1ſuppoſed equal to the Section A, in magnitude; but of velocity
equal to the Section B, and let it be G, and as the Section A is
40[Figure 40]
to the Section B, ſo let the line F be to the line D; and as the
velocity A, is to the velocity by B, ſo let the line D be to the
line R: Therefore the Water which paſſeth thorow A, ſhall be
to that which paſſeth through G (in regard the Sections A and
G are of equal bigneſs, but of unequal velocity) as the velocity
through A, to the velocity through G; But as the velocity
through A, is to the velocity through G, ſo is the velocity through
A, to the velocity through B; namely, as the line D, to the
line R: therefore the quantity of the Water which paſſe the
through A, ſhall be to the quantity which paſſeth through G, as
the line D is to the line R; but the quantity which paſſeth
through G, is to that which paſſeth through B, (in regard the
Sections G, and B, are equally ſwift) as the Section G to the Se
ction B; that is, as the Section A, to the Section B; that is, as
the line F, to the line D: Therefore by the equal and perturbed
proportionality, the quantity of the Water which paſſeth through
A, hath the ſame proportion to that which paſſeth through B,
that the line F hath to the line R; but F to R, hath a proportion
compounded of the proportions of F to D, and of D to R; that
is, of the Section A to the Section B; and of the velocity through
A, to the velocity through B. Therefore alſo the quantity of
Water which paſſeth through the Section A, ſhall have a propor
tion to that which paſſeth through the Section B, compounded of
the proportions of the Section A, to the Section B; and of
the velocity through A, to the velocity through B: And
therefore in two Sections of Rivers, the quantity of Water which
paſſeth by the firſt, &c. which was to be demonſtrated.
equal to the Section B, and let it be G, and as the Section A is
40[Figure 40]to the Section B, ſo let the line F be to the line D; and as the
velocity A, is to the velocity by B, ſo let the line D be to the
line R: Therefore the Water which paſſeth thorow A, ſhall be
to that which paſſeth through G (in regard the Sections A and
G are of equal bigneſs, but of unequal velocity) as the velocity
through A, to the velocity through G; But as the velocity
through A, is to the velocity through G, ſo is the velocity through
A, to the velocity through B; namely, as the line D, to the
line R: therefore the quantity of the Water which paſſe the
through A, ſhall be to the quantity which paſſeth through G, as
the line D is to the line R; but the quantity which paſſeth
through G, is to that which paſſeth through B, (in regard the
Sections G, and B, are equally ſwift) as the Section G to the Se
ction B; that is, as the Section A, to the Section B; that is, as
the line F, to the line D: Therefore by the equal and perturbed
proportionality, the quantity of the Water which paſſeth through
A, hath the ſame proportion to that which paſſeth through B,
that the line F hath to the line R; but F to R, hath a proportion
compounded of the proportions of F to D, and of D to R; that
is, of the Section A to the Section B; and of the velocity through
A, to the velocity through B. Therefore alſo the quantity of
Water which paſſeth through the Section A, ſhall have a propor
tion to that which paſſeth through the Section B, compounded of
the proportions of the Section A, to the Section B; and of
the velocity through A, to the velocity through B: And
therefore in two Sections of Rivers, the quantity of Water which
paſſeth by the firſt, &c. which was to be demonſtrated.
COROLLARIE.