Archimedes Texts

69
not give me a certain and stable measure and quantity of Water,
began deservedly to be suspected by me, as difficult and defective,
being alwayes various, and the measure, on the contrary, being
to be alwayes determinate, and the same; it is therefore written,
that Pondus & Pondus, Mensura & Mensura, utrumque abomi
nabile est apud Deum, Exod. I considered that in the Terri
tory of Brescia, my native Countrey, and in other places, where
Waters are divided to overflow the Grounds, by the like way of
measuring them, there were committed grievous and most impor
tant errours, to the great prejudice of the Publique and of Pri
vate persons, neither they that sell, nor they that buy under
standing the true quantity of that which is sold and bought: In
regard that the same square measure, as is accustomed in those
parts, assigned one particular person, carried to sometimes above
twice or thrice as much water, as did the same square measure as
signed to another. Which thing proveth to be the same incon
venience, as if the measure wherewith Wine and Oil is bought
and sold, should hold twice or thrice as much Wine or Oil at one
time as at another. Now this Consideration invited my minde
and curiosity to the finding out of the true measure of Running
Waters. And in the end, by occasion of a most important bu
sinesse that I was imployed in some years since, with great in
tensenesse of minde, and with the sure direction of Geometry, I
have discovered the mistake, which was, that we being upon the
businesse of taking the measure of the Waters that move, do make
use of two dimensions onely, namely, breadth and depth, keep
ing no account of the length. And yet the Water being, though
running, a Body, it is necessary in forming a conceit of its quan
tity, in relation to another, to keep account of all the three Di
mensions, that is of length, breadth, and depth.

Here an objection hath been put to me, in behalf of the ordi
nary way of measuring Running Waters, in opposition to what
I have above considered and proposed: and I was told, Its true,
that in measuring a Body that stands still, one ought to take all
the three Dimensions; but in measuring a Body that continually
moveth, as the Water, the case is not the same: For the length
is not to be had, the length of the water that moveth being infi
nite, as never finishing its running; and consequently is incom
prehensible by humane understanding, and therefore with reason,
nay upon necessity it cometh to be omitted.

In answer to this, I say, that in the abovesaid Discourse, two
things are to be considered distinctly; First, whether it be possible
to frame any conceit of the quantity of the Body of the Water
with two Dimensions onely. And secondly, whether this length
be to be found. As to the first, I am very certain that no man, let