Archimedes Texts

9
the River, in such a case there must follow very great and irre
pable innundations.

From what hath been demonstrated, we may with facility re
solve the doubt which hath troubled, and still poseth the most
diligent, but incautelous observers of Rivers, who measuring
the Streams and Torrents which fall into another River; as those
for instance, which enter into the Po, or those which fall into Ti
ber; and having summed the total of these measures, and con
ferring the measures of the Rivers and Brooks, which fall into
Tiber, with the measure of Tiber, and the measures of those which
disimbogue into Po, with the measure of Po, they find them not
equal, as, it seems to them, they ought to be, and this is because
they have not well noted the most important point of the varia
tion of velocity, and how that it is the most potent cause of won
derfully altering the measures of running Waters; but we most
facilly resolving the doubt, may say that these Waters diminish
the measure, being once entered the principal Channel, because
they increase in velocity.

Through the ignorance of the force of the velocity of the Wa
ter, in altering its measure, & augmenting it when the velocity
diminisheth; and diminishing it when the velocity augmenteth:
The Architect Giovanni Fontana, endeavoured to measure, and
and to cause to be measured by his Nephew, all the Brooks and
Rivers which discharged their Waters into Tiber, at the time of
the Innundation; which happened at Rome in the year 1598,
and published a small Treatise thereof, wherein he summeth up
the measures of the extraordinary Water which fell into Tiber,
and made account that it was about five hundred Ells more than
ordinary; and in the end of that Treatise concludeth, that to re
move the Innundation wholly from Rome, it would be necessary
to make two other Channels, equal to that at present, and that
lesse would not suffice; and finding afterwards that the whole
Stream passed under the Bridge Quattro-Capi, (the Arch where
of is of a far less measure then five hundred Ells) concludeth,
that under the said Bridge past a hundred fifty one Ells of Water
compressed, (I have set down the precise term of comprest Wa
ter, written by Fontana) wherein I finde many errors.

The first of which is to think that the measures of these Wa
ters compressed in the Channels of those Brooks and Rivers,