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
="
043/01/021.jpg
"
pagenum
="
13
"/>
EF. quæ ſuntin latera homologa duorum triangulorum
<
lb
/>
ABC, DEF. </
s
>
<
s
>Ex definitione igitur, duo puncta G, H,
<
lb
/>
in triangulis ABC, DEF, ſimiliter poſita erunt. </
s
>
<
s
>At
<
lb
/>
enim ſi fieri poteſt ſit aliud punctum K, in triangulo
<
lb
/>
DEF, ſimiliter poſitum puncto G. </
s
>
<
s
>Vel igitur punctum
<
lb
/>
K in aliquo triangulorum, quorum eſt communis vertex
<
lb
/>
H, vel in aliquo eorundem latere cadet. </
s
>
<
s
>cadat in latere
<
lb
/>
FH, & iungatur DK: triangulum ergo DFK, ſimile
<
lb
/>
erit triangulo ACG. </
s
>
<
s
>Sed & triangulum EDF, ſimile
<
lb
/>
eſt triangulo BAC; vtraque igitur horum ad illorum ſi
<
lb
/>
bi reſpondens triangulorum duplicatam eorundem late
<
lb
/>
rum homologorum AC, DF, habebunt proportionem:
<
lb
/>
vt igitur eſt triangulum EDF, ad triangulum BAC, ita
<
lb
/>
erit triangulum DFK, ad triangulum ACG: & per
<
lb
/>
mutando, vt triangulum ACG, ad triangulum ABC,
<
lb
/>
ita triangulum DFK, ad triangulum EDF: eadem ra
<
lb
/>
tione, vt triangulum ACG, ad triangulum ABC, ita
<
lb
/>
erit triangulum DFH, ad triangulum DEF: vt igitur
<
lb
/>
triangulum DFK, ad triangulum EDF; ita erit trian
<
lb
/>
gulum DFH, ad triangulum EDF; triangulum ergo
<
lb
/>
DFK, triangulo DFH, æquale erit, pars toti, quod eſt
<
lb
/>
abſurdum: idem autem abſurdum ſequeretur, ſi punctum
<
lb
/>
<
emph
type
="
italics
"/>
K
<
emph.end
type
="
italics
"/>
, poneretur in aliquo prædictorum triangulorum, vt in
<
lb
/>
triangulo DFH; Non igitur aliud punctum à puncto H,
<
lb
/>
in triangulo EDF, ſimiliter poſitum erit puncto G.
<
lb
/>
</
s
>
<
s
>Quod demonſtrandum erat. </
s
>
</
p
>
<
p
type
="
head
">
<
s
>
<
emph
type
="
italics
"/>
PROPOSITIO V.
<
emph.end
type
="
italics
"/>
</
s
>
</
p
>
<
p
type
="
main
">
<
s
>Cuilibet figuræ planæ rectangulum æquale
<
lb
/>
poteſt eſſe. </
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>