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
>
<
p
type
="
main
">
<
s
>
<
pb
xlink:href
="
040/01/1047.jpg
"
pagenum
="
352
"/>
<
emph
type
="
italics
"/>
of the Portion of the Sphære is N M; and of the Portion B G C the Axis is G M: Wherefore
<
lb
/>
the Centre of Gravity of them both ſhall be in the Line N M: And becauſe that from the Por
<
lb
/>
tion B N C the Portion B G C, not having the ſame Centre of Gravity, is cut off, the Centre
<
lb
/>
of Gravity of the remainder of the Magnitude that is above the Surface of the Liquid ſhall be
<
lb
/>
in the Line N K; namely, in the Line which conjoyneth the Centres of Gravity of the ſaid
<
lb
/>
Portions by the foreſaid 8 of
<
emph.end
type
="
italics
"/>
Archimedis de Centro Gravitatis Planorum.</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg1158
"/>
A</
s
>
</
p
>
<
p
type
="
main
">
<
s
>NIC. </
s
>
<
s
>Truth is, that in ſome of theſe Figures C is put for X, and ſo it was in
<
lb
/>
the Greek Copy that I followed.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>RIC. </
s
>
<
s
>This Demoſtration is very difficult, to my thinking; but I believe that
<
lb
/>
it is becauſe I have not in memory the Propoſitions of that Book entituled
<
emph
type
="
italics
"/>
De Cen
<
lb
/>
tris Gravium.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>NIC. </
s
>
<
s
>It is ſo.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>RIC. </
s
>
<
s
>We will take a more convenient time to diſcourſe of that, and now return
<
lb
/>
<
arrow.to.target
n
="
marg1159
"/>
<
lb
/>
to ſpeak of the two laſt Propoſitions. </
s
>
<
s
>And I ſay that the Figures incerted in the
<
lb
/>
demonſtration would in my opinion, have been better and more intelligble unto
<
lb
/>
me, drawing the Axis according to its proper Poſition; that is in the half Arch of
<
lb
/>
theſe Figures, and then, to ſecond the Objection of the Adverſary, to ſuppoſe
<
lb
/>
that the ſaid Figures ſtood ſomewhat Obliquely, to the end that the ſaid Axis, if it
<
lb
/>
were poſſible, did not ſtand according to the Perpendicular ſo often mentioned,
<
lb
/>
which doing, the Propoſition would be proved in the ſame manner as before:
<
lb
/>
and this way would be more naturall and clear.
<
lb
/>
<
arrow.to.target
n
="
marg1160
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg1159
"/>
A</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg1160
"/>
B</
s
>
</
p
>
<
p
type
="
main
">
<
s
>NIC. </
s
>
<
s
>You are in the right, but becauſe thus they were in the Greek Copy,
<
lb
/>
I thought not fit to alter them, although unto the better.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>RIC. Companion, you have thorowly ſatisfied me in all that in the beginning
<
lb
/>
of our Diſcourſe I asked of you, to morrow, God permitting, we will treat of
<
lb
/>
ſome other ingenious Novelties.</
s
>
</
p
>
<
p
type
="
head
">
<
s
>THE TRANSLATOR.</
s
>
</
p
>
<
p
type
="
main
">
<
s
>I ſay that the Figures, &c. </
s
>
<
s
>would have been more intelligible to </
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
arrow.to.target
n
="
marg1161
"/>
<
lb
/>
me, drawing the Axis Z T according to its proper Poſition, that
<
lb
/>
is in the half Arch of theſe Figures.]
<
emph
type
="
italics
"/>
And in this conſideration I have followed
<
lb
/>
the Schemes of
<
emph.end
type
="
italics
"/>
Commandine,
<
emph
type
="
italics
"/>
who being the Reſtorer of the Demonſtrations of theſe two laſt
<
lb
/>
Propoſitions, hath well conſidered what
<
emph.end
type
="
italics
"/>
Ricardo
<
emph
type
="
italics
"/>
here propoſeth, and therefore hath drawn the
<
lb
/>
ſaid Axis (which in the Manuſcripts that he had by him is lettered F T, and not as in that of
<
emph.end
type
="
italics
"/>
<
lb
/>
Tartaylia
<
emph
type
="
italics
"/>
Z T,) according to that its proper Poſition.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg1161
"/>
A</
s
>
</
p
>
<
p
type
="
main
">
<
s
>But becauſe thus they were in the Greek Copy, I thought not
<
lb
/>
<
arrow.to.target
n
="
marg1162
"/>
<
lb
/>
fit to alter them although unto the better.]
<
emph
type
="
italics
"/>
The Schemes of thoſe Manu-
<
emph.end
type
="
italics
"/>
<
lb
/>
<
figure
id
="
id.040.01.1047.1.jpg
"
xlink:href
="
040/01/1047/1.jpg
"
number
="
244
"/>
<
lb
/>
<
emph
type
="
italics
"/>
ſcripts that
<
emph.end
type
="
italics
"/>
Tartaylia
<
emph
type
="
italics
"/>
had ſeen were more imperfect then thoſe
<
lb
/>
in Commandines Copies; but for variety ſake, take here one
<
lb
/>
of
<
emph.end
type
="
italics
"/>
Tartaylia,
<
emph
type
="
italics
"/>
it being that of the Portion of a Sphære, equall
<
lb
/>
to an Hemiſphære, with its Axis oblique, and its Baſe dimitted
<
lb
/>
into the Liquid, and Lettered as in this Edition.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
>
<
margin.target
id
="
marg1162
"/>
B</
s
>
</
p
>
<
p
type
="
main
">
<
s
>
<
emph
type
="
italics
"/>
Now Courteous Readers, I hope that you may, amidſt the
<
lb
/>
great Obſcurity of the Originall in the Demonſtrations of theſe
<
lb
/>
two laſt Propoſitions, be able from the joynt light of theſe two Famous Commentators of our
<
lb
/>
more famous Author, to diſcern the truth of the Doctrine affirmed, namely, That Solids of the
<
lb
/>
Figure of Portions of Sphæres demitted into the Liquid with their Baſes upwards ſhall ſtand
<
lb
/>
erectly, that is, with their Axis according to the Perpendicular drawn from the Centre of the
<
lb
/>
Earth unto its Circumference: And that if the ſaid Portions be demitted with their Baſes
<
lb
/>
oblique and touching the Liquid in one Point, they ſhall not rest in that Obliquity, but ſhall
<
lb
/>
return to Rectitude: And that laſtly, if theſe Portions be demitted with their Baſes downwards,
<
lb
/>
they ſhall continue erect with their Axis according to the Perpendicular aforeſaid: ſo that no
<
lb
/>
more remains to be done, but that weſet before you the 2 Books of this our Admirable Author.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>