Archimedes Texts

98
aforementioned Cases, and in the present one that we are in hand
with, there have, in times past, very grosse Errours been com
mitted, through the not having ever well understood the true
measure of Running waters; and here it is to be noted, that the
businesse is, that in Venice, the diversion of the waters of the
Lake, by diverting the Brent was debated, and in part executed,
without consideration had how great abatement of water might
follow in the Lake, if the Brent were diverted, as I have shewn
in the first Consideration upon this particular, from which act
there hath insued very bad consequences, not only the difficulty
of Navigation, but it hath infected the wholsomnesse of the Air,
and caused the stoppage of the Ports of Venice. And on the
contrary, the same inadvertency of not considering what rising of
the Water the Reno, and other Rivers being opened into the Val
leys of Bologna and Ferrara, might cause in the said Valleys, is
the certain cause that so many rich and fertile Fields are drown
ed under water, converting the happy habitations and dwellings
of men into miserable receptacles for Fishes: Things which
doubtlesse would never have happened, if those Rivers had been
kept at their height, and Reno had been turn'd into Main-Po,
and the other Rivers into that of Argenta, and of Volano. Now
there having sufficient been spoken by the above-named Monsig.
Corsini in his Relation, I will only adde one conceit of my own,
which after the Rivers should be regulated, as hath been said, I
verily believe would be of extraordinary profit, I much doubt in
deed that I shall finde it a hard matter to perswade men to be of
my mind, but yet nevertheless I will not question, but that those,
at least, who shall have understood what I have said and demon
strated concerning the manners and proportions, according to
which the abatements and risings of Running waters proceed,
that are made by the Diversions and Introductions of Waters,
will apprehend that my conjecture is grounded upon Reason.
And although I descend not to the exactnesse of particulars, I
will open the way to others, who having observed the requisite
Rules of considering the quantity of the waters that are intro
duced, or that happen to be diverted, shall be able with punctu
ality to examine the whole businesse, and then resolve on that
which shall be expedient to be done.

Reflecting therefore upon the first Proposition, that the
Risings of a Running Water made by the accession of new water
into the River, are to one another, as the Square-Roots of the
quantity of the water that runneth; and consequently, that the
same cometh to pass in the Diversions: Insomuch, that a River
running in height one such a certain measure, to make it encrease
double in height, the water is to be encreased to three times as