Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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040/01/611.jpg
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44
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<
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>PROPOSITION V.</
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If a River diſcharge a certain quantitie of Water
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in a certain time; and after that there come into it
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a Flood, the quantity of Water which is diſchar
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ged in as much time at the Flood, is to that which
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was diſcharged before, whilſt the River was low,
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in a proportion compounded of the proportions of
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the velocity of the Flood, to the velocity of the first
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Water, and of the height of the Flood, to the
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height of the first Water.
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type
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<
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>Suppoſe a River, which whilſt it is low, runs by the Section
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AF; and after a Flood cometh into the ſame, and runneth
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through the Section D F, I ſay, that the quantity of the Wa
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ter which is diſcharged through D F, is to that which is diſcharged
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through A F, in a proportion compounded of the proportions of
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the velocity through D F, to the velocity through A F, and of
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the height D
<
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type
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"/>
B,
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type
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to the height A
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type
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"/>
B
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type
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"/>
; As the velocity through DF
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/>
is to the velocity through A F, ſo let the line R, to the line S;
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and as the height D
<
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type
="
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"/>
B
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type
="
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"/>
is to the height A
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type
="
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"/>
B,
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type
="
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"/>
ſo let the line S, to
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the line T; and let us ſuppoſe a Section L M N, equal to D F
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in height and breadth; that is L M equal to D
<
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type
="
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"/>
B,
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emph.end
type
="
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"/>
and M N equal
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/>
to
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type
="
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"/>
B F
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type
="
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"/>
; but let it be in velocity equal to the Section A F, there
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/>
fore the quantity of Water which runneth through D F, ſhall be
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to that which runneth through LN, as the velocity through DF,
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is to the velocity through L N, that is, to the velocity through
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/>
<
emph
type
="
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"/>
A F
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type
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; and the line R being to the line S, as the velocity through
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D
<
emph
type
="
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"/>
F,
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emph.end
type
="
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"/>
to the velocity through
<
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type
="
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"/>
A F
<
emph.end
type
="
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"/>
; therefore the quantity which
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/>
runneth through D
<
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type
="
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"/>
F,
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type
="
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"/>
to that which runneth through L N, ſhall
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have the proportion of R to S; but the quantity which runneth
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/>
through L N, to that which runneth through
<
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type
="
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"/>
A F,
<
emph.end
type
="
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"/>
(the Sections </
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>
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</
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