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
>
<
p
type
="
main
">
<
s
>
<
pb
xlink:href
="
040/01/1065.jpg
"
pagenum
="
371
"/>
Portion demitted into the Liquid, like as hath been ſaid, ſhall ſtand
<
lb
/>
enclined ſo as that its Axis do make an Angle with the Surface of
<
lb
/>
the Liquid equall unto the Angle E B
<
foreign
lang
="
grc
">Ψ.</
foreign
>
For demit any Portion
<
lb
/>
into the Liquid ſo as that its Baſe
<
lb
/>
<
figure
id
="
id.040.01.1065.1.jpg
"
xlink:href
="
040/01/1065/1.jpg
"
number
="
265
"/>
<
lb
/>
touch not the Liquids Surface;
<
lb
/>
and, if it can be done, let the
<
lb
/>
Axis not make an Angle with the
<
lb
/>
Liquids Surface equall to the
<
lb
/>
Angle E B
<
foreign
lang
="
grc
">Ψ</
foreign
>
; but firſt, let it be
<
lb
/>
greater: and the Portion being
<
lb
/>
cut thorow the Axis by a Plane e
<
lb
/>
rect unto [
<
emph
type
="
italics
"/>
or upon
<
emph.end
type
="
italics
"/>
] the Surface of
<
lb
/>
the Liquid, let the Section be A P
<
lb
/>
O L the Section of a Rightangled
<
lb
/>
Cone; the Section of the Surface of the Liquid X S; and let the
<
lb
/>
Axis of the Portion and Diameter of the Section be N O: and
<
lb
/>
draw P Y parallel to X S, and touching the Section A P O L in P;
<
lb
/>
and P M parallel to N O; and P I perpendicular to N O: and
<
lb
/>
moreover, let B R be equall to O
<
foreign
lang
="
grc
">ω,</
foreign
>
and R K to T
<
foreign
lang
="
grc
">ω;</
foreign
>
and let
<
foreign
lang
="
grc
">ω</
foreign
>
H
<
lb
/>
be perpendicular to the Axis. </
s
>
<
s
>Now becauſe it hath been ſuppoſed
<
lb
/>
<
arrow.to.target
n
="
marg1241
"/>
<
lb
/>
that the Axis of the Portion doth make an Angle with the Surface
<
lb
/>
of the Liquid greater than the Angle B, the Angle P Y I ſhall be
<
lb
/>
greater than the Angle B: Therefore the Square P I hath greater
<
lb
/>
<
arrow.to.target
n
="
marg1242
"/>
<
lb
/>
proportion to the Square Y I, than the Square E
<
foreign
lang
="
grc
">Ψ</
foreign
>
hath to the
<
lb
/>
Square
<
foreign
lang
="
grc
">Ψ</
foreign
>
B: But as the Square P I is to the Square Y I, ſo is the
<
lb
/>
<
arrow.to.target
n
="
marg1243
"/>
<
lb
/>
Line K R unto the Line I Y; and as the Square E
<
foreign
lang
="
grc
">Ψ</
foreign
>
is to the Square
<
lb
/>
<
arrow.to.target
n
="
marg1244
"/>
<
lb
/>
<
foreign
lang
="
grc
">Ψ</
foreign
>
B, ſo is half of the Line K R unto the Line
<
foreign
lang
="
grc
">Ψ</
foreign
>
B: Wherefore
<
lb
/>
<
emph
type
="
italics
"/>
(a)
<
emph.end
type
="
italics
"/>
K R hath greater proportion to I Y, than the half of K R hath
<
lb
/>
<
arrow.to.target
n
="
marg1245
"/>
<
lb
/>
to
<
foreign
lang
="
grc
">Ψ</
foreign
>
B: And, conſequently, I Y isleſſe than the double of
<
foreign
lang
="
grc
">Ψ</
foreign
>
B,
<
lb
/>
and is the double of O I: Therefore O I is leſſe than
<
foreign
lang
="
grc
">Ψ</
foreign
>
B; and I
<
foreign
lang
="
grc
">ω</
foreign
>
<
lb
/>
<
arrow.to.target
n
="
marg1246
"/>
<
lb
/>
greater than
<
foreign
lang
="
grc
">Ψ</
foreign
>
R: but
<
foreign
lang
="
grc
">Ψ</
foreign
>
R is equall to F: Therefore I
<
foreign
lang
="
grc
">ω</
foreign
>
is greater
<
lb
/>
<
arrow.to.target
n
="
marg1247
"/>
<
lb
/>
than F. </
s
>
<
s
>And becauſe that the Portion is ſuppoſed to be in Gra
<
lb
/>
vity unto the Liquid, as the Square F Q is to the Square B D; and
<
lb
/>
ſince that as the Portion is to the Liquid in Gravity, ſo is the part
<
lb
/>
thereof ſubmerged unto the whole Portion; and in regard that as
<
lb
/>
the part thereof ſubmerged is to the whole, ſo is the Square P M to
<
lb
/>
the Square O N; It followeth, that the Square P M is to the Square
<
lb
/>
N O, as the Square F Q is to the Square B D: And therefore F
<
lb
/>
<
arrow.to.target
n
="
marg1248
"/>
<
lb
/>
Q is equall to P M: But it hath been demonſtrated that P H is
<
lb
/>
<
arrow.to.target
n
="
marg1249
"/>
<
lb
/>
greater than F: It is manifeſt, therefore, that P M is leſſe than
<
lb
/>
ſeſquialter of P H: And conſequently that P H is greater than
<
lb
/>
the double of H M. </
s
>
<
s
>Let P Z be double to Z M: T ſhall be the Cen
<
lb
/>
tre of Gravity of the whole Solid; the Centre of that part of it
<
lb
/>
which is within the Liquid, the Point Z; and of the remaining
<
lb
/>
<
arrow.to.target
n
="
marg1250
"/>
<
lb
/>
part the Centre ſhall be in the Line Z T prolonged unto G. </
s
>
<
s
>In </
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>