1ſuppoſe that the Moveable G is to the Moveable H, as F A is to
F C; and then the Equilibrium ſhall follow, that is, the Moveables
H and G ſhall have equal Moments, and the Motion of the ſaid
Moveables ſhall ceaſe. And becauſe we ſee that the Impetus,
Energy, Moment, or Propenſion of a Moveable to Motion is the
ſame as is the Force or ſmalleſt Reſiſtance that ſufficeth to ſtop it;
and becauſe it hath been concluded, that the Grave Body H is ſuf.
ficient to arreſt the Motion of
88[Figure 88]
the Grave Body G: Therefore
the leſſer Weight H, which in
the Perpendicular F C imploy
eth its total Moment, ſhall be
the preciſe meaſure of the par
tial Moment that the greater
Weight G exerciſeth along the
inclined Plane F A: But the
meaſure of the total Moment of
the ſaid Grave Body G, is the
ſelf ſame, (ſince that to impede
the Perpendicular Deſcent of a
Grave Body there is required the oppoſition of ſuch another Grave
Body, which likewiſe is at liberty to move Perpendicularly:)
Therefore the partial Impetus or Moment of G along the inclined
Plane F A ſhall be to the grand and total Impetus of the ſame G
along the Perpendicular F C, as the Weight H to the Weight G:
that is, by Conſtruction, as the ſaid Perpendicular F C, the Eleva
tion of the inclined Plane, is to the ſame inclined Plane F A:
Which is that that by the Lemma was propoſed to be demon
ſtrated, and which by our Author, as we ſhall ſee, is ſuppoſed as
known in the ſecond part of the Sixth Propoſition of the preſent
Treatiſe.
F C; and then the Equilibrium ſhall follow, that is, the Moveables
H and G ſhall have equal Moments, and the Motion of the ſaid
Moveables ſhall ceaſe. And becauſe we ſee that the Impetus,
Energy, Moment, or Propenſion of a Moveable to Motion is the
ſame as is the Force or ſmalleſt Reſiſtance that ſufficeth to ſtop it;
and becauſe it hath been concluded, that the Grave Body H is ſuf.
ficient to arreſt the Motion of
88[Figure 88]the Grave Body G: Therefore
the leſſer Weight H, which in
the Perpendicular F C imploy
eth its total Moment, ſhall be
the preciſe meaſure of the par
tial Moment that the greater
Weight G exerciſeth along the
inclined Plane F A: But the
meaſure of the total Moment of
the ſaid Grave Body G, is the
ſelf ſame, (ſince that to impede
the Perpendicular Deſcent of a
Grave Body there is required the oppoſition of ſuch another Grave
Body, which likewiſe is at liberty to move Perpendicularly:)
Therefore the partial Impetus or Moment of G along the inclined
Plane F A ſhall be to the grand and total Impetus of the ſame G
along the Perpendicular F C, as the Weight H to the Weight G:
that is, by Conſtruction, as the ſaid Perpendicular F C, the Eleva
tion of the inclined Plane, is to the ſame inclined Plane F A:
Which is that that by the Lemma was propoſed to be demon
ſtrated, and which by our Author, as we ſhall ſee, is ſuppoſed as
known in the ſecond part of the Sixth Propoſition of the preſent
Treatiſe.
* Or inclined
Plane.
Plane.
SAGR. From this that you have already concluded I conceive
one may eaſily deduce, arguing ex æquali by perturbed Proportion,
that the Moments of the ſame Moveable, along Planes variouſly
inclined (as F A and F I) that have the ſame Elevation, are to each
other in Reciprocal proportion to the ſame Planes.
one may eaſily deduce, arguing ex æquali by perturbed Proportion,
that the Moments of the ſame Moveable, along Planes variouſly
inclined (as F A and F I) that have the ſame Elevation, are to each
other in Reciprocal proportion to the ſame Planes.
SALV. A moſt certain Concluſion. This being agreed on, we
will paſs in the next place to demonſtrate the Theoreme, namely,
that
will paſs in the next place to demonſtrate the Theoreme, namely,
that