51

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.

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

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
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