<s>PROPOSITION III.</s>

 <s><emph type="italics"/>In two Sections unequal, through which pa&longs;s equal <lb/>
quantities of Water in equal times, the Sections <lb/>
have to one another, reciprocal proportion to their <lb/>
velocitie.<emph.end type="italics"/></s>

 <s>Let the two unequal Sections, by which pa&longs;s equal quantities <lb/>
of Water in equal times be A, the greater; and B, the le&longs;&longs;er: <lb/>
I &longs;ay, that the Section A, &longs;hall have the &longs;ame Proportion <lb/>
to the Section B, that reciprocally the velocity through B, hath to <lb/>
the velocity through A; for &longs;uppo&longs;ing that as the Water that <lb/>
pa&longs;&longs;eth through A, is to that which pa&longs;&longs;eth through B, &longs;o is the <lb/>
<figure id="id.040.01.608.1.jpg" xlink:href="040/01/608/1.jpg"/><lb/>
line E to the line F: therefore the quantity of water which pa&longs;<lb/>
&longs;eth through A, being equal to that which pa&longs;&longs;eth through B, <lb/>
the line E &longs;hall al&longs;o be equal to the line F: Suppo&longs;ing moreover, <lb/>
That as the Section A, is to the Section B, &longs;o is the line F, to the <lb/>
line G; and becau&longs;e the quantity of water which pa&longs;&longs;eth <lb/>
through the Section A, is to that which pa&longs;&longs;eth through the <lb/>
Section B, in a proportion compo&longs;ed of the proportions of the <lb/>
Section A, to the Section B, and of the velocity through A, to the <lb/>
velocity through B; therefore the line E, &longs;hall be the line to F, in <lb/>
a proportion compounded of the &longs;ame proportions; namely, of <lb/>
the proportion of the Section A, to the Section B, and of the ve<lb/>
locity through A, to the velocity through B; but the line E, hath <lb/>
to the line G, the proportion of the Section A, to the Section B, <lb/>
therefore the proportion remaining of the line G, to the line F, <lb/>
&longs;hall be the proportion of the velocity through A, to the velocity <lb/>
through B; therefore al&longs;o the line G, &longs;hall be to the line E, as <lb/>
the velocity by A, to the velocity by B: And conver&longs;ly, the ve<lb/>
locity through B, &longs;hall be to the velocity through A, as the line <lb/>
E, to the line G; that is to &longs;ay, as the Section A, to the Section B, <lb/>
and therefore in two Sections, &c. </s> <s>which was to be demon&longs;trated.</s>