PROPOSITION II. THEOREM I.
If a River moving with ſuch a certain velocitie
through its Regulator, ſhall have a given quick
height, and afterwards by new water ſhall increaſe
to be double, it ſhall alſo increaſe double in ve
locitie.
through its Regulator, ſhall have a given quick
height, and afterwards by new water ſhall increaſe
to be double, it ſhall alſo increaſe double in ve
locitie.
Let the quick height of a River in the Regulator A B C D,
be the perpendicular F B, and afterwards, by new water that
is added to the River, let the water be ſuppoſed to be raiſ
ed to G, ſo that G B may be double to E B. I ſay, that all the
water G C ſhall be double in velocity to
13[Figure 13]
that of E C: For the water G F, having
for its bed the bottom E F, equally in
clined as the bed B C, and its quick
height G E being equal to the quick
height E C, and having the ſame breadth
B C, it ſhall have of it ſelf a velocity e
qual to the velocity of the firſt water
F C: but becauſe, beſides its own moti
on, which is imparted to it by the motion of the water E C, it
hath alſo over and above its own motion, the motion of E C. And
becauſe the two waters G C, and E C, are alike in velocity, by
the third Suppoſition; therefore the whole water G C ſhall be
double in velocity to the water E C; which was that which we
were to demonſtrate.
be the perpendicular F B, and afterwards, by new water that
is added to the River, let the water be ſuppoſed to be raiſ
ed to G, ſo that G B may be double to E B. I ſay, that all the
water G C ſhall be double in velocity to
13[Figure 13]that of E C: For the water G F, having
for its bed the bottom E F, equally in
clined as the bed B C, and its quick
height G E being equal to the quick
height E C, and having the ſame breadth
B C, it ſhall have of it ſelf a velocity e
qual to the velocity of the firſt water
F C: but becauſe, beſides its own moti
on, which is imparted to it by the motion of the water E C, it
hath alſo over and above its own motion, the motion of E C. And
becauſe the two waters G C, and E C, are alike in velocity, by
the third Suppoſition; therefore the whole water G C ſhall be
double in velocity to the water E C; which was that which we
were to demonſtrate.
This demonſtration is not here inſerted, as perfect, the Authour ha
ving by ſeveral letters to his friends confeſſed himſelf unſatisfi
ed therewith; and that he intended not to publiſh the Theorem
without a more ſolid demonſtration, which he was in hope to light
upon. But being overtaken by Death, he could not give the
finiſhing touch either to this, or to the rest of the ſecond Book. In
conſideration of which, it ſeemed good to the Publiſher of the
ſame, rather to omit it, than to do any thing contrary to the mind of
the Authour. And this he hints, by way of advertiſement, to
thoſe that have Manuſcript Copies of this Book, with the ſaid de
monſtration. For this time let the Reader content himſelf with
the knowledge of ſo ingenious and profitable a Concluſion; of the
truth of which he may, with ſmall expence and much pleaſure, be
aſſured by means of the experiment to be made in the ſame man
ner, with that which is laid down in the ſecond Corollary of
ving by ſeveral letters to his friends confeſſed himſelf unſatisfi
ed therewith; and that he intended not to publiſh the Theorem
without a more ſolid demonſtration, which he was in hope to light
upon. But being overtaken by Death, he could not give the
finiſhing touch either to this, or to the rest of the ſecond Book. In
conſideration of which, it ſeemed good to the Publiſher of the
ſame, rather to omit it, than to do any thing contrary to the mind of
the Authour. And this he hints, by way of advertiſement, to
thoſe that have Manuſcript Copies of this Book, with the ſaid de
monſtration. For this time let the Reader content himſelf with
the knowledge of ſo ingenious and profitable a Concluſion; of the
truth of which he may, with ſmall expence and much pleaſure, be
aſſured by means of the experiment to be made in the ſame man
ner, with that which is laid down in the ſecond Corollary of
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