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
7[Figure 7]
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
7[Figure 7]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.
The ſame followeth, though the quantity of the Water which
paſſeth through the Section A, be equal to the quantity of
Water which paſſeth through the Section B, as is manifeſt by the
ſame demonſtration.
paſſeth through the Section A, be equal to the quantity of
Water which paſſeth through the Section B, as is manifeſt by the
ſame demonſtration.