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,