COROLLARIE.
Hence it is manifeſt, that Sections of the ſame River (which
are no other than the vulgar meaſures of the River) have
betwixt themſelves reciprocal proportions to their veloci
ties; for in the firſt Propoſition we have demonſtrated that the
Sections of the ſame River, diſcharge equal quantities of Water
in equal times; therefore, by what hath now been demonſtrated
the Sections of the ſame River ſhall have reciprocal proportion
to their velocities; And therefore the ſame running water chan
geth meaſure, when it changeth velocity; namely, increaſeth the
meaſure, when it decreaſeth the velocity, and decreaſeth the
meaſure, when it increaſeth the velocity.
are no other than the vulgar meaſures of the River) have
betwixt themſelves reciprocal proportions to their veloci
ties; for in the firſt Propoſition we have demonſtrated that the
Sections of the ſame River, diſcharge equal quantities of Water
in equal times; therefore, by what hath now been demonſtrated
the Sections of the ſame River ſhall have reciprocal proportion
to their velocities; And therefore the ſame running water chan
geth meaſure, when it changeth velocity; namely, increaſeth the
meaſure, when it decreaſeth the velocity, and decreaſeth the
meaſure, when it increaſeth the velocity.
On which principally depends all that which hath been ſaid
above in the Diſcourſe, and obſerved in the Corollaries and Ap
pendixes; and therefore is worthy to be well underſtood and
heeded.
above in the Diſcourſe, and obſerved in the Corollaries and Ap
pendixes; and therefore is worthy to be well underſtood and
heeded.
PROPOSITION IV.
If a River fall into another River, the height of the
firſt in its own Chanel ſhall be to the height that it
ſhall make in the ſecond Chanel, in a proportion
compounded of the proportions of the breadth of
the Chanel of the ſecond, to the breadth of the
Chanel of the firſt, and of the velocitie acquired in
the Chanel of the ſecond, to that which it had in
its proper and first Chanel.
firſt in its own Chanel ſhall be to the height that it
ſhall make in the ſecond Chanel, in a proportion
compounded of the proportions of the breadth of
the Chanel of the ſecond, to the breadth of the
Chanel of the firſt, and of the velocitie acquired in
the Chanel of the ſecond, to that which it had in
its proper and first Chanel.
Let the River A B, whoſe height is A C, and breadth C B,
that is, whoſe Section is A C B; let it enter, I ſay, into a
nother River as broad as the line E F, and let it therein make
the riſe or height D E, that is to ſay, let it have its Section in
the River whereinto it falls D E F; I ſay, that the height A C
hath to the height D E the proportion compounded of the pro
portions of the breadth E F, to the breadth C B, and of the ve
locity through D F, to the velocity through A B. Let us ſup
poſe the Section G, equal in velocity to the Section A B, and in
breadth equal to E F, which carrieth a quantity of Water e
qual to that which the Section A B carrieth, in equal times,
and conſequently, equal to that which D F carrieth. Moreover,
as the breadth E F is to the breadth C B, ſo let the line H be to
that is, whoſe Section is A C B; let it enter, I ſay, into a
nother River as broad as the line E F, and let it therein make
the riſe or height D E, that is to ſay, let it have its Section in
the River whereinto it falls D E F; I ſay, that the height A C
hath to the height D E the proportion compounded of the pro
portions of the breadth E F, to the breadth C B, and of the ve
locity through D F, to the velocity through A B. Let us ſup
poſe the Section G, equal in velocity to the Section A B, and in
breadth equal to E F, which carrieth a quantity of Water e
qual to that which the Section A B carrieth, in equal times,
and conſequently, equal to that which D F carrieth. Moreover,
as the breadth E F is to the breadth C B, ſo let the line H be to