1equal. And that two points at pleaſure D and E being taken, equally
remote from the Angle B, the Tranſition along D B is made in a Time
equal to the Time of the Reflection along B E, we may collect from hence:
Draw D F, which ſhall be Parallel to B C; for it is manifeſt that the
Deſcent along A D is reflected along D F: And if after D the Move
able paſſe along the Horizontal Plane D E, the Impetus in E ſhall be
the ſame as the Impetus in D: Therefore it will aſcend from E to C:
And therefore the degree of Velocity in D is equal to the degree in E.
From theſe things, therefore, we may rationally affirm, that, if a de
ſcent be made along any inclined Plane, after which a Reflection may
follow along an elevated Plane, the Moveable may by the conceived
Impetus aſcend untill it attain the ſame beight, or Elevation from the
Horizon. As if a Deſcent be made along A B, the Moveable would
paſſe along the Reflected Plane B C, untill it arrive at the Horizon
A C D; and that not only when the Inclinations of the Planes are
equal, but alſo when they are unequal, as is the Plane B D: For it was
first ſuppoſed, that the degrees of Velocity are equal, which are acqui
red upon Planes unequally inclined, ſo long as the Elevation of thoſe
Planes above the Horizon was the ſame: But, if there being the ſame
Inclination of the Planes E B and B D, the Deſcent along E B ſufficeth
to drive the Moveable along the Plane BD as far as D, ſeeing this Impulſe
121[Figure 121]
is made by the Impe
tus of Velocity in the
point B; and if the
Impetus be the ſame
in B, whether the
Moveable deſcend a
long A B, or along E B: It is manifeſt, that the Moveable ſhall be in
the ſame manner driven along B D, after the Deſcent along A B, and
after that along E B: But it will happen that the Time of the Aſcent
along B D ſhall be longer than along B C, like as the Deſcent along
E B is made in a longer time than along A B: But the Proportion of
thoſe Times was before demonſtrated to be the ſame as the Lengths of
thoſe Planes. Now it follows, that we ſeek the proportion of the Spaces
paſt in equal Times along Planes, whoſe Inclinations are different, but
their Elevations the ſame; that is, which are comprehended between
the ſame Horizontal Parallels. And this hapneth according to the fol
lowing Propoſition.
remote from the Angle B, the Tranſition along D B is made in a Time
equal to the Time of the Reflection along B E, we may collect from hence:
Draw D F, which ſhall be Parallel to B C; for it is manifeſt that the
Deſcent along A D is reflected along D F: And if after D the Move
able paſſe along the Horizontal Plane D E, the Impetus in E ſhall be
the ſame as the Impetus in D: Therefore it will aſcend from E to C:
And therefore the degree of Velocity in D is equal to the degree in E.
From theſe things, therefore, we may rationally affirm, that, if a de
ſcent be made along any inclined Plane, after which a Reflection may
follow along an elevated Plane, the Moveable may by the conceived
Impetus aſcend untill it attain the ſame beight, or Elevation from the
Horizon. As if a Deſcent be made along A B, the Moveable would
paſſe along the Reflected Plane B C, untill it arrive at the Horizon
A C D; and that not only when the Inclinations of the Planes are
equal, but alſo when they are unequal, as is the Plane B D: For it was
first ſuppoſed, that the degrees of Velocity are equal, which are acqui
red upon Planes unequally inclined, ſo long as the Elevation of thoſe
Planes above the Horizon was the ſame: But, if there being the ſame
Inclination of the Planes E B and B D, the Deſcent along E B ſufficeth
to drive the Moveable along the Plane BD as far as D, ſeeing this Impulſe
121[Figure 121]is made by the Impe
tus of Velocity in the
point B; and if the
Impetus be the ſame
in B, whether the
Moveable deſcend a
long A B, or along E B: It is manifeſt, that the Moveable ſhall be in
the ſame manner driven along B D, after the Deſcent along A B, and
after that along E B: But it will happen that the Time of the Aſcent
along B D ſhall be longer than along B C, like as the Deſcent along
E B is made in a longer time than along A B: But the Proportion of
thoſe Times was before demonſtrated to be the ſame as the Lengths of
thoſe Planes. Now it follows, that we ſeek the proportion of the Spaces
paſt in equal Times along Planes, whoſe Inclinations are different, but
their Elevations the ſame; that is, which are comprehended between
the ſame Horizontal Parallels. And this hapneth according to the fol
lowing Propoſition.
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