&longs;uppo&longs;ed equal to the Section A, in magnitude; but of velocity <lb/>
equal to the Section B, and let it be G, and as the Section A is <lb/>
<figure id="id.040.01.607.1.jpg" xlink:href="040/01/607/1.jpg"/><lb/>
to the Section B, &longs;o let the line F be to the line D; and as the <lb/>
velocity A, is to the velocity by B, &longs;o let the line D be to the <lb/>
line R: Therefore the Water which pa&longs;&longs;eth thorow A, &longs;hall be <lb/>
to that which pa&longs;&longs;eth through G (in regard the Sections A and <lb/>
G are of equal bigne&longs;s, but of unequal velocity) as the velocity <lb/>
through A, to the velocity through G; But as the velocity <lb/>
through A, is to the velocity through G, &longs;o is the velocity through <lb/>
A, to the velocity through B; namely, as the line D, to the <lb/>
line R: therefore the quantity of the Water which pa&longs;&longs;e the <lb/>
through A, &longs;hall be to the quantity which pa&longs;&longs;eth through G, as <lb/>
the line D is to the line R; but the quantity which pa&longs;&longs;eth <lb/>
through G, is to that which pa&longs;&longs;eth through B, (in regard the <lb/>
Sections G, and B, are equally &longs;wift) as the Section G to the Se<lb/>
ction B; that is, as the Section A, to the Section B; that is, as <lb/>
the line F, to the line D: Therefore by the equal and perturbed <lb/>
proportionality, the quantity of the Water which pa&longs;&longs;eth through <lb/>
A, hath the &longs;ame proportion to that which pa&longs;&longs;eth through B, <lb/>
that the line F hath to the line R; but F to R, hath a proportion <lb/>
compounded of the proportions of F to D, and of D to R; that <lb/>
is, of the Section A to the Section B; and of the velocity through <lb/>
A, to the velocity through B. </s> <s>Therefore al&longs;o the quantity of <lb/>
Water which pa&longs;&longs;eth through the Section A, &longs;hall have a propor<lb/>
tion to that which pa&longs;&longs;eth through the Section B, compounded of <lb/>
the proportions of the Section A, to the Section B; and of <lb/>
the velocity through A, to the velocity through B: And <lb/>
therefore in two Sections of Rivers, the quantity of Water which <lb/>
pa&longs;&longs;eth by the fir&longs;t, <emph type="italics"/>&c.<emph.end type="italics"/> which was to be demon&longs;trated.</s>

 <s><emph type="italics"/>COROLLARIE.<emph.end type="italics"/></s>

 <s>The &longs;ame followeth, though the quantity of the Water which <lb/>
pa&longs;&longs;eth through the Section A, be equal to the quantity of <lb/>
Water which pa&longs;&longs;eth through the Section B, as is manife&longs;t by the <lb/>
&longs;ame demon&longs;tration.</s>