Archimedes Texts

93
for that amongst so many tryals as have been made, that also
was light upon, on which the improvement and remedy to the
disorder did depend. And to us my fore-named Treatise shall
serve for a Rule, which being well understood, shall make us to
know wherein consisteth, and whereon dependeth this miscarri
age, and consequently it will be easie to apply thereunto a seaso
nable remedy.

And first I say, That there is no doubt but that the waters
continue so high on those Plains because they are so high in the
principal River, which ought to receive them, and carry them
into the Sea. Now the Causes of the height of the River, may
in my judgement be reduced to one alone; which is that by me
so often mentioned for the most Potent one, and declared in my
afore-named Tractate; to wit, The tardity of the motion of the
waters, which doth alwayes infallibly, and precisely cause the
self same Running Water to change the measure of its thickness
at such a rate, that the more it encreaseth in velocity, the more
it decreaseth in measure; and the more it decreaseth in velocity,
the more it encreaseth in measure: As for example; If a River
run in such a place with the velocity of moving a mile in the
space of an hour, and afterwards the same River in another place
doth encrease in velocity, so as to make three miles an hour;
that same River shall diminish in thickness two thirds: And on
the contrary, If it shall diminish in velocity so, as that it runneth
but half a mile in the same time, it shall encrease the double in
thickness and measure. And in a word, look what proportion
the velocity in the first place, hath to the velocity in the second,
and such hath reciprocally the measure of the thickness in the
second place, to the measure in the first; as I have clearly demon
strated in my Treatise: Which I repeat so frequently, that I
fear the Professors of Polite Learning will charge me with Tua
tologie, and vain Repetition. But I am so desirous in this most
important point to be well understood, because it will then be
easie to comprehend all the rest; and without this it is impossible
(I will not say difficult, but absolutely impossible) to understand,
or ever to effect any thing to purpose. And the better to ex
plain the example, let it be supposed,

That the water of a River A D,
runneth high at the level of A F,
with such a certain velocity; and let
it, by the same water, be velocitated
three times more; I say, that it will
abate 1/3, and shall stand at the level
in B E; and if it shall more veloci
tate, it will abate the more at the Sea; But if it should retard