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
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
<
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
="
040/01/987.jpg
"
pagenum
="
293
"/>
riſing or aſcending: it of neceſſity remaineth manifeſt, that in the
<
lb
/>
Superficies which is exactly equilibrated, the ſaid Ball remaineth in
<
lb
/>
different and dubious between Motion and Reſt, ſo that every ſmall
<
lb
/>
Force is ſufficient to move it, as on the contrary, every ſmall Reſi
<
lb
/>
ſtance, and no greater than that of the meer Air that environs it, is
<
lb
/>
able to hold it ſtill.</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg1116
"/>
* Or along.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>From whence we may take this Concluſion for indubitable, That
<
lb
/>
Crave Bodies, all Extern and Adventitious Impediments being re
<
lb
/>
moved, may be moved along the Plane of the Horizon by any ne
<
lb
/>
ver ſo ſmall Force: but when the ſame Grave is to be thrown along
<
lb
/>
an Aſcending Plane, then, it beginning to ſtrive againſt that aſcent,
<
lb
/>
having an inclination to the contrary Motion, there ſhall be requi
<
lb
/>
red greater Violence, and ſtill greater the more Elevation that ſame
<
lb
/>
Plane ſhall have. </
s
>
<
s
>As for example, the Moveable G, being poſited
<
lb
/>
upon the Line A B parallel to the Horizon, it ſhall, as hath been
<
lb
/>
ſaid, be indifferent on it either to Motion or Reſt, ſo that it may
<
lb
/>
be moved by a very ſmall Force: But if we ſhall have the Planes
<
lb
/>
Elevated, they ſhall not be driven along without Violence; which
<
lb
/>
<
figure
id
="
id.040.01.987.1.jpg
"
xlink:href
="
040/01/987/1.jpg
"
number
="
199
"/>
<
lb
/>
Violence will be required to be
<
lb
/>
greater to move it along the Line
<
lb
/>
A D, than along A C; and ſtill
<
lb
/>
greater along A E than along A D:
<
lb
/>
The which hapneth, becauſe it hath
<
lb
/>
greater
<
emph
type
="
italics
"/>
Impetus
<
emph.end
type
="
italics
"/>
of going down
<
lb
/>
wards along A E than along A D,
<
lb
/>
and along A D than along A C. </
s
>
<
s
>So
<
lb
/>
that we may likewiſe conclude
<
lb
/>
Grave Bodies to have greater Reſiſtance upon Planes differently
<
lb
/>
Elevared, to their being moved along the ſame, according as one
<
lb
/>
ſhall be more or leſs elevated than the other; and, in fine, that the
<
lb
/>
greateſt Reſiſtance of the ſame Grave to its being raiſed is in the
<
lb
/>
Perpendicular A F. </
s
>
<
s
>But it will be neceſſary to declare exactly what
<
lb
/>
proportion the Force muſt have to the Weight, that it may be able
<
lb
/>
to carry it along ſeveral elevated Planes, before we proceed any
<
lb
/>
farther, to the end that we may perfectly underſtand all that which
<
lb
/>
remains to be ſpoken.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>Letting, therefore, Perpendiculars fall from the points C, D,
<
lb
/>
and E unto the Horizontal Line A B, which let be C H, D I, and
<
lb
/>
E K: it ſhall be demonſtrated that the ſame Weight ſhall be mo
<
lb
/>
ved along the Plane A C with leſſer Force than along the Perpendi
<
lb
/>
cular A F, (where it is raiſed by a Force equal to it ſelf) accor
<
lb
/>
ding to the proportion by which the Perpendicular C H is leſs than
<
lb
/>
A C: and that along the Plane A D, the Force hath the ſame pro
<
lb
/>
portion to the Weight, that the Perpendicular I D hath to D A:
<
lb
/>
and, laſtly, that in the Plane A E the
<
emph
type
="
italics
"/>
F
<
emph.end
type
="
italics
"/>
orce to the Weight obſer
<
lb
/>
veth the proportion of E K and E A.</
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>