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