And the ſame alſo hapneth if the precedent Motion be not made
along the Perpendicular, but along an Inclined Plane; and the Demon
ſtration is the ſame, provided that the Reflex Plane be leſſe riſing, that is,
longer than the declining Plane.
along the Perpendicular, but along an Inclined Plane; and the Demon
ſtration is the ſame, provided that the Reflex Plane be leſſe riſing, that is,
longer than the declining Plane.
THEOR. XVI. PROP. XXV.
If after the Deſcent along any Inclined Plane a
Motion follow along the Plane of the Hori
zon, the Time of the Deſcent along the Incli
ned Plane ſhall be to the Time of the Motion
along any Horizontal Line; as the double
Length of the Inclined Plane is to the Line ta
ken in the Horizon.
Motion follow along the Plane of the Hori
zon, the Time of the Deſcent along the Incli
ned Plane ſhall be to the Time of the Motion
along any Horizontal Line; as the double
Length of the Inclined Plane is to the Line ta
ken in the Horizon.
Let the Horizontal Line be C B, the inclined Plane A B, and after
the Deſcent along A B let a Motion follow along the Horizon, in
which take any Space B D. I ſay, that the Time of the Deſcent
along A B to the Time of the Motion along B D is as the double of A B
to B D. For B C being ſuppoſed
the double of A B, it is manifeſt by
123[Figure 123]
what hath already been demonſtra
ted that the Time of the Deſcent
along A B is equal to the Time of
the Motion along B C: But the
Time of the Motion along B C is to
the Time of the Motion along B D, as the Line C B is to the Line B D:
Therefore the Time of the Motion along A B is the Time along B D, as
the Double of A B is to B D: Which was to be proved.
the Deſcent along A B let a Motion follow along the Horizon, in
which take any Space B D. I ſay, that the Time of the Deſcent
along A B to the Time of the Motion along B D is as the double of A B
to B D. For B C being ſuppoſed
the double of A B, it is manifeſt by
123[Figure 123]what hath already been demonſtra
ted that the Time of the Deſcent
along A B is equal to the Time of
the Motion along B C: But the
Time of the Motion along B C is to
the Time of the Motion along B D, as the Line C B is to the Line B D:
Therefore the Time of the Motion along A B is the Time along B D, as
the Double of A B is to B D: Which was to be proved.
PROBL X. PROP. XXVI.
A Perpendicular between two Horizontal Paral
lel Lines, as alſo a Space greater than the ſaid
Perpendicular, but leſſe than double the ſame,
being given, to raiſe a Plane between the ſaid
Parallels from the loweſt Term of the Per
pendicular, along which the Moveable may
with a Reflex Motion after the Fall along the
Perpendicular paſſe a Space equal to the Space
given, and in a Time equal to the Time of the
Fall along the Perpendicular.
lel Lines, as alſo a Space greater than the ſaid
Perpendicular, but leſſe than double the ſame,
being given, to raiſe a Plane between the ſaid
Parallels from the loweſt Term of the Per
pendicular, along which the Moveable may
with a Reflex Motion after the Fall along the
Perpendicular paſſe a Space equal to the Space
given, and in a Time equal to the Time of the
Fall along the Perpendicular.
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