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
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
<
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
="
040/01/1022.jpg
"
pagenum
="
328
"/>
of Direction
<
emph
type
="
italics
"/>
A
<
emph.end
type
="
italics
"/>
D H and
<
emph
type
="
italics
"/>
A
<
emph.end
type
="
italics
"/>
E I are Right
<
emph
type
="
italics
"/>
A
<
emph.end
type
="
italics
"/>
ngles, we ſuppoſe that
<
lb
/>
theſe two
<
emph
type
="
italics
"/>
F
<
emph.end
type
="
italics
"/>
orces I and H weigh alike upon the Center
<
emph
type
="
italics
"/>
A
<
emph.end
type
="
italics
"/>
as if they
<
lb
/>
were nearer to the Center, at the equal Diſtances
<
emph
type
="
italics
"/>
A
<
emph.end
type
="
italics
"/>
B and A C,
<
lb
/>
and we alſo ſuppoſe the ſame if theſe very
<
emph
type
="
italics
"/>
F
<
emph.end
type
="
italics
"/>
orces were ſuſpended
<
lb
/>
both together in
<
emph
type
="
italics
"/>
A,
<
emph.end
type
="
italics
"/>
the
<
emph
type
="
italics
"/>
A
<
emph.end
type
="
italics
"/>
ngles of Directions being ſtill Right
<
lb
/>
<
emph
type
="
italics
"/>
A
<
emph.end
type
="
italics
"/>
ngles.</
s
>
</
p
>
<
p
type
="
head
">
<
s
>PROPOSITION I.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>Theſe Principles agreed upon, we will eaſily demonſtrate,
<
lb
/>
in Imitation of
<
emph
type
="
italics
"/>
Archimedes,
<
emph.end
type
="
italics
"/>
that upon a ſtraight Balance
<
lb
/>
the
<
emph
type
="
italics
"/>
F
<
emph.end
type
="
italics
"/>
orces, of which and of all their parts the Lines of Dire
<
lb
/>
ction are parallel to one another, and perpendicular to the Balance,
<
lb
/>
ſhall couuterpoiſe and make an
<
emph
type
="
italics
"/>
Equilibrium,
<
emph.end
type
="
italics
"/>
when the ſaid
<
emph
type
="
italics
"/>
F
<
emph.end
type
="
italics
"/>
orces
<
lb
/>
ſhall be to one another in Reciprocal proportion of their Arms,
<
lb
/>
which we think to be ſo manifeſt to you, that we thence ſhall de
<
lb
/>
rive the Demonſtration of this Univerſal Propoſition to which we
<
lb
/>
haſten.</
s
>
</
p
>
<
p
type
="
head
">
<
s
>PROPOS. II.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>In every Balance or Leaver, if the proportion of the
<
emph
type
="
italics
"/>
F
<
emph.end
type
="
italics
"/>
orces is
<
lb
/>
reciprocal to that of the Perpendicular Lines drawn from the
<
lb
/>
Center or Point of the
<
emph
type
="
italics
"/>
F
<
emph.end
type
="
italics
"/>
ulciment unto the Lines of Direction
<
lb
/>
of the
<
emph
type
="
italics
"/>
F
<
emph.end
type
="
italics
"/>
orces, drawing the one againſt the other, they ſhall make
<
lb
/>
an
<
emph
type
="
italics
"/>
Equilibrium,
<
emph.end
type
="
italics
"/>
and drawing on one and the ſame ſide, they ſhall
<
lb
/>
have a like Effect, that is to ſay, that they ſhall have as much
<
emph
type
="
italics
"/>
F
<
emph.end
type
="
italics
"/>
orce
<
lb
/>
the one as the other, to move the Balance.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>In this
<
emph
type
="
italics
"/>
F
<
emph.end
type
="
italics
"/>
igure let the Center of the Balance be
<
emph
type
="
italics
"/>
A,
<
emph.end
type
="
italics
"/>
the
<
emph
type
="
italics
"/>
A
<
emph.end
type
="
italics
"/>
rm
<
emph
type
="
italics
"/>
A
<
emph.end
type
="
italics
"/>
B,
<
lb
/>
bigger than
<
emph
type
="
italics
"/>
A
<
emph.end
type
="
italics
"/>
C, and firſt let the
<
emph
type
="
italics
"/>
L
<
emph.end
type
="
italics
"/>
ines of Direction B D, and E C
<
lb
/>
be perpendicular to the
<
emph
type
="
italics
"/>
A
<
emph.end
type
="
italics
"/>
rms
<
emph
type
="
italics
"/>
A
<
emph.end
type
="
italics
"/>
B and
<
emph
type
="
italics
"/>
A
<
emph.end
type
="
italics
"/>
C, by which Lines the
<
lb
/>
<
emph
type
="
italics
"/>
F
<
emph.end
type
="
italics
"/>
orces D and E (which may be made of Weights if one will) do
<
lb
/>
draw; and that there is the ſame rate
<
lb
/>
<
figure
id
="
id.040.01.1022.1.jpg
"
xlink:href
="
040/01/1022/1.jpg
"
number
="
225
"/>
<
lb
/>
of the
<
emph
type
="
italics
"/>
F
<
emph.end
type
="
italics
"/>
orce D to the Force E as there
<
lb
/>
is betwixt the
<
emph
type
="
italics
"/>
A
<
emph.end
type
="
italics
"/>
rm
<
emph
type
="
italics
"/>
A
<
emph.end
type
="
italics
"/>
C to the Arm
<
lb
/>
<
emph
type
="
italics
"/>
A
<
emph.end
type
="
italics
"/>
B: the Forces drawing one againſt
<
lb
/>
the other, I ſay, that they will make an
<
lb
/>
<
emph
type
="
italics
"/>
Equilibrium
<
emph.end
type
="
italics
"/>
upon the Balance
<
emph
type
="
italics
"/>
C
<
emph.end
type
="
italics
"/>
A B.
<
lb
/>
</
s
>
<
s
>For let the
<
emph
type
="
italics
"/>
A
<
emph.end
type
="
italics
"/>
rm C
<
emph
type
="
italics
"/>
A
<
emph.end
type
="
italics
"/>
be prolonged
<
lb
/>
unto F, ſo as that
<
emph
type
="
italics
"/>
A
<
emph.end
type
="
italics
"/>
F may be equal to
<
lb
/>
<
emph
type
="
italics
"/>
A
<
emph.end
type
="
italics
"/>
B: and let C
<
emph
type
="
italics
"/>
A
<
emph.end
type
="
italics
"/>
F be conſidered as a
<
lb
/>
ſtreight Balance, of which let the Center be
<
emph
type
="
italics
"/>
A
<
emph.end
type
="
italics
"/>
: and let there be
<
lb
/>
ſuppoſed two Forces G and H, of which and of all their parts the
<
lb
/>
Lines of Direction are parallel to the Line C E, and that the
<
lb
/>
Force G be equal to the Force D, and H to E, the one, to wit G, </
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>