1

The greater

city exactly

penſates thegreater

gravity.

city exactly

penſates thegreater

gravity.

SAGR. But do you think that the velocity doth fully make

good the gravity? that is, that the moment and force of a

able of v. g. four pounds weight, is as great as that of one of an

hundred weight, whenſoever that the firſt hath an hundred degrees

of velocity, and the later but four onely?

good the gravity? that is, that the moment and force of a

able of v. g. four pounds weight, is as great as that of one of an

hundred weight, whenſoever that the firſt hath an hundred degrees

of velocity, and the later but four onely?

SALV. Yes doubtleſs, as I am able by many experiments to

demonſtrate: but for the preſent, let this onely of the ſtiliard

ſuffice: in which you ſee that the light end of the beam is then

able to ſuſtain and equilibrate the great Wool ſack, when its

ſtance from the centre, upon which the ſtiliard reſteth and

eth, ſhall ſo much exceed the leſſer diſtance, by how much the

ſolute gravity of the Wool-ſack exceedeth that of the pendent

weight. And we ſee nothing that can cauſe this inſufficiencie in

the great ſack of Wool, to raiſe with its weight the pendent

weight ſo much leſs grave, ſave the diſparity of the motions which

the one and the other ſhould make, whilſt that the Wool ſack by

deſcending but one inch onely, will raiſe the pendent weight an

hundred inclies: (ſuppoſing that the ſack did weigh an hundred

times as much, and that the diſtance of the ſmall weight from the

centre of the beam were an hundred times greater, than the

ſtance between the ſaid centre and the point of the ſacks

on.) And again, the pendent weight its moving the ſpace of an

hundred inches, in the time that the ſack moveth but one inch

onely, is the ſame as to ſay, that the velocity of the motion of the

little pendent weight, is an hundred times greater than the

city of the motion of the ſack. Now fix it in your belief, as a

true and manifeſt axiom, that the reſiſtance which proceedeth from

the velocity of motion, compenſateth that which dependeth on

the gravity of another moveable: So that conſequently, a

able of one pound, that moveth with an hundred degrees of

locity, doth as much reſiſt all obſtruction, as another moveable

of an hundred weight, whoſe velocity is but one degree onely.

And two equal moveables will equally reſiſt their being moved,

if that they ſhall be moved with equal velocity: but if one be

to be moved more ſwiftly than the other, it ſhall make greater

ſiſtance, according to the greater velocity that ſhall be conferred

on it. Theſe things being premiſed, let us proceed to the

nation of our Problem; and for the better underſtanding of

things, let us make a ſhort Scheme thereof. Let two unequal

wheels be deſcribed about this centre A, [in Fig. 7.] and let the

circumference of the leſſer be B G, and of the greater C E H, and

let the ſemidiameter A B C, be perpendicular to the Horizon; and

by the points B and C, let us draw the right lined Tangents B F

and C D; and in the arches B G and C E, take two equal parts

B G and C E: and let the two wheels be ſuppoſed to be turn'd

demonſtrate: but for the preſent, let this onely of the ſtiliard

ſuffice: in which you ſee that the light end of the beam is then

able to ſuſtain and equilibrate the great Wool ſack, when its

ſtance from the centre, upon which the ſtiliard reſteth and

eth, ſhall ſo much exceed the leſſer diſtance, by how much the

ſolute gravity of the Wool-ſack exceedeth that of the pendent

weight. And we ſee nothing that can cauſe this inſufficiencie in

the great ſack of Wool, to raiſe with its weight the pendent

weight ſo much leſs grave, ſave the diſparity of the motions which

the one and the other ſhould make, whilſt that the Wool ſack by

deſcending but one inch onely, will raiſe the pendent weight an

hundred inclies: (ſuppoſing that the ſack did weigh an hundred

times as much, and that the diſtance of the ſmall weight from the

centre of the beam were an hundred times greater, than the

ſtance between the ſaid centre and the point of the ſacks

on.) And again, the pendent weight its moving the ſpace of an

hundred inches, in the time that the ſack moveth but one inch

onely, is the ſame as to ſay, that the velocity of the motion of the

little pendent weight, is an hundred times greater than the

city of the motion of the ſack. Now fix it in your belief, as a

true and manifeſt axiom, that the reſiſtance which proceedeth from

the velocity of motion, compenſateth that which dependeth on

the gravity of another moveable: So that conſequently, a

able of one pound, that moveth with an hundred degrees of

locity, doth as much reſiſt all obſtruction, as another moveable

of an hundred weight, whoſe velocity is but one degree onely.

And two equal moveables will equally reſiſt their being moved,

if that they ſhall be moved with equal velocity: but if one be

to be moved more ſwiftly than the other, it ſhall make greater

ſiſtance, according to the greater velocity that ſhall be conferred

on it. Theſe things being premiſed, let us proceed to the

nation of our Problem; and for the better underſtanding of

things, let us make a ſhort Scheme thereof. Let two unequal

wheels be deſcribed about this centre A, [in Fig. 7.] and let the

circumference of the leſſer be B G, and of the greater C E H, and

let the ſemidiameter A B C, be perpendicular to the Horizon; and

by the points B and C, let us draw the right lined Tangents B F

and C D; and in the arches B G and C E, take two equal parts

B G and C E: and let the two wheels be ſuppoſed to be turn'd