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
>
31
32
33
34
35
36
37
38
39
40
<
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
>
<
pb
xlink:href
="
068/01/055.jpg
"
pagenum
="
41
"/>
<
p
type
="
head
">
<
s
>PROPOSITION III.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
In two Sections unequal, through which paſs equal
<
lb
/>
quantities of Water in equal times, the Sections
<
lb
/>
have to one another, reciprocal proportion to their
<
lb
/>
velocitie.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>Let the two unequal Sections, by which paſs equal quantities
<
lb
/>
of Water in equal times be A, the greater; and B, the leſſer:
<
lb
/>
I ſay, that the Section A, ſhall have the ſame Proportion
<
lb
/>
to the Section B, that reciprocally the velocity through B, hath to
<
lb
/>
the velocity through A; for ſuppoſing that as the Water that
<
lb
/>
paſſeth through A, is to that which paſſeth through B, ſo is the
<
lb
/>
<
figure
id
="
id.068.01.055.1.jpg
"
xlink:href
="
068/01/055/1.jpg
"
number
="
8
"/>
<
lb
/>
line E to the line F: therefore the quantity of water which paſ
<
lb
/>
ſeth through A, being equal to that which paſſeth through B,
<
lb
/>
the line E ſhall alſo be equal to the line F: Suppoſing moreover,
<
lb
/>
That as the Section A, is to the Section B, ſo is the line F, to the
<
lb
/>
line G; and becauſe the quantity of water which paſſeth
<
lb
/>
through the Section A, is to that which paſſeth through the
<
lb
/>
Section B, in a proportion compoſed of the proportions of the
<
lb
/>
Section A, to the Section B, and of the velocity through A, to the
<
lb
/>
velocity through B; therefore the line E, ſhall be the line to F, in
<
lb
/>
a proportion compounded of the ſame proportions; namely, of
<
lb
/>
the proportion of the Section A, to the Section B, and of the ve
<
lb
/>
locity through A, to the velocity through B; but the line E, hath
<
lb
/>
to the line G, the proportion of the Section A, to the Section B,
<
lb
/>
therefore the proportion remaining of the line G, to the line F,
<
lb
/>
ſhall be the proportion of the velocity through A, to the velocity
<
lb
/>
through B; therefore alſo the line G, ſhall be to the line E, as
<
lb
/>
the velocity by A, to the velocity by B: And converſly, the ve
<
lb
/>
locity through B, ſhall be to the velocity through A, as the line
<
lb
/>
E, to the line G; that is to ſay, as the Section A, to the Section B,
<
lb
/>
and therefore in two Sections, &c. </
s
>
<
s
>which was to be demonſtrated.</
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>