Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Figures
Thumbnails
Page concordance
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 300
301 - 330
331 - 360
361 - 390
391 - 420
421 - 450
451 - 480
481 - 510
511 - 540
541 - 570
571 - 600
601 - 630
631 - 660
661 - 690
691 - 701
>
Scan
Original
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 300
301 - 330
331 - 360
361 - 390
391 - 420
421 - 450
451 - 480
481 - 510
511 - 540
541 - 570
571 - 600
601 - 630
631 - 660
661 - 690
691 - 701
>
page
|<
<
of 701
>
>|
<
archimedes
>
<
text
>
<
body
>
<
chap
>
<
p
type
="
main
">
<
s
>
<
pb
xlink:href
="
040/01/618.jpg
"
pagenum
="
52
"/>
<
emph
type
="
italics
"/>
the fourth
<
emph.end
type
="
italics
"/>
Theorem
<
emph
type
="
italics
"/>
of this, with its Table, and the uſe there
<
lb
/>
of annexed.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
head
">
<
s
>
<
emph
type
="
italics
"/>
COROLLARIE
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>Hence it followeth, that when a River increaſeth in quick
<
lb
/>
height by the addition of new water, it alſo increaſeth in ve
<
lb
/>
locity; ſo that the velocity hath the ſame proportion to the velo
<
lb
/>
city that the quick height hath to the quick height; as may be
<
lb
/>
demonſtrated in the ſame manner.</
s
>
</
p
>
<
p
type
="
head
">
<
s
>PROPOS. III. PROBLEME II.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Achanel of Water being given whoſe breadth exceeds not
<
lb
/>
twenty Palms, or thereabouts, and whoſe quick beight
<
lb
/>
is leſs than five Palms, to meaſure the quantity of the
<
lb
/>
Water that runneth thorow the Chanel in a time
<
lb
/>
given.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>Place in the Chanel a Regulator, and obſerve the quick
<
lb
/>
height in the ſaid Regulator; then let the water be turned
<
lb
/>
away from the Chanel by a Chanellet of three or four Palms
<
lb
/>
in breadth, or thereabouts: And that being done, meaſure the
<
lb
/>
quantity of the water which paſſeth thorow the ſaid Chanellet,
<
lb
/>
as hath been taught in the ſecond Propoſition; and at the ſame
<
lb
/>
time obſerve exactly how much the quick height ſhall be abated
<
lb
/>
in the greater Chanel, by means of the diverſion of the Chancl
<
lb
/>
let; and all theſe particulars being performed, multiply the quick
<
lb
/>
height of the greater Chanel into it ſelf, and likewiſe multiply
<
lb
/>
into it ſelf the leſſer height of the ſaid bigger Chanel, and the
<
lb
/>
leſſer ſquare being taken, from the greater, the remainder ſhall
<
lb
/>
have the ſame proportion to the whole greater ſquare, as the wa
<
lb
/>
ter of the Chanellet diverted, hath to the water of the bigger
<
lb
/>
Chanel: And becauſe the water of the Chanellet is known by
<
lb
/>
the Method laid down in the firſt Theorem, and the terms of the
<
lb
/>
Theorem being alſo known, the quantity of the water which run
<
lb
/>
neth thorow the bigger Chanel, ſhall be alſo known by the Gol
<
lb
/>
den
<
emph
type
="
italics
"/>
R
<
emph.end
type
="
italics
"/>
ule, which was that that was deſired to be known. </
s
>
<
s
>We
<
lb
/>
will explain the whole buſineſs by an example.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>Let a Chanel be, for example, 15 Palms broad, its quick height
<
lb
/>
before its diverſion by the Chanellet ſhall be ſuppoſed to be 24
<
lb
/>
inches; but after the diverſion, let the quick height of the Chanel
<
lb
/>
be onely 22 inches. </
s
>
<
s
>Therefore the greater height to the leſſer,
<
lb
/>
is as the number 11. to 12. But the ſquare of 11. is 121, and the
<
lb
/>
ſquare of 12. is 144, the difference between the ſaid leſſer </
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>