1the line I; and as the velocity of D F is to the velocity of A B,
ſo let the line I be to the line L; becauſe therefore the two
Sections A B and G are equally ſwift, and diſcharge equal quan
tity of Water in equal times, they ſhall be equal Sections; and
9[Figure 9]
therefore the height of A B to the height of G, ſhall be as the
breadth of G, to the breadth of A B, that is, as E F to C B,
that is, as the line H to the line I: but becauſe the Water which
paſſeth through G, is equal to that which paſſeth through D E F,
therefore the Section G, to the Section D E F, ſhall have the re
ciprocal proportion of the velocity through D E F, to the velo
city through G; but alſo the height of G, is to the height D E,
as the Section G, to the Section D E F: Therefore the height of
G, is to the height D E, as the velocity through D E F, is to the
velocity through G; that is, as the velocity through D E F, is to
the velocity through A B; That is, finally, as the line I, to the
line L; Therefore, by equal proportion, the height of A B, that
is, A C, ſhall be to the height D E; as H to L, that is, com
pounded of the proportions of the breadth E F, to the breadth
C B, and of the velocity through D F, to the velocity through
A B: So that if a River fall into another River, &c. which was
to be demonſtrated.
ſo let the line I be to the line L; becauſe therefore the two
Sections A B and G are equally ſwift, and diſcharge equal quan
tity of Water in equal times, they ſhall be equal Sections; and
9[Figure 9]therefore the height of A B to the height of G, ſhall be as the
breadth of G, to the breadth of A B, that is, as E F to C B,
that is, as the line H to the line I: but becauſe the Water which
paſſeth through G, is equal to that which paſſeth through D E F,
therefore the Section G, to the Section D E F, ſhall have the re
ciprocal proportion of the velocity through D E F, to the velo
city through G; but alſo the height of G, is to the height D E,
as the Section G, to the Section D E F: Therefore the height of
G, is to the height D E, as the velocity through D E F, is to the
velocity through G; that is, as the velocity through D E F, is to
the velocity through A B; That is, finally, as the line I, to the
line L; Therefore, by equal proportion, the height of A B, that
is, A C, ſhall be to the height D E; as H to L, that is, com
pounded of the proportions of the breadth E F, to the breadth
C B, and of the velocity through D F, to the velocity through
A B: So that if a River fall into another River, &c. which was
to be demonſtrated.