1Impetus is made along ſeveral Inclinations or Declivities of
Planes.
Planes.
As, for example, in the inclined Plane A F, drawing its Eleva
tion above the Horizontal, that is, the Line F C, along the which
the Impetus of a Grave Body, and the Moment of Deſcent is the
greateſt; it is ſought what proportion this Moment hath to the
Moment of the ſame Moveable along the Declivity F A: Which
Proportion, I ſay, is Reciprocal to the ſaid Lengths. And this is
the Lemma that was to go before the Theorem, which I hope to be
able anon to Demonſtrate. Hence it is manifeſt, That the Impetus
of Deſcent of a Grave Body is as much as the Reſiſtance or leaſt
force that ſufficeth to arreſt and ſtay it. For this Force or Reſi
ſtance, and its meaſure, I will make uſe of the Gravity of another
Moveable. Let us now upon the Plane F A put the Moveable G
tyed to a thread which ſliding over F hath faſtned at its other end
the Weight H: and let us conſider that the Space of the Deſcent
or Aſcent of the Weight H along the Perpendicular, is alwaies
equal to the whole Aſcent or Deſcent of the other Moveable G
along the ^{*} Declivity A F, but yet not to the Aſcent or Deſcent
tion above the Horizontal, that is, the Line F C, along the which
the Impetus of a Grave Body, and the Moment of Deſcent is the
greateſt; it is ſought what proportion this Moment hath to the
Moment of the ſame Moveable along the Declivity F A: Which
Proportion, I ſay, is Reciprocal to the ſaid Lengths. And this is
the Lemma that was to go before the Theorem, which I hope to be
able anon to Demonſtrate. Hence it is manifeſt, That the Impetus
of Deſcent of a Grave Body is as much as the Reſiſtance or leaſt
force that ſufficeth to arreſt and ſtay it. For this Force or Reſi
ſtance, and its meaſure, I will make uſe of the Gravity of another
Moveable. Let us now upon the Plane F A put the Moveable G
tyed to a thread which ſliding over F hath faſtned at its other end
the Weight H: and let us conſider that the Space of the Deſcent
or Aſcent of the Weight H along the Perpendicular, is alwaies
equal to the whole Aſcent or Deſcent of the other Moveable G
along the ^{*} Declivity A F, but yet not to the Aſcent or Deſcent
along the Perpendicular, in which only the ſaid Moveable G (like
as every other Moveable) exerciſeth its Reſiſtance. Which is
manifeſt: for conſidering in the Triangle AFC the Motion of
the Moveable G, as for example, upwards from A to F, to be com
poſed of the tranſverſe Horizontal Line A C, and of the Perpendi
cular C F: And in regard, that as to the Horizontal Plane along
which the Moveable, as hath been ſaid, hath no Reſiſtance to mo
ving (it not making by that Motion any loſs, nor yet acquiſt in
regard of its particular diſtance from the Common Center of Grave
Matters, which in the Horizon continueth ſtill the ſame) it remai
neth that the Reſiſtance be only in reſpect of the Aſcent that it is to
make along the Perpendicular C F. Whilſt therefore the Grave
Moveable G, moving from A to F, hath only the Perpendicular
Space C F to reſiſt in its Aſcent, and whilſt the other Grave Move
able H deſcendeth along the Perpendicular of neceſſity as far as
the whole Space F A, and that the ſaid proportion of Aſcent and
Deſcent maintains it ſelf alwaies the ſame, be the Motion of the
ſaid Moveables little or much (by reaſon they are tyed toge
ther) we may confidently affirm, that in caſe there were an Equi
librium, that is Reſt, to enſue betwixt the ſaid Moveables, the Mo
ments, the Velocities, or their Propenſions to Motion, that is the
Spaces which they would paſs in the ſame Time ſhould anſwer re
ciprocally to their Gravities, according to that which is demonſtra
ted in all caſes of Mechanick Motions: ſo that it ſhall ſuffice to
impede the deſcent of G, if H be but ſo much leſs grave than it, as
in proportion the Space C F is leſſer than the Space F A. Therefore