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
="
040/01/223.jpg
"
pagenum
="
205
"/>
ſide A C, as many equal parts as we pleaſe, A D, D E, E F, F G,
<
lb
/>
and drawing by the points D, E, F, G, right lines parallel to the baſe
<
lb
/>
B C. </
s
>
<
s
>Now let us imagine the parts marked in the line A C, to be
<
lb
/>
equal times, and let the parallels drawn by the points D, E, F, G,
<
lb
/>
repreſent unto us the degrees of velocity accelerated, and
<
lb
/>
ing equally in equal times; and let the point A be the ſtate of reſt,
<
lb
/>
from which the moveable departing, hath
<
emph
type
="
italics
"/>
v. </
s
>
<
s
>g.
<
emph.end
type
="
italics
"/>
in the time A D,
<
lb
/>
acquired the degree of velocity D H, in the ſecond time we will
<
lb
/>
ſuppoſe, that it hath increaſed the velocity from D H, as far as to
<
lb
/>
E I, and ſo ſuppoſing it to have grown greater in the ſucceeding
<
lb
/>
times, according to the increaſe of the lines F K, G L,
<
emph
type
="
italics
"/>
&c.
<
emph.end
type
="
italics
"/>
but
<
lb
/>
<
arrow.to.target
n
="
marg407
"/>
<
lb
/>
becauſe the acceleration is made continually from moment to
<
lb
/>
ment, and not disjunctly from one certain part of time to another;
<
lb
/>
the point A being put for the loweſt moment of velocity, that is,
<
lb
/>
for the ſtate of reſt, and A D for the firſt inſtant of time
<
lb
/>
ing; it is manifeſt, that before the acquiſt of the degree of velocity
<
lb
/>
D H, made in the time A D, the moveable muſt have paſt by
<
lb
/>
infinite other leſſer and leſſer degrees gained in the infinite inſtants
<
lb
/>
that are in the time D A, anſwering the infinite points that are in
<
lb
/>
the line D A; therefore to repreſent unto us the infinite degrees
<
lb
/>
of velocity that precede the degree D H, it is neceſſary to imagine
<
lb
/>
infinite lines ſucceſſively leſſer and leſſer, which are ſuppoſed to
<
lb
/>
be drawn by the infinite points of the line D A, and parallels to
<
lb
/>
D H, the which infinite lines repreſent unto us the ſuperficies of
<
lb
/>
the Triangle A H D, and thus we may imagine any ſpace paſſed
<
lb
/>
by the moveable, with a motion which begining at reſt, goeth
<
lb
/>
formly accelerating, to have ſpent and made uſe of infinite degrees
<
lb
/>
of velocity, increaſing according to the infinite lines that
<
lb
/>
ing from the point A, are ſuppoſed to be drawn parallel to the
<
lb
/>
line H D, and to the reſt I E, K F, L G, the motion continuing as
<
lb
/>
far as one will.</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg407
"/>
<
emph
type
="
italics
"/>
The acceleration
<
lb
/>
of grave bodies
<
lb
/>
turally deſcendent,
<
lb
/>
increaſeth from
<
lb
/>
moment to moment.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>Now let us compleat the whole Parallelogram A M B C, and let
<
lb
/>
us prolong as far as to the ſide thereof B M, not onely the Parallels
<
lb
/>
marked in the Triangle, but thoſe infinite others imagined to be
<
lb
/>
drawn from all the points of the ſide A C; and like as B C, was
<
lb
/>
the greateſt of thoſe infinite parallels of the Triangle,
<
lb
/>
ing unto us the greateſt degree of velocity acquired by the
<
lb
/>
able in the accelerate motion, and the whole ſuperficies of the ſaid
<
lb
/>
Triangle, was the maſs and ſum of the whole velocity, wherewith
<
lb
/>
in the time A C it paſſed ſuch a certain ſpace, ſo the parallelogram
<
lb
/>
is now a maſs and aggregate of a like number of degrees of
<
lb
/>
locity, but each equal to the greateſt B C, the which maſs of
<
lb
/>
locities will be double to the maſs of the increaſing velocities in
<
lb
/>
the Triangle, like as the ſaid Parallelogram is double to the
<
lb
/>
angle: and therefore if the moveable, that falling did make uſe </
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>