, and two Weights of equal Moment
in the extreams B and C; ſo that the Line A C being a Leaver,
or Ballance moveable about the Center B, the Weight C ſhall
come to be ſuſtained by the Weight A. But if we ſhall imagine
the Arm of the Ballance B C to be inclined downwards according
to the Line B F, but yet in ſuch a manner that the two Lines A B
and B F do continue ſolidly conjoyned in the point B, in this caſe
the Moment of the Weight C ſhall not be equal to the Moment
200[Figure 200]of the Weight A, for that the Di
ſtance of the point F from the Line
of Direction, which goeth accord
ing to B I, from the Fulciment B un
to the Center of the Earth, is dimi
niſhed: But if from the point F we
erect a Perpendicular unto B C, as is
F K, the Moment of the Weight in
F ſhall be as if it did hang by the
Line K F, and look how much the
Diſtance K B is diminiſhed by the
Diſtance B A, ſo much is the Moment of the Weight F diminiſhed
by the Moment of the Weight A. And in this faſhion inclining
the Weight more, as for inſtance, according to B L, its Moment ſhall
ſtill diminiſh and ſhall be as if it did hang at the Diſtance B M, ac
cording to the Line M L, in which point L it ſhall be ſuſtained by
a Weight placed in A, ſo much leſs than it ſelf, by how much the
Diſtance B A is greater than the Diſtance B M. See therefore that
the Weight placed in the extream of the Leaver B C, in inclining
downwards along the Circumference C F L I, cometh to diminiſh
its Moment and Impetus of going downwards from time to time,