Castelli, Benedetto
,
Of the mensuration of running waters
,
1661
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Figures
Thumbnails
List of thumbnails
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 137
>
51
52
53
54
55
56
57
58
59
60
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 137
>
page
|<
<
of 137
>
>|
<
archimedes
>
<
text
>
<
body
>
<
chap
>
<
p
type
="
main
">
<
s
>
<
pb
xlink:href
="
068/01/107.jpg
"
pagenum
="
93
"/>
for that amongſt ſo many tryals as have been made, that alſo
<
lb
/>
was light upon, on which the improvement and remedy to the
<
lb
/>
diſorder did depend. </
s
>
<
s
>And to us my fore-named Treatiſe ſhall
<
lb
/>
ſerve for a Rule, which being well underſtood, ſhall make us to
<
lb
/>
know wherein conſiſteth, and whereon dependeth this miſcarri
<
lb
/>
age, and conſequently it will be eaſie to apply thereunto a ſeaſo
<
lb
/>
nable remedy.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>And firſt I ſay, That there is no doubt but that the waters
<
lb
/>
continue ſo high on thoſe Plains becauſe they are ſo high in the
<
lb
/>
principal River, which ought to receive them, and carry them
<
lb
/>
into the Sea. </
s
>
<
s
>Now the Cauſes of the height of the River, may
<
lb
/>
in my judgement be reduced to one alone; which is that by me
<
lb
/>
ſo often mentioned for the moſt Potent one, and declared in my
<
lb
/>
afore-named Tractate; to wit, The tardity of the motion of the
<
lb
/>
waters, which doth alwayes infallibly, and preciſely cauſe the
<
lb
/>
ſelf ſame Running Water to change the meaſure of its thickneſs
<
lb
/>
at ſuch a rate, that the more it encreaſeth in velocity, the more
<
lb
/>
it decreaſeth in meaſure; and the more it decreaſeth in velocity,
<
lb
/>
the more it encreaſeth in meaſure: As for example; If a River
<
lb
/>
run in ſuch a place with the velocity of moving a mile in the
<
lb
/>
ſpace of an hour, and afterwards the ſame River in another place
<
lb
/>
doth encreaſe in velocity, ſo as to make three miles an hour;
<
lb
/>
that ſame River ſhall diminiſh in thickneſs two thirds: And on
<
lb
/>
the contrary, If it ſhall diminiſh in velocity ſo, as that it runneth
<
lb
/>
but half a mile in the ſame time, it ſhall encreaſe the double in
<
lb
/>
thickneſs and meaſure. </
s
>
<
s
>And in a word, look what proportion
<
lb
/>
the velocity in the firſt place, hath to the velocity in the ſecond,
<
lb
/>
and ſuch hath reciprocally the meaſure of the thickneſs in the
<
lb
/>
ſecond place, to the meaſure in the firſt; as I have clearly demon
<
lb
/>
ſtrated in my Treatiſe: Which I repeat ſo frequently, that I
<
lb
/>
fear the Profeſſors of Polite Learning will charge me with Tua
<
lb
/>
tologie, and vain Repetition. </
s
>
<
s
>But I am ſo deſirous in this moſt
<
lb
/>
important point to be well underſtood, becauſe it will then be
<
lb
/>
eaſie to comprehend all the reſt; and without this it is impoſſible
<
lb
/>
(I will not ſay difficult, but abſolutely impoſſible) to underſtand,
<
lb
/>
or ever to effect any thing to purpoſe. </
s
>
<
s
>And the better to ex
<
lb
/>
plain the example, let it be ſuppoſed,
<
lb
/>
<
figure
id
="
id.068.01.107.1.jpg
"
xlink:href
="
068/01/107/1.jpg
"
number
="
17
"/>
<
lb
/>
That the water of a River A D,
<
lb
/>
runneth high at the level of A F,
<
lb
/>
with ſuch a certain velocity; and let
<
lb
/>
it, by the ſame water, be velocitated
<
lb
/>
three times more; I ſay, that it will
<
lb
/>
abate 1/3, and ſhall ſtand at the level
<
lb
/>
in B E; and if it ſhall more veloci
<
lb
/>
tate, it will abate the more at the Sea; But if it ſhould retard </
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>