1being equally ſwift) ſhall be in proportion as the Section L N, to
the Section A F; that is, as D B, to A B; that is as the line S, to
the line T: Therefore by equal proportion, the quantity of the
water which runneth through D F, ſhall be in proportion to that
which runneth through A F, as R is to T; that is, compounded of
the proportions of the height D B, to the height A B, and of the
velocity through D F, to the velocity through A F; and therefore
if a River diſcharge a certain quantity, &c. which was to be de
monſtrated.
the Section A F; that is, as D B, to A B; that is as the line S, to
the line T: Therefore by equal proportion, the quantity of the
water which runneth through D F, ſhall be in proportion to that
which runneth through A F, as R is to T; that is, compounded of
the proportions of the height D B, to the height A B, and of the
velocity through D F, to the velocity through A F; and therefore
if a River diſcharge a certain quantity, &c. which was to be de
monſtrated.
ANNOTATION.
The ſame might have been demonſtrated by the ſecond
Propoſition above demonſtrated, as is manifeſt.
Propoſition above demonſtrated, as is manifeſt.
PROPOSITION VI.
If two equal ſtreams of the ſame Torrent, fall into a
River at divers times, the heights made in the Ri
ver by the Torrent, ſhall have between them
ſelves the reciprocal proportion of the velocities
acquired in the River.
River at divers times, the heights made in the Ri
ver by the Torrent, ſhall have between them
ſelves the reciprocal proportion of the velocities
acquired in the River.
Let A and B, be two equal ſtreams of the ſame Torrent,
which falling into a River at divers times, make the heights
C D, and F G; that is the ſtream A, maketh the height
C D, and the ſtream B, maketh the height F G; that is, Let
their Sections in the River, into which they are fallen, be C E,
and FH; I ſay, that the height C D, ſhall be to the height F G,
in reciprocal proportion, as the velocity through F H, to the ve
locity through C E; for the quantity of water which paſſeth
through A, being equal to the quantity which paſſeth through B,
in equal times; alſo the quantity which paſſeth through C E, ſhall
44[Figure 44]
be equal to that which paſſeth through F H: And therefore the
proportion that the Section C E, hath to the Section F H; ſhall
be the ſame that the velocity through F H, hath to the velocity
through C E; But the Section C E, is to the Section F H, as
C D, to F G, by reaſon they are of the ſame breadth: Therefore
C D, ſhall be to F G, in reciprocal proportion, as the velocity
through F H, is to the velocity through C E, and therefore if two
equal ſtreams of the ſame Torrent, &c. which was to be de
monſtrated.
which falling into a River at divers times, make the heights
C D, and F G; that is the ſtream A, maketh the height
C D, and the ſtream B, maketh the height F G; that is, Let
their Sections in the River, into which they are fallen, be C E,
and FH; I ſay, that the height C D, ſhall be to the height F G,
in reciprocal proportion, as the velocity through F H, to the ve
locity through C E; for the quantity of water which paſſeth
through A, being equal to the quantity which paſſeth through B,
in equal times; alſo the quantity which paſſeth through C E, ſhall
44[Figure 44]be equal to that which paſſeth through F H: And therefore the
proportion that the Section C E, hath to the Section F H; ſhall
be the ſame that the velocity through F H, hath to the velocity
through C E; But the Section C E, is to the Section F H, as
C D, to F G, by reaſon they are of the ſame breadth: Therefore
C D, ſhall be to F G, in reciprocal proportion, as the velocity
through F H, is to the velocity through C E, and therefore if two
equal ſtreams of the ſame Torrent, &c. which was to be de
monſtrated.
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