1
86[Figure 86]
as VS is to SX. For it is demonſtrated, that Spaces
paſſed are in duplicate proportion to the Times, or, (which
is the ſame) are as the Squares of the Times: But the pro
portion of the Space VS to the Space ST is double to the
proportion of V S to SX, or is the ſame that V S, and S X
ſquared have to one another: Therefore, the proportion of
the Times of the Motion by V S, and ST, is as the Spaces or
Lines V S to S X.
86[Figure 86]as VS is to SX. For it is demonſtrated, that Spaces
paſſed are in duplicate proportion to the Times, or, (which
is the ſame) are as the Squares of the Times: But the pro
portion of the Space VS to the Space ST is double to the
proportion of V S to SX, or is the ſame that V S, and S X
ſquared have to one another: Therefore, the proportion of
the Times of the Motion by V S, and ST, is as the Spaces or
Lines V S to S X.
SCHOLIUM.
That which is demonſtrated in Motions that are made Perpendicu
larly, may be underſtood alſo to hold true in the Motions made along
Planes of any whatever Inclination; for it is ſuppoſed, that in them
the degree of Acceleration encreaſeth in the ſame proportion; that
is, according to the encreaſe of the Time; or, if you will, according
to the ſimple and primary Series of Numbers.
larly, may be underſtood alſo to hold true in the Motions made along
Planes of any whatever Inclination; for it is ſuppoſed, that in them
the degree of Acceleration encreaſeth in the ſame proportion; that
is, according to the encreaſe of the Time; or, if you will, according
to the ſimple and primary Series of Numbers.
SALV. Here I deſire Sagredus, that I alſo may be allowed, al
beit perhaps with too much tediouſneſſe in the opinion of Simplici
us, to defer for a little time the preſent Reading, untill I may have
explained what from that which hath been already ſaid and de
monſtrated, and alſo from the knowledge of certain Mechanical
Concluſions heretofore learnt of our Academick, I now remember
to adjoyn for the greater confirmation of the truth of the Princi
ple, which hath been examined by us even now with probable
Reaſons and Experiments: and, which is of more importance, for
the Geometrical proof of it, let me firſt demonſtrate one ſole Ele
mental Lemma in the Contemplation of Impetus's.
beit perhaps with too much tediouſneſſe in the opinion of Simplici
us, to defer for a little time the preſent Reading, untill I may have
explained what from that which hath been already ſaid and de
monſtrated, and alſo from the knowledge of certain Mechanical
Concluſions heretofore learnt of our Academick, I now remember
to adjoyn for the greater confirmation of the truth of the Princi
ple, which hath been examined by us even now with probable
Reaſons and Experiments: and, which is of more importance, for
the Geometrical proof of it, let me firſt demonſtrate one ſole Ele
mental Lemma in the Contemplation of Impetus's.
SAGR. If our advantage ſhall be ſuch as you promiſeus, there
is no time that I would not moſt willingly ſpend in diſcourſing
about the confirmation and thorow eſtabliſhing theſe Sciences of
Motion: and as to my own particular, I not only grant you liber
ty to ſatisfie your ſelf in this particular, but moreover entreat you
to gratifie, as ſoon as you can, the Curioſity which you have begot
in me touching the ſame: and I believe that Simplicius alſo is of the
ſame mind.
is no time that I would not moſt willingly ſpend in diſcourſing
about the confirmation and thorow eſtabliſhing theſe Sciences of
Motion: and as to my own particular, I not only grant you liber
ty to ſatisfie your ſelf in this particular, but moreover entreat you
to gratifie, as ſoon as you can, the Curioſity which you have begot
in me touching the ſame: and I believe that Simplicius alſo is of the
ſame mind.
SIMP. I cannot deny what you ſay.
SALV. Seeing then that I have your permiſſion, I will in the
firſt place conſider, as an Effect well known, That
firſt place conſider, as an Effect well known, That