Valerio, Luca
,
De centro gravitatis solidorvm libri tres
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Figures
Thumbnails
page
|<
<
of 283
>
>|
<
archimedes
>
<
text
>
<
body
>
<
chap
>
<
p
type
="
main
">
<
s
>
<
pb
xlink:href
="
043/01/226.jpg
"
pagenum
="
47
"/>
eadem ratione triangulum BDC, trianguli CRB mi xti
<
lb
/>
erit ſeſquialterum: totum igitur triangulum ABC ſeſqui
<
lb
/>
alterum eſt compoſiti ex triangulis mixtis ANB, CRB.
<
lb
/>
</
s
>
<
s
>Et quoniam quarta pars eſt GH ipſius BD, & DK ter
<
lb
/>
tia, DG verò dimidia; qualium duodecim partium æqua
<
lb
/>
lium eſt BD, talium erit DK quatuor, & GH trium, &
<
lb
/>
DG ſex, & reliqua KG duarum; ſeſquialtera igitur eſt
<
lb
/>
GH ipſius GK: quare vt triangulum ABC ad compo
<
lb
/>
ſitum ex prædictis triangulis mixtis, ita ex contraria parte
<
lb
/>
eſt HG ad G
<
emph
type
="
italics
"/>
K
<
emph.end
type
="
italics
"/>
: cum igitur dicti compoſiti ſit centrum
<
lb
/>
grauitatis H, trianguli autem ABC centrum grauitatis
<
lb
/>
K; erit dicti compoſiti, & trianguli ABC ſimul centrum
<
lb
/>
grauitatis G. Rurſus, quoniam triangulum ABC ſeſ
<
lb
/>
quialterum eſt compoſiti ex triangulis mixtis ſupra dictis,
<
lb
/>
& compoſitum ex duabus ſemiparabolis ABD, CBD
<
lb
/>
ſeſquitertium trianguli ABC; crit compoſitum ex trian
<
lb
/>
gulis mixtis vnà cum triangulo ABC, quintuplum com
<
lb
/>
poſiti ex portionibus AEB, BFC; hoc eſt vt ex contra
<
lb
/>
ria parte LM ad MG: cum igitur G ſit centrum graui
<
lb
/>
tatis compoſiti ex triangulis mixtis, & triangulo ABC, &
<
lb
/>
compoſiti ex portionibus AEB, BFC centrum grauita
<
lb
/>
tis L; erit vtriuſque dicti compoſiti, hoc eſt totius AR
<
lb
/>
parallelogrammi centrum grauitatis L: ſed & punctum G
<
lb
/>
ex primo libro eſt centrum grauitatis parallelogrammi
<
lb
/>
AR; eiuſdem igitur parallelogrammi AR erunt duo cen
<
lb
/>
tra grauitatis G, L. </
s
>
<
s
>Quod fieri non poteſt: duarum igitur
<
lb
/>
portionum AEB, BFC ſimul centrum grauitatis erit G.
<
lb
/>
</
s
>
<
s
>Quod eſt propoſitum. </
s
>
</
p
>
<
p
type
="
head
">
<
s
>
<
emph
type
="
italics
"/>
PROPOSITIO XXIIII.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>Omnis figuræ circa axim in alteram partem de
<
lb
/>
ficientis, cuius baſis eſt circulus, vel ellipſis, ſiue-</
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>