PROPOSITION V.
If a River diſcharge a certain quantitie of Water
in a certain time; and after that there come into it
a Flood, the quantity of Water which is diſchar
ged in as much time at the Flood, is to that which
was diſcharged before, whilſt the River was low,
in a proportion compounded of the proportions of
the velocity of the Flood, to the velocity of the first
Water, and of the height of the Flood, to the
height of the first Water.
in a certain time; and after that there come into it
a Flood, the quantity of Water which is diſchar
ged in as much time at the Flood, is to that which
was diſcharged before, whilſt the River was low,
in a proportion compounded of the proportions of
the velocity of the Flood, to the velocity of the first
Water, and of the height of the Flood, to the
height of the first Water.
Suppoſe a River, which whilſt it is low, runs by the Section
AF; and after a Flood cometh into the ſame, and runneth
through the Section D F, I ſay, that the quantity of the Wa
ter which is diſcharged through D F, is to that which is diſcharged
43[Figure 43]
through A F, in a proportion compounded of the proportions of
the velocity through D F, to the velocity through A F, and of
the height D B, to the height A B; As the velocity through DF
is to the velocity through A F, ſo let the line R, to the line S;
and as the height D B is to the height A B, ſo let the line S, to
the line T; and let us ſuppoſe a Section L M N, equal to D F
in height and breadth; that is L M equal to D B, and M N equal
to B F; but let it be in velocity equal to the Section A F, there
fore the quantity of Water which runneth through D F, ſhall be
to that which runneth through LN, as the velocity through DF,
is to the velocity through L N, that is, to the velocity through
A F; and the line R being to the line S, as the velocity through
D F, to the velocity through A F; therefore the quantity which
runneth through D F, to that which runneth through L N, ſhall
have the proportion of R to S; but the quantity which runneth
through L N, to that which runneth through A F, (the Sections
AF; and after a Flood cometh into the ſame, and runneth
through the Section D F, I ſay, that the quantity of the Wa
ter which is diſcharged through D F, is to that which is diſcharged
43[Figure 43]through A F, in a proportion compounded of the proportions of
the velocity through D F, to the velocity through A F, and of
the height D B, to the height A B; As the velocity through DF
is to the velocity through A F, ſo let the line R, to the line S;
and as the height D B is to the height A B, ſo let the line S, to
the line T; and let us ſuppoſe a Section L M N, equal to D F
in height and breadth; that is L M equal to D B, and M N equal
to B F; but let it be in velocity equal to the Section A F, there
fore the quantity of Water which runneth through D F, ſhall be
to that which runneth through LN, as the velocity through DF,
is to the velocity through L N, that is, to the velocity through
A F; and the line R being to the line S, as the velocity through
D F, to the velocity through A F; therefore the quantity which
runneth through D F, to that which runneth through L N, ſhall
have the proportion of R to S; but the quantity which runneth
through L N, to that which runneth through A F, (the Sections
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