1the Fall along A C to be as the Line A C; C E ſhall be the Time along
E C, and C F or C A the Time of the Motion along C G. Therefore
it is to be proved that the
115[Figure 115]
Space C G is more than
double, and leſſe than
triple the ſaid C A. For
in regard that as C E is
to E F, ſo is F E to E G;
therefore alſo ſo is C F to
F G. But E C is leſſe
than E F: Therefore C F
ſhall be leſſe than F G, and
G C more than double to
F C or A C. And moreover, in regard that F E is leſſe than double to
E C, (for E C is greater than C A or C F) G F ſhall alſo be leſſe
than double to F C, and G C leſſe than triple to C F or C A: Which
was to be demonſtrated.
E C, and C F or C A the Time of the Motion along C G. Therefore
it is to be proved that the
115[Figure 115]Space C G is more than
double, and leſſe than
triple the ſaid C A. For
in regard that as C E is
to E F, ſo is F E to E G;
therefore alſo ſo is C F to
F G. But E C is leſſe
than E F: Therefore C F
ſhall be leſſe than F G, and
G C more than double to
F C or A C. And moreover, in regard that F E is leſſe than double to
E C, (for E C is greater than C A or C F) G F ſhall alſo be leſſe
than double to F C, and G C leſſe than triple to C F or C A: Which
was to be demonſtrated.
And the ſame may be more generally propounded: for that which
hapneth in the Perpendicular and Inclined Plane, holdeth true alſo if
after the Motion a Plane ſomewhat inclined it be inflected along a more
inclining Plane, as is ſeen in the other Figure: And the Demonſtration
is the ſame.
hapneth in the Perpendicular and Inclined Plane, holdeth true alſo if
after the Motion a Plane ſomewhat inclined it be inflected along a more
inclining Plane, as is ſeen in the other Figure: And the Demonſtration
is the ſame.
PROBL. VIII. PROP. XXII.
Two unequall Times being given, and a Space
that is paſt ex quiete along the Perpendicular
in the ſhorteſt of thoſe given Times, to inflect
a Plane from the higheſt point of the Perpen
dicular unto the Horizon, along which the
Moveable may deſcend in a Time equal to the
longeſt of thoſe Times given.
that is paſt ex quiete along the Perpendicular
in the ſhorteſt of thoſe given Times, to inflect
a Plane from the higheſt point of the Perpen
dicular unto the Horizon, along which the
Moveable may deſcend in a Time equal to the
longeſt of thoſe Times given.
Let the unsqual Times be A the greater, and B the leſſer; and let
the Space that is paſt ex quiete along the Perpendicular in the
Time B, be C D. It is required from the Term C to inflect [or
116[Figure 116]
bend] a Plane untill it reach the Horizon that may be paſſed in the
the Space that is paſt ex quiete along the Perpendicular in the
Time B, be C D. It is required from the Term C to inflect [or
116[Figure 116]bend] a Plane untill it reach the Horizon that may be paſſed in the
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