Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
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 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 220
221 - 230
231 - 240
241 - 250
251 - 260
261 - 270
271 - 280
281 - 290
291 - 300
301 - 310
311 - 320
321 - 330
331 - 340
341 - 350
351 - 360
361 - 370
371 - 380
381 - 390
391 - 400
401 - 410
411 - 420
421 - 430
431 - 440
441 - 450
451 - 460
461 - 470
471 - 480
481 - 490
491 - 500
501 - 510
511 - 520
521 - 530
531 - 540
541 - 550
551 - 560
561 - 570
571 - 580
581 - 590
591 - 600
601 - 610
611 - 620
621 - 630
631 - 640
641 - 650
651 - 660
661 - 670
671 - 680
681 - 690
691 - 700
701 - 701
>
241
242
243
244
245
246
247
248
249
250
<
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 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 220
221 - 230
231 - 240
241 - 250
251 - 260
261 - 270
271 - 280
281 - 290
291 - 300
301 - 310
311 - 320
321 - 330
331 - 340
341 - 350
351 - 360
361 - 370
371 - 380
381 - 390
391 - 400
401 - 410
411 - 420
421 - 430
431 - 440
441 - 450
451 - 460
461 - 470
471 - 480
481 - 490
491 - 500
501 - 510
511 - 520
521 - 530
531 - 540
541 - 550
551 - 560
561 - 570
571 - 580
581 - 590
591 - 600
601 - 610
611 - 620
621 - 630
631 - 640
641 - 650
651 - 660
661 - 670
671 - 680
681 - 690
691 - 700
701 - 701
>
page
|<
<
of 701
>
>|
<
archimedes
>
<
text
>
<
body
>
<
chap
>
<
pb
xlink:href
="
040/01/1055.jpg
"
pagenum
="
361
"/>
<
p
type
="
head
">
<
s
>PROP. V. THEOR. V.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
The Right Portion of a Right-Angled Conoid lighter
<
lb
/>
than the Liquid, when it ſhall have its Axis great
<
lb
/>
er than
<
emph.end
type
="
italics
"/>
Seſquialter
<
emph
type
="
italics
"/>
of the Semi-parameter, if it have
<
lb
/>
not greater proportion in Gravity to the Liquid [of
<
lb
/>
equal Maſs] than the Exceſſe by which the Square
<
lb
/>
made of the Axis is greater than the Square made
<
lb
/>
of the Exceſſe by which the Axis is greater than
<
emph.end
type
="
italics
"/>
<
lb
/>
ſeſquialter
<
emph
type
="
italics
"/>
of the Semi-Parameter hath to the
<
lb
/>
Square made of the Axis being demitted into the Li
<
lb
/>
quid, ſo as that its Baſe be wholly within the Liquid,
<
lb
/>
and being ſet inclining, it ſhall not remain ſo inclined,
<
lb
/>
but ſhall turn about till that its Axis ſhall be accor
<
lb
/>
ding to the Perpendicular.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>For let any Portion be demitted into the Liquid, as hath been
<
lb
/>
ſaid; and let its Baſe be wholly within the Liquid, And being
<
lb
/>
cut thorow its Axis by a Plain erect upon the Surface of the
<
lb
/>
Liquid; its Section ſhall be the Section
<
lb
/>
<
figure
id
="
id.040.01.1055.1.jpg
"
xlink:href
="
040/01/1055/1.jpg
"
number
="
254
"/>
<
lb
/>
of a Rightangled Cone: Let it be
<
lb
/>
A P O L, and let the Axis of the Por
<
lb
/>
tion and Diameter of the Section be
<
lb
/>
N O; and the Section of the Surface of
<
lb
/>
the Liquid I S. </
s
>
<
s
>And becauſe the Axis
<
lb
/>
is not according to the Perpendicu
<
lb
/>
lar, N O will not be at equall angles
<
lb
/>
with I S. </
s
>
<
s
>Draw K
<
foreign
lang
="
grc
">ω</
foreign
>
touching the Se
<
lb
/>
ction A P O L in P, and parallel unto
<
lb
/>
I S: and thorow P, draw P F parallel unto N O: and take the
<
lb
/>
Centres of Gravity; and of the Solid A P O L let the Centre be
<
lb
/>
R; and of that which lyeth above the Liquid let the Centre be B;
<
lb
/>
and draw a Line from B to R, prolonging it to G; which let be the
<
lb
/>
Centre of Gravity of the Solid demerged within the Liquid: and
<
lb
/>
moreover, take R H equall to the Semi-parameter, and let O H be
<
lb
/>
double to H M; and do in the reſt as hath been ſaid
<
emph
type
="
italics
"/>
(a)
<
emph.end
type
="
italics
"/>
above.
<
lb
/>
<
arrow.to.target
n
="
marg1206
"/>
<
lb
/>
Now foraſmuch as it was ſuppoſed that the Portion hath not greater
<
lb
/>
proportion in Gravity to the Liquid, than the Exceſſe by which
<
lb
/>
the Square N O is greater than the Square M O, hath to the ſaid
<
lb
/>
Square N O: And in regard that whatever proportion in Gravity </
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>