1him be never ſo great a Wit, can never promiſe to frame a con
ceit of the quantity of the Body of Water, without the third
Dimenſion of length: and hereupon I return to affirm, that the
vulgar Rule of meaſuring Running water is vain and erroneous.
This point being agreed on, I come to the ſecond, which is, Whe
ther the third Dimenſion of length may be meaſured. And I ſay,
that if one would know the whole length of the water of a
Fountain or River, thereby to come to know the quantity of all
the Water, it would prove an impoſſible enterprize, nay the
knowing of it would not be uſeful. But if one would know how
much water a Fountain, or a River carrieth in a determinate time
of an hour, of a day, or of a moneth, &c. I ſay, that it is a very
poſſible and profitable enquiry, by reaſon of the innumerable
benefits that may be derived thence, it much importing to know
how much Water a Chanel carrieth in a time given; and I have
demonſtrated the ſame above in the beginning of this Book; and
of this we ſtand in need in the buſineſſe of the Lake, that ſo we
may be able to determine how much ſhall be the height of the
Brent, when it is ſpread all over the Lake: For the three dimen
ſions of a Body being given, the Body is known; and the quan
tity of a Body being given, if you have but two dimenſions, the
third ſhall be known. And thus diving farther and farther into
this Conſideration, I found that the Velocity of the courſe of the
water may be an hundred times greater or leſſer in one part of
its Chanel than in another. And therefore although there ſhould
be two mouths of Waters equal in bigneſſe; yet nevertheleſs it
might come to paſſe, that one might diſcharge an hundred or a
thouſand times more water than another: and this would be, if
the water in one of the mouths ſhould run with an hundred or a
thouſand times greater velocity, than the other; for that it
would be the ſame as to ſay, that the ſwifter was an hundred or
a thouſand times longer, than the ſlower: and in this manner I
diſcovered that to keep account of the velocity, was the keeping
account of the Length.
ceit of the quantity of the Body of Water, without the third
Dimenſion of length: and hereupon I return to affirm, that the
vulgar Rule of meaſuring Running water is vain and erroneous.
This point being agreed on, I come to the ſecond, which is, Whe
ther the third Dimenſion of length may be meaſured. And I ſay,
that if one would know the whole length of the water of a
Fountain or River, thereby to come to know the quantity of all
the Water, it would prove an impoſſible enterprize, nay the
knowing of it would not be uſeful. But if one would know how
much water a Fountain, or a River carrieth in a determinate time
of an hour, of a day, or of a moneth, &c. I ſay, that it is a very
poſſible and profitable enquiry, by reaſon of the innumerable
benefits that may be derived thence, it much importing to know
how much Water a Chanel carrieth in a time given; and I have
demonſtrated the ſame above in the beginning of this Book; and
of this we ſtand in need in the buſineſſe of the Lake, that ſo we
may be able to determine how much ſhall be the height of the
Brent, when it is ſpread all over the Lake: For the three dimen
ſions of a Body being given, the Body is known; and the quan
tity of a Body being given, if you have but two dimenſions, the
third ſhall be known. And thus diving farther and farther into
this Conſideration, I found that the Velocity of the courſe of the
water may be an hundred times greater or leſſer in one part of
its Chanel than in another. And therefore although there ſhould
be two mouths of Waters equal in bigneſſe; yet nevertheleſs it
might come to paſſe, that one might diſcharge an hundred or a
thouſand times more water than another: and this would be, if
the water in one of the mouths ſhould run with an hundred or a
thouſand times greater velocity, than the other; for that it
would be the ſame as to ſay, that the ſwifter was an hundred or
a thouſand times longer, than the ſlower: and in this manner I
diſcovered that to keep account of the velocity, was the keeping
account of the Length.
And therefore it is manifeſt, that when two Mouths diſcharge
the ſame quantity of Wa r in an equal velocity, it is neceſſary
that the leſs ſwift Mouth be ſo much bigger than the more ſwift;
as the more ſwift exceedeth in velocity the leſs ſwift; as for
example.
the ſame quantity of Wa r in an equal velocity, it is neceſſary
that the leſs ſwift Mouth be ſo much bigger than the more ſwift;
as the more ſwift exceedeth in velocity the leſs ſwift; as for
example.
In caſe two Rivers ſhould carry equal quantity of water in
equal times, but that one of them ſhould be four times more
ſwift than the other, the more ſlow ſhould of neceſſity be four
times more large. And becauſe the ſame River in any part
thereof alwaies diſchargeth the ſame quantity of Water in equal
times (as is demonſtrated in the firſt Propoſition of the firſt
equal times, but that one of them ſhould be four times more
ſwift than the other, the more ſlow ſhould of neceſſity be four
times more large. And becauſe the ſame River in any part
thereof alwaies diſchargeth the ſame quantity of Water in equal
times (as is demonſtrated in the firſt Propoſition of the firſt