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
="
040/01/211.jpg
"
pagenum
="
193
"/>
round upon their centres with equal velocities, ſo as that two
<
lb
/>
veables, which ſuppoſe for example to be two ſtones placed in the
<
lb
/>
points B and C, come to be carried along the circumferences B G
<
lb
/>
and C E, with equal velocities; ſo that in the ſame time that the
<
lb
/>
ſtone B ſhall have run the arch B G, the ſtone C will have paſt the
<
lb
/>
arch C E. </
s
>
<
s
>I ſay now, that the whirl or
<
emph
type
="
italics
"/>
vertigo
<
emph.end
type
="
italics
"/>
of the leſſer wheel
<
lb
/>
is much more potent to make the projection of the ſtone B, than
<
lb
/>
the
<
emph
type
="
italics
"/>
vertigo
<
emph.end
type
="
italics
"/>
of the bigger wheel to make that of the ſtone C.
<
lb
/>
</
s
>
<
s
>Therefore the projection, as we have already declared, being to be
<
lb
/>
made along the tangent, when the ſtones B and C are to ſeparate
<
lb
/>
from their wheels, and to begin the motion of projection from the
<
lb
/>
points B and C, then ſhall they be extruded by the
<
emph
type
="
italics
"/>
impetus
<
emph.end
type
="
italics
"/>
<
lb
/>
ceived from the
<
emph
type
="
italics
"/>
vertigo
<
emph.end
type
="
italics
"/>
by (or along) the tangents B F and C D.
<
lb
/>
</
s
>
<
s
>The two ſtones therefore have equal impetuoſities of running
<
lb
/>
long the tangents B F and C D, and would run along the ſame, if
<
lb
/>
they were not turn'd aſide by ſome other force: is it not ſo
<
emph
type
="
italics
"/>
<
lb
/>
gredus
<
emph.end
type
="
italics
"/>
?</
s
>
</
p
>
<
p
type
="
main
">
<
s
>SAGR. </
s
>
<
s
>In my opinion the buſineſſe is as you ſay.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>SALV. </
s
>
<
s
>But what force, think you, ſhould that be which averts
<
lb
/>
the ſtones from moving by the tangents, along which they are
<
lb
/>
tainly driven by the
<
emph
type
="
italics
"/>
impetus
<
emph.end
type
="
italics
"/>
of the
<
emph
type
="
italics
"/>
vertigo.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>SAGR. </
s
>
<
s
>It is either their own gravity, or elſe ſome glutinous
<
lb
/>
matter that holdeth them faſt and cloſe to the wheels.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>SALV. </
s
>
<
s
>But for the diverting of a moveable from the motion
<
lb
/>
to which nature inciteth it, is there not required greater or leſſer
<
lb
/>
force, according as the deviation is intended to be greater or
<
lb
/>
ſer? </
s
>
<
s
>that is, according as the ſaid moveable in its deviation hath a
<
lb
/>
greater or leſſer ſpace to move in the ſame time?</
s
>
</
p
>
<
p
type
="
main
">
<
s
>SAGR. </
s
>
<
s
>Yes certainly: for it was concluded even now, that to
<
lb
/>
make a moveable to move; the movent vertue muſt be increaſed
<
lb
/>
in proportion to the velocity wherewith it is to move.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>SALV. </
s
>
<
s
>Now conſider, that for the deviating the ſtone upon
<
lb
/>
the leſſe wheel from the motion of projection, which it would
<
lb
/>
make by the tangent B F, and for the holding of it faſt to the
<
lb
/>
wheel, it is required, that its own gravity draw it back the whole
<
lb
/>
length of the ſecant F G, or of the perpendicular raiſed from the
<
lb
/>
point G, to the line B F, whereas in the greater wheel the
<
lb
/>
on needs to be no more than the ſecant D E, or the
<
lb
/>
lar let fall from the tangent D G to the point E, leſſe by much
<
lb
/>
than F G, and alwayes leſſer and leſſer according as the wheel is
<
lb
/>
made bigger. </
s
>
<
s
>And foraſmuch as theſe retractions (as I may call
<
lb
/>
them) are required to be made in equal times, that is, whil'ſt the
<
lb
/>
wheels paſſe the two equal arches B G and C E, that of the ſtone
<
lb
/>
B, that is, the retraction F G ought to be more ſwift than the
<
lb
/>
ther D E; and therefore much greater force will be required for </
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>