Archimedes Texts

70
him 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.

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.

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