1able hath upon the inclined Plane C A hath to its total Moment
wherewith it gravitates in the Perpendicular to the Horizon C P the
ſame proportion that the ſaid Line P C hath to C A. And if thus it
be, it is manifeſt, that like as the Force that ſuſtai
neth the Weight in the Perpendiculation P C ought
201[Figure 201]
to be equal to the ſame, ſo for ſuſtaining it in the
inclined Plane C A, it will ſuffice that it be ſo much
leſſer, by how much the ſaid Perpendicular C P wan
teth of the Line C A: and becauſe, as ſometimes we
ſce, it ſufficeth, that the Force for moving of the
Weight do inſenſibly ſuperate that which ſuſtaineth it, therefore
we will infer this univerſal Propoſition, [That upon an Elevated
Plane the Force hath to the Weight the ſame proportion, as the
Perpendicular let fall from the Plane unto the Horizon hath to the
Length of the ſaid Plane.]
wherewith it gravitates in the Perpendicular to the Horizon C P the
ſame proportion that the ſaid Line P C hath to C A. And if thus it
be, it is manifeſt, that like as the Force that ſuſtai
neth the Weight in the Perpendiculation P C ought
201[Figure 201]to be equal to the ſame, ſo for ſuſtaining it in the
inclined Plane C A, it will ſuffice that it be ſo much
leſſer, by how much the ſaid Perpendicular C P wan
teth of the Line C A: and becauſe, as ſometimes we
ſce, it ſufficeth, that the Force for moving of the
Weight do inſenſibly ſuperate that which ſuſtaineth it, therefore
we will infer this univerſal Propoſition, [That upon an Elevated
Plane the Force hath to the Weight the ſame proportion, as the
Perpendicular let fall from the Plane unto the Horizon hath to the
Length of the ſaid Plane.]
* Or along
Returning now to our firſt Intention, which was to inveſtigate
the Nature of the Screw, we will conſider the Triangle A B C, of
which the Line A B is Horizontal, B C perpendicular to the ſaid
Horizon, and A C a Plane elevated; upon which the Moveable D
ſhall be drawn by a Force ſo much leſs than it, by how much the
Line B C is ſhorter than C A: But to elevate or raiſe the ſaid
Weight along the ſaid Plane A C, is as much as if the Triangle
C A B ſtanding ſtill, the Weight
202[Figure 202]
D be moved towards C, which is
the ſame, as if the ſame Weight
never removing from the Perpen
dicular A E, the Triangle did
preſs forwards towards H. For if
it were in the Site F H G, the
Moveable would be found to
have mounted the height A I.
Now, in fine, the primary Form and Eſſence of the Screw is no
thing elſe but ſuch a Triangle A C B, which being forced for
wards, ſhall work it ſelf under the Grave Body to be raiſed, and
lifteth it up, as we ſay, by the ^{*} head and ſhoulders. And this was
its firſt Original: For its firſt Inventor (whoever he was) conſi
dering how that the Triangle A B C going forwards raiſeth the
Weight D, he might have framed an Inſtrument like to the ſaid
Triangle, of a very ſolid Matter, which being thruſt forwards did
raiſe up the propoſed Weight: But afterwards conſidering better,
how that that ſame Machine might be reduced into a much leſſer
and more commodious Form, taking the ſame Triangle he twined
and wound it about the Cylinder A B C D in ſuch a faſhion, that
the height of the ſaid Triangle, that is the Line C B, did make the
Height of the Cylinder, and the Aſcending Plane did beget upon
the Nature of the Screw, we will conſider the Triangle A B C, of
which the Line A B is Horizontal, B C perpendicular to the ſaid
Horizon, and A C a Plane elevated; upon which the Moveable D
ſhall be drawn by a Force ſo much leſs than it, by how much the
Line B C is ſhorter than C A: But to elevate or raiſe the ſaid
Weight along the ſaid Plane A C, is as much as if the Triangle
C A B ſtanding ſtill, the Weight
202[Figure 202]D be moved towards C, which is
the ſame, as if the ſame Weight
never removing from the Perpen
dicular A E, the Triangle did
preſs forwards towards H. For if
it were in the Site F H G, the
Moveable would be found to
have mounted the height A I.
Now, in fine, the primary Form and Eſſence of the Screw is no
thing elſe but ſuch a Triangle A C B, which being forced for
wards, ſhall work it ſelf under the Grave Body to be raiſed, and
lifteth it up, as we ſay, by the ^{*} head and ſhoulders. And this was
its firſt Original: For its firſt Inventor (whoever he was) conſi
dering how that the Triangle A B C going forwards raiſeth the
Weight D, he might have framed an Inſtrument like to the ſaid
Triangle, of a very ſolid Matter, which being thruſt forwards did
raiſe up the propoſed Weight: But afterwards conſidering better,
how that that ſame Machine might be reduced into a much leſſer
and more commodious Form, taking the ſame Triangle he twined
and wound it about the Cylinder A B C D in ſuch a faſhion, that
the height of the ſaid Triangle, that is the Line C B, did make the
Height of the Cylinder, and the Aſcending Plane did beget upon