Salusbury, Thomas
,
Mathematical collections and translations (Tome I)
,
1667
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Figures
Thumbnails
page
|<
<
of 701
>
>|
<
archimedes
>
<
text
>
<
body
>
<
chap
>
<
pb
xlink:href
="
040/01/031.jpg
"
pagenum
="
15
"/>
<
p
type
="
main
">
<
s
>SALV. </
s
>
<
s
>And have you no other conceit thereof than this?</
s
>
</
p
>
<
p
type
="
main
">
<
s
>SIMPL. </
s
>
<
s
>This I think to be the proper definition of equal
<
lb
/>
tions.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
arrow.to.target
n
="
marg47
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg47
"/>
<
emph
type
="
italics
"/>
Velocities are ſaid
<
lb
/>
to be equal, when
<
lb
/>
the ſpaces paſſed
<
lb
/>
are proportionate to
<
lb
/>
their time.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>SAGR. </
s
>
<
s
>We will add moreover this other: and call that equal
<
lb
/>
velocity, when the ſpaces paſſed have the ſame proportion, as the
<
lb
/>
times wherein they are paſt, and it is a more univerſal definition.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>SALV. </
s
>
<
s
>It is ſo: for it comprehendeth the equal ſpaces paſt in
<
lb
/>
equal times, and alſo the unequal paſt in times unequal, but
<
lb
/>
portionate to thoſe ſpaces. </
s
>
<
s
>Take now the ſame Figure, and
<
lb
/>
ing the conceipt that you had of the more haſtie motion, tell me
<
lb
/>
why you think the velocity of the Cadent by C B, is greater
<
lb
/>
than the velocity of the Deſcendent by C A?</
s
>
</
p
>
<
p
type
="
main
">
<
s
>SIMPL. </
s
>
<
s
>I think ſo; becauſe in the ſame time that the Cadent
<
lb
/>
ſhall paſs all C B, the Deſcendent ſhall paſs in C A, a part leſs
<
lb
/>
than C B.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>SALV. True; and thus it is proved, that the moveable moves
<
lb
/>
more ſwiftly by the perpendicular, than by the inclination. </
s
>
<
s
>Now
<
lb
/>
conſider, if in this ſame Figure one may any way evince the
<
lb
/>
ther conceipt, and finde that the moveables were equally ſwift
<
lb
/>
by both the lines C A and C B.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>SIMPL. </
s
>
<
s
>I ſee no ſuch thing; nay rather it ſeems to contradict
<
lb
/>
what was ſaid before.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>SALV. </
s
>
<
s
>And what ſay you,
<
emph
type
="
italics
"/>
Sagredus
<
emph.end
type
="
italics
"/>
? </
s
>
<
s
>I would not teach you
<
lb
/>
what you knew before, and that of which but juſt now you
<
lb
/>
duced me the definition.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>SAGR. </
s
>
<
s
>The definition I gave you, was, that moveables may
<
lb
/>
be called equally ſwift, when the ſpaces paſſed are proportional
<
lb
/>
to the times in which they paſſed; therefore to apply the
<
lb
/>
tion to the preſent caſe, it will be requiſite, that the time of
<
lb
/>
ſcent by C A, to the time of falling by C B, ſhould have the
<
lb
/>
ſame proportion that the line C A hath to the line C B; but I
<
lb
/>
underſtand not how that can be, for that the motion by C B is
<
lb
/>
ſwifter than by C A.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>SALV. </
s
>
<
s
>And yet you muſt of neceſſity know it. </
s
>
<
s
>Tell me a little,
<
lb
/>
do not theſe motions go continually accelerating?</
s
>
</
p
>
<
p
type
="
main
">
<
s
>SAGR. </
s
>
<
s
>They do; but more in the perpendicular than in the
<
lb
/>
inclination.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>SALV. </
s
>
<
s
>But this acceleration in the perpendicular, is it yet
<
lb
/>
withſtanding ſuch in compariſon of that of the inclined, that
<
lb
/>
two equal parts being taken in any place of the ſaid
<
lb
/>
lar and inclining lines, the motion in the parts of the
<
lb
/>
lar is alwaies more ſwift, than in the part of the inclination?</
s
>
</
p
>
<
p
type
="
main
">
<
s
>SAGR. </
s
>
<
s
>I ſay not ſo: but I could take a ſpace in the
<
lb
/>
on, in which the velocity ſhall be far greater than in the like ſpace
<
lb
/>
taken in the perpendicular; and this ſhall be, if the ſpace in the </
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>