1neſe territories, and many other places, where very great ſuits
and differences ariſe, which not being to be determined with in
telligible reaſons, come oftentimes to be decided, by force of
armes; and inſtead of flowing their Grounds with Waters, they
cruelly flow them with the ſhedding of humane blood, impiouſly
inverting the courſe of Peace and Juſtice, ſowing ſuch diſorders
and feuds, as that they are ſometimes accompanied with the ru
ine of whole Cities, or elſe unprofitably charge them with vain,
and ſometimes prejudicial expences.
and differences ariſe, which not being to be determined with in
telligible reaſons, come oftentimes to be decided, by force of
armes; and inſtead of flowing their Grounds with Waters, they
cruelly flow them with the ſhedding of humane blood, impiouſly
inverting the courſe of Peace and Juſtice, ſowing ſuch diſorders
and feuds, as that they are ſometimes accompanied with the ru
ine of whole Cities, or elſe unprofitably charge them with vain,
and ſometimes prejudicial expences.
PROPOS. IV. THEOR. II.
If a River increaſe in quick height, the quantitie of
Water which the River diſchargeth after the in
creaſe, hath the Proportion compounded of the
Proportions of the Quick height to the Quick
height, and of the velocity to the velocity.
Water which the River diſchargeth after the in
creaſe, hath the Proportion compounded of the
Proportions of the Quick height to the Quick
height, and of the velocity to the velocity.
Let there be a River, which whilſt it is low, runneth thorow
the Regulator D F, with the Quick height A B, and after
wards let a Flood come; and then let it run with the height
D B, I ſay, that the quantity of the Water that is diſcharged
through D F, to that which diſchargeth through A F, hath the
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 D F is to the
velocity through A F, ſo let the line R be to the line S; and as
the height D B is to the height A B; ſo let the line S be to the
47[Figure 47]
line T. And let a Section be ſuppoſed L M N equal to the
Section D F in height and length, but let it be in velocity equal
to the Section AF. Therefore the quantity of the Water that run
neth through D F to that which runneth through L N, ſhall be
the Regulator D F, with the Quick height A B, and after
wards let a Flood come; and then let it run with the height
D B, I ſay, that the quantity of the Water that is diſcharged
through D F, to that which diſchargeth through A F, hath the
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 D F is to the
velocity through A F, ſo let the line R be to the line S; and as
the height D B is to the height A B; ſo let the line S be to the
47[Figure 47]line T. And let a Section be ſuppoſed L M N equal to the
Section D F in height and length, but let it be in velocity equal
to the Section AF. Therefore the quantity of the Water that run
neth through D F to that which runneth through L N, ſhall be