1velocity of the parts of the thread paſſed the hole, than the volo
city of the parts before the hole: Inſomuch that if verbi gratia
the thickneſſe of the thread before the hole, were double to the
thickneſſe after the hole, in ſuch caſe the velocity of the parts of
the thread paſſed the hole, ſhould be double to the velocity of the
parts of the thread before the hole; and thus the thickneſſe
compenſates the velocity, and the velocity compenſates the thick
neſſe. So that the ſame occurreth in the ſolid Metals of Gold,
Silver, Braſs, Iron, &c. that eveneth alſo in the fluid Element of
Water, and other liquids, namely, That the velocity beareth the
ſame proportion to the velocity, that the thickneſſe of the Me
tal, or Water, hath to the thickneſſe.
city of the parts before the hole: Inſomuch that if verbi gratia
the thickneſſe of the thread before the hole, were double to the
thickneſſe after the hole, in ſuch caſe the velocity of the parts of
the thread paſſed the hole, ſhould be double to the velocity of the
parts of the thread before the hole; and thus the thickneſſe
compenſates the velocity, and the velocity compenſates the thick
neſſe. So that the ſame occurreth in the ſolid Metals of Gold,
Silver, Braſs, Iron, &c. that eveneth alſo in the fluid Element of
Water, and other liquids, namely, That the velocity beareth the
ſame proportion to the velocity, that the thickneſſe of the Me
tal, or Water, hath to the thickneſſe.
And therefore granting this diſcourſe, we may ſay, that as of
ten as two Taps with different velocity diſcharge equal quanti
ties of Water in equal times, it will be neceſſary that the Tap
leſſe ſwift be ſo much greater, and larger, than the Tap more
ſwift, by how much the ſwifter ſuperates in velocity the ſlower;
and to pronounce the Propoſition in more proper terms, we ſay;
That if two Taps of unequal velocity, diſcharge in equal times
equal quantities of Water, the greatneſſe of the firſt ſhall be to
the greatneſſe of the ſecond, in reciprocal proportion, as the ve
locity of the ſecond to the velocity of the firſt. As for example,
if the firſt Tap ſhall be ten times ſwifter than the ſecond Tap, it
will be neceſſary, that the ſecond be ten times bigger and larger
than the firſt; and in ſuch caſe the Taps ſhall diſcharge equall
quantities of water in equal times; and this is the principal and
moſt important point, which ought to be kept alwayes in minde,
for that on it well underſtood depend many things profitable,
and worthy of our knowledge.
ten as two Taps with different velocity diſcharge equal quanti
ties of Water in equal times, it will be neceſſary that the Tap
leſſe ſwift be ſo much greater, and larger, than the Tap more
ſwift, by how much the ſwifter ſuperates in velocity the ſlower;
and to pronounce the Propoſition in more proper terms, we ſay;
That if two Taps of unequal velocity, diſcharge in equal times
equal quantities of Water, the greatneſſe of the firſt ſhall be to
the greatneſſe of the ſecond, in reciprocal proportion, as the ve
locity of the ſecond to the velocity of the firſt. As for example,
if the firſt Tap ſhall be ten times ſwifter than the ſecond Tap, it
will be neceſſary, that the ſecond be ten times bigger and larger
than the firſt; and in ſuch caſe the Taps ſhall diſcharge equall
quantities of water in equal times; and this is the principal and
moſt important point, which ought to be kept alwayes in minde,
for that on it well underſtood depend many things profitable,
and worthy of our knowledge.
Now applying all that hath been ſaid neerer to our purpoſe, I
conſider, that it being moſt true, that in divers parts of the ſame
River or Current of running water, there doth always paſſe equal
quantity of Water in equal time (which thing is alſo demon
ſtrated in out firſt Propoſition) and it being alſo true, that in di
vers parts the ſame River may have various and different veloci
ty; it follows of neceſſary conſequence, that where the River
hath leſſe velocity, it ſhall be of greater meaſure, and in thoſe
parts, in which it hath greater velocity, it ſhall be of leſſe mea
ſure; and in ſum, the velocity of ſeveral parts of the ſaid River,
ſhall have eternally reciprocall and like proportion with
their meaſures. This principle and fundamental well eſtabliſh
ed, that the ſame Current of Water changeth meaſure, accor
ding to its varying of velocity; that is, leſſening the meaſure,
when the velocity encreaſeth, and encreaſing the meaſure, when
the velocity decreaſeth; I paſſe to the conſideration of many
conſider, that it being moſt true, that in divers parts of the ſame
River or Current of running water, there doth always paſſe equal
quantity of Water in equal time (which thing is alſo demon
ſtrated in out firſt Propoſition) and it being alſo true, that in di
vers parts the ſame River may have various and different veloci
ty; it follows of neceſſary conſequence, that where the River
hath leſſe velocity, it ſhall be of greater meaſure, and in thoſe
parts, in which it hath greater velocity, it ſhall be of leſſe mea
ſure; and in ſum, the velocity of ſeveral parts of the ſaid River,
ſhall have eternally reciprocall and like proportion with
their meaſures. This principle and fundamental well eſtabliſh
ed, that the ſame Current of Water changeth meaſure, accor
ding to its varying of velocity; that is, leſſening the meaſure,
when the velocity encreaſeth, and encreaſing the meaſure, when
the velocity decreaſeth; I paſſe to the conſideration of many
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