PROPOSITION I.
The Sections of the ſame River diſcharge equal quan
tities of Water in equal times, although the Secti
ons themſelves he unequal.
tities of Water in equal times, although the Secti
ons themſelves he unequal.
Let the two Sections be A and B, in the River C, running
from A, towards B; I ſay, that they diſcharge equal quan
tity of Water in equal times; for if greater quantity of Wa
ter ſhould paſs through A, than paſſeth through B, it would
39[Figure 39]
follow that the Water in the intermediate ſpace of the River C,
would increaſe continually, which is manifeſtly falſe, but if
more Water ſhould iſſue through the Section B, than entreth at
the Section A, the Water in the intermediate ſpace C, would
grow continually leſs, and alwaies ebb, which is likewiſe falſe;
therefore the quantity of Water that paſſeth through the Secti
on B, is equal to the quantity of Water which paſſeth through
the Section A, and therefore the Sections of the ſame River diſ
charge, &c. Which w s to be demonſtrated.
from A, towards B; I ſay, that they diſcharge equal quan
tity of Water in equal times; for if greater quantity of Wa
ter ſhould paſs through A, than paſſeth through B, it would
39[Figure 39]follow that the Water in the intermediate ſpace of the River C,
would increaſe continually, which is manifeſtly falſe, but if
more Water ſhould iſſue through the Section B, than entreth at
the Section A, the Water in the intermediate ſpace C, would
grow continually leſs, and alwaies ebb, which is likewiſe falſe;
therefore the quantity of Water that paſſeth through the Secti
on B, is equal to the quantity of Water which paſſeth through
the Section A, and therefore the Sections of the ſame River diſ
charge, &c. Which w s to be demonſtrated.
PROPOSITION II.
In two Sections of Rivers, the quantity of the Water
which paſſeth by one Section, is to that which paſ
ſeth by the ſecond, in a Proportion compounded of
the proportions of the firſt Section to the ſecond, and
of the velocitie through the first, to the velocitie
of the ſecond.
which paſſeth by one Section, is to that which paſ
ſeth by the ſecond, in a Proportion compounded of
the proportions of the firſt Section to the ſecond, and
of the velocitie through the first, to the velocitie
of the ſecond.
I Et A, and B be two Sections of a River; I ſay, that the
quantity of Water which paſſeth through A, is to that which
paſſeth through B, in a proportion compounded of the pro
portions of the firſt Section A, to the Section B; and of the velo
city through A, to the velocity through B: Let a Section be
quantity of Water which paſſeth through A, is to that which
paſſeth through B, in a proportion compounded of the pro
portions of the firſt Section A, to the Section B; and of the velo
city through A, to the velocity through B: Let a Section be
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