Archimedes Texts

6
particular accidents in this admirable matter, and all depending
on this sole Proposition, the sense of which I have oft repeated,
that it might be well understood.

And first, we hence conclude, that the same Streams of a
Torrent, namely, those streams which carry equal quantity of
Water in equal times, make not the same depths or measures in
the River, in which they enter, unlesse when in the entrance in
to the River they acquire; or to say better, keep the same velo
city; because if the velocicities acquired in the River shall be
different, also the measures shall be diverse; and consequently
the depths, as is demonstrated.

And because successively, as the River is more and more full,
it is constituted ordinarily in greater & greater velocity: hence
it is that the same streams of the Torrent, that enter into the Ri
ver, make lesse and lesse depths, as the River grows more and
more full; since that also the Waters of the Torrent being en
tered into the River, go acquiring greater and greater velocities,
and therefore diminish in measure and height.

We observe also, that while the main River is shallow, if there
fall but a gentle rain, it suddenly much increaseth and riseth;
but when the River is already swelled, though there fall again a
nother new violent shower, yet it increaseth not at the same rate
as before, proportionably to the rain which fell: which thing
we may affirm particularly to depend on this, that in the first
case, while the River is low, it is found also very slow, and there
fore the little water which entereth into it, passeth and runs with
little velocity, and consequently occupieth a great measure:
But when the River is once augmented, by new water being also
made more swift, it causeth the great Flood of water which fal
leth, to bear a lesse measure, and not to make such a depth.

From the things demonstrated is manifest also, that whilst a
Torrent entereth into a River, at the time of Ebbe, then the
Torrent moveth with such a certain velocity, what ever it be,