THEOREM.
The degrees of Velocity of a Moveable deſcending with a Natural
Motion from the ſame height along Planes in any manner inclined
at the arrival to the Horizon are alwaies equal, Impediments be
ing removed.
Motion from the ſame height along Planes in any manner inclined
at the arrival to the Horizon are alwaies equal, Impediments be
ing removed.
Here we are in the firſt place to advertiſe you, that it having
been proved, that in any Inclination of the Plane the Move
able from its receſſion from Quieſſence goeth encreaſing its Ve
locity, or quantity of its Impetus, with the proportion of the
Time (according to the Definition which the Author giveth of
Motion naturally Accelerate) whereupon, as he hath by the pre
cedent Propoſition demonſtrated, the Spaces paſſed are in dupli
cate proportion to the Times, and, conſequently, to the degrees
of Velocity: look what the Impetus's were in that which was firſt
moved, ſuch proportionally ſhall be the degrees of Velocity gai
ned in the ſame Time; ſeeing that both theſe and thoſe encreaſe
with the ſame proportion in the ſame Time.
been proved, that in any Inclination of the Plane the Move
able from its receſſion from Quieſſence goeth encreaſing its Ve
locity, or quantity of its Impetus, with the proportion of the
Time (according to the Definition which the Author giveth of
Motion naturally Accelerate) whereupon, as he hath by the pre
cedent Propoſition demonſtrated, the Spaces paſſed are in dupli
cate proportion to the Times, and, conſequently, to the degrees
of Velocity: look what the Impetus's were in that which was firſt
moved, ſuch proportionally ſhall be the degrees of Velocity gai
ned in the ſame Time; ſeeing that both theſe and thoſe encreaſe
with the ſame proportion in the ſame Time.
Now let the inclined Plane be A B, its elevation above the Ho
rizon the Perpendicular A C, and the Horizontal Plane C B: and
becauſe, as was even now concluded, the Impetus of a Moveable
along the Perpendicular A C is to the Impetus of the ſame along
the inclined Plane A B, as A B is to A C, let there be taken in the
inclined Plane A B, A D a third proportional to A B and A C:
The Impetus, therefore, along A C is to the Impetus along A B,
that is along A D, as A C is to
89[Figure 89]
A D: And therefore the Move
able in the ſame Time that it
would paſs the Perpendicular
Space AC, ſhall likewiſe paſs the
Space A D, in the inclined Plane
A B, (the Moments being as
the Spaces:) And the degree of Velocity in C ſhall have the ſame
proportion to the degree of Velocity in D, as A C hath to A D:
But the degree of Velocity in B is to the ſame degree in D, as the
Time along A B is to the Time along AD, by the definition of
Accelerate Motion; And the Time along AB is to the Time along
A D, as the ſame A C, the Mean Proportional between B A and
A D, is to A D, by the laſt Corollary of the ſecond Propoſition:
Therefore the degrees of Velocity in B and in C have to the de
gree in D, the ſame Proportion as A C hath to A D; and therefore
are equal: Which is the Theorem intended to be demonſtrated.
rizon the Perpendicular A C, and the Horizontal Plane C B: and
becauſe, as was even now concluded, the Impetus of a Moveable
along the Perpendicular A C is to the Impetus of the ſame along
the inclined Plane A B, as A B is to A C, let there be taken in the
inclined Plane A B, A D a third proportional to A B and A C:
The Impetus, therefore, along A C is to the Impetus along A B,
that is along A D, as A C is to
89[Figure 89]A D: And therefore the Move
able in the ſame Time that it
would paſs the Perpendicular
Space AC, ſhall likewiſe paſs the
Space A D, in the inclined Plane
A B, (the Moments being as
the Spaces:) And the degree of Velocity in C ſhall have the ſame
proportion to the degree of Velocity in D, as A C hath to A D:
But the degree of Velocity in B is to the ſame degree in D, as the
Time along A B is to the Time along AD, by the definition of
Accelerate Motion; And the Time along AB is to the Time along
A D, as the ſame A C, the Mean Proportional between B A and
A D, is to A D, by the laſt Corollary of the ſecond Propoſition:
Therefore the degrees of Velocity in B and in C have to the de
gree in D, the ſame Proportion as A C hath to A D; and therefore
are equal: Which is the Theorem intended to be demonſtrated.
By this we may more concludingly prove the enſuing third