Commandino, Federico
,
Liber de centro gravitatis solidorum
,
1565
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Figures
Thumbnails
page
|<
<
of 101
>
>|
<
archimedes
>
<
text
>
<
body
>
<
chap
>
<
p
type
="
main
">
<
s
id
="
s.000823
">
<
pb
pagenum
="
39
"
xlink:href
="
023/01/085.jpg
"/>
dem, cuius baſis eſt quadratum abcd, & altitudo eg: &
<
lb
/>
in pyramidem, cuius
<
expan
abbr
="
eadẽ
">eadem</
expan
>
baſis,
<
expan
abbr
="
altitudoq;
">altitudoque</
expan
>
fg; ut ſint eg,
<
lb
/>
gf ſemidiametri ſphæræ, & linea una. </
s
>
<
s
id
="
s.000824
">
<
expan
abbr
="
Cũ
">Cum</
expan
>
igitur g ſit ſphæ
<
lb
/>
ræ centrum, erit etiam centrum circuli, qui circa
<
expan
abbr
="
quadratũ
">quadratum</
expan
>
<
lb
/>
abcd deſcribitur: & propterea eiuſdem quadrati grauita
<
lb
/>
tis centrum: quod in prima propoſitione huius demon
<
lb
/>
ſtratum eſt. </
s
>
<
s
id
="
s.000825
">quare pyramidis abcde axis erit eg: & pyra
<
lb
/>
midis abcdf axis fg. </
s
>
<
s
id
="
s.000826
">Itaque ſit h centrum grauitatis py
<
lb
/>
ramidis abcde, & pyramidis abcdf centrum ſit
<
emph
type
="
italics
"/>
K:
<
emph.end
type
="
italics
"/>
per
<
lb
/>
ſpicuum eſt ex uigeſima ſecunda propoſitione huius,
<
expan
abbr
="
lineã
">lineam</
expan
>
<
lb
/>
<
figure
id
="
id.023.01.085.1.jpg
"
xlink:href
="
023/01/085/1.jpg
"
number
="
74
"/>
<
lb
/>
ch triplam eſſe hg:
<
expan
abbr
="
cõ
">com</
expan
>
<
lb
/>
<
expan
abbr
="
ponendoq;
">ponendoque</
expan
>
eg ipſius g
<
lb
/>
h quadruplam. </
s
>
<
s
id
="
s.000827
">&
<
expan
abbr
="
eadẽ
">eadem</
expan
>
<
lb
/>
ratione fg
<
expan
abbr
="
quadruplã
">quadruplam</
expan
>
<
lb
/>
ipſius gk quod cum e
<
lb
/>
g, gf ſint æquales, & h
<
lb
/>
g, g
<
emph
type
="
italics
"/>
K
<
emph.end
type
="
italics
"/>
neceſſario æqua
<
lb
/>
les erunt. </
s
>
<
s
id
="
s.000828
">ergo ex quar
<
lb
/>
ta propoſitione primi
<
lb
/>
libri Archimedis de
<
expan
abbr
="
cẽ-tro
">cen
<
lb
/>
tro</
expan
>
grauitatis
<
expan
abbr
="
planorũ
">planorum</
expan
>
,
<
lb
/>
totius octahedri, quod
<
lb
/>
ex dictis pyramidibus
<
lb
/>
conſtat, centrum graui
<
lb
/>
tatis erit punctum g idem, quod ipſius ſphæræ centrum.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.000829
">Sit icoſahedrum ad deſcriptum in ſphæra, cuius
<
expan
abbr
="
centrũ
">centrum</
expan
>
<
lb
/>
ſit g. </
s
>
<
s
id
="
s.000830
">Dico g ipſius icoſahedri grauitatis eſſe centrum. </
s
>
<
s
id
="
s.000831
">Si
<
lb
/>
enim ab angulo a per g ducatur recta linea uſque ad ſphæ
<
lb
/>
ræ ſuperficiem; conſtat ex ſexta decima propoſitione libri
<
lb
/>
tertii decimi elementorum, cadere eam in angulum ipſi a
<
lb
/>
oppoſitum. </
s
>
<
s
id
="
s.000832
">cadat in d:
<
expan
abbr
="
ſitq;
">ſitque</
expan
>
una aliqua baſis icoſahedri tri
<
lb
/>
angulum abc: & iunctæ bg, producantur, & cadant in
<
lb
/>
angulos ef, ipſis bc oppoſitos. </
s
>
<
s
id
="
s.000833
">Itaque per triangula
<
lb
/>
abc, def ducantur plana ſphæram ſecantia.</
s
>
<
s
id
="
s.000834
"> erunt hæ </
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>