SAGR. You argue very well, and make no ſeruple at all of
granting, that be the Force of the Mover never ſo ſmall it ſhall ſu
perate any what ever great Reſiſtance at all times when that ſhall
more exceed in Velocity than this doth in Force and Gravity.
Now come we to the caſe of the Rope. And drawing a ſmall
Scheme be pleaſed to underſtand for once that this Line A B, reſt
ing upon the two fixed and ſtanding points A and B, to have hang
ing at its ends, as you ſee, two immenſe Weights C and D, which
drawing it with great Force make it to ſtand directly diſtended, it
being a ſimple Line without any gravity. And here I proceed, and
tell you, that if at the midſt of that which is the point E, you ſhould
hang any never ſo little a Weight, as is this H, the Line A B would
yield, and inclining towards the point F, and by conſequence
lengthening, will conſtrain the two great Weights C and D to
aſcend upwards: which I demonſtrate to you in this manner:
About the two points A and B as Centers I deſcribe two Quadrants
E F G, and E L M, and in regard that the two Semidiameters AI
and B L are equal to the two Semidiameters A E and E B, the exceſ
ſes F I and F L ſhall be the quantity of the prolongations of the
parts A F and F B, above A E and E B; and of conſequence ſhall
164[Figure 164]
determine the Aſcents
of the Weights C and
D, in caſe that the
Weight H had had a
power to deſcend to F:
which might then be
in caſe the Line E F,
which is the quantity
of the Deſcent of the
ſaid Weight H, had
greater proportion to
the Line F I which de
termineth the Aſcent of
the two Weights C &
D, than the pondero
ſity of both thoſe Weights hath to the ponderoſity of the Weight
H. But this will neceſſarily happen, be the ponderoſity of the
Weights C and D never ſo great, and that of H never ſo ſmall; for
the exceſs of the Weights C and D above the Weight His not ſo
great, but that the exceſs of the Tangent E F above the part of the
Secant F I may bear a greater proportion. Which we will prove
thus: Let there be a Circle whoſe Diameter is G A I; and look
what proportion the ponderoſity of the Weights C and D have to
the ponderoſity of H, let the Line B O have the ſame proportion to
another, which let be C, than which let D be leſſer: So that B O
granting, that be the Force of the Mover never ſo ſmall it ſhall ſu
perate any what ever great Reſiſtance at all times when that ſhall
more exceed in Velocity than this doth in Force and Gravity.
Now come we to the caſe of the Rope. And drawing a ſmall
Scheme be pleaſed to underſtand for once that this Line A B, reſt
ing upon the two fixed and ſtanding points A and B, to have hang
ing at its ends, as you ſee, two immenſe Weights C and D, which
drawing it with great Force make it to ſtand directly diſtended, it
being a ſimple Line without any gravity. And here I proceed, and
tell you, that if at the midſt of that which is the point E, you ſhould
hang any never ſo little a Weight, as is this H, the Line A B would
yield, and inclining towards the point F, and by conſequence
lengthening, will conſtrain the two great Weights C and D to
aſcend upwards: which I demonſtrate to you in this manner:
About the two points A and B as Centers I deſcribe two Quadrants
E F G, and E L M, and in regard that the two Semidiameters AI
and B L are equal to the two Semidiameters A E and E B, the exceſ
ſes F I and F L ſhall be the quantity of the prolongations of the
parts A F and F B, above A E and E B; and of conſequence ſhall
164[Figure 164]determine the Aſcents
of the Weights C and
D, in caſe that the
Weight H had had a
power to deſcend to F:
which might then be
in caſe the Line E F,
which is the quantity
of the Deſcent of the
ſaid Weight H, had
greater proportion to
the Line F I which de
termineth the Aſcent of
the two Weights C &
D, than the pondero
ſity of both thoſe Weights hath to the ponderoſity of the Weight
H. But this will neceſſarily happen, be the ponderoſity of the
Weights C and D never ſo great, and that of H never ſo ſmall; for
the exceſs of the Weights C and D above the Weight His not ſo
great, but that the exceſs of the Tangent E F above the part of the
Secant F I may bear a greater proportion. Which we will prove
thus: Let there be a Circle whoſe Diameter is G A I; and look
what proportion the ponderoſity of the Weights C and D have to
the ponderoſity of H, let the Line B O have the ſame proportion to
another, which let be C, than which let D be leſſer: So that B O