Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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<
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0116
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116
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FED. COMMANDINI
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quæ quidem in centro conueniunt. </
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>
<
s
xml:id
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echoid-s2876
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xml:space
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">idem igitur eſt centrum
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lb
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grauitatis quadrati, & </
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<
s
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echoid-s2877
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">circuli centrum.</
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<
s
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</
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<
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<
s
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">Sit pentagonum æquilaterum, & </
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>
<
s
xml:id
="
echoid-s2880
"
xml:space
="
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">æquiangulum in circu-
<
lb
/>
lo deſcriptum a b c d e: </
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<
s
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xml:space
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">& </
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<
s
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xml:space
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">iun-
<
lb
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<
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fig-0116-01
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number
="
72
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0116-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0116-01
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>
cta b d, bifariamq́; </
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>
<
s
xml:id
="
echoid-s2883
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xml:space
="
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">in ſ diuiſa,
<
lb
/>
ducatur c f, & </
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>
<
s
xml:id
="
echoid-s2884
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xml:space
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">producatur ad
<
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/>
circuli circumferentiam in g;
<
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/>
</
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>
<
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xml:space
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">quæ lineam a e in h ſecet: </
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>
<
s
xml:id
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echoid-s2886
"
xml:space
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">de-
<
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inde iungantur a c, c e. </
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>
<
s
xml:id
="
echoid-s2887
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xml:space
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">Eodem
<
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/>
modo, quo ſupra demonſtra-
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bimus angulum b c f æqualem
<
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eſſe angulo d c f; </
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>
<
s
xml:id
="
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xml:space
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">& </
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<
s
xml:id
="
echoid-s2889
"
xml:space
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">angulos
<
lb
/>
ad f utroſque rectos: </
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>
<
s
xml:id
="
echoid-s2890
"
xml:space
="
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">& </
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>
<
s
xml:id
="
echoid-s2891
"
xml:space
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">idcir-
<
lb
/>
colineam c f g per circuli cen
<
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/>
trum tranſire. </
s
>
<
s
xml:id
="
echoid-s2892
"
xml:space
="
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">Quoniam igi-
<
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/>
tur latera c b, b a, & </
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>
<
s
xml:id
="
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"
xml:space
="
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">c d, d e æqualia ſunt; </
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>
<
s
xml:id
="
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"
xml:space
="
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">& </
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>
<
s
xml:id
="
echoid-s2895
"
xml:space
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">æquales anguli
<
lb
/>
c b a, c d e: </
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>
<
s
xml:id
="
echoid-s2896
"
xml:space
="
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">erit baſis c a baſi c e, & </
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>
<
s
xml:id
="
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xml:space
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">angulus b c a angulo
<
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/>
<
note
position
="
left
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xlink:label
="
note-0116-01
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xlink:href
="
note-0116-01a
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xml:space
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">4. Primi.</
note
>
d c e æqualis. </
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<
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">ergo & </
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<
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">reliquus a c h, reliquo e c h. </
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>
<
s
xml:id
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xml:space
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">eſt au-
<
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/>
tem c h utrique triangulo a c h, e c h communis. </
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>
<
s
xml:id
="
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xml:space
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">quare
<
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/>
baſis a h æqualis eſt baſi h e: </
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>
<
s
xml:id
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xml:space
="
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">& </
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>
<
s
xml:id
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xml:space
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">anguli, quiad h recti: </
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>
<
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="
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">ſuntq́;
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/>
</
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>
<
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="
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">recti, qui ad f. </
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>
<
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xml:id
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xml:space
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">ergo lineæ a e, b d inter ſe ſe æquidiſtant. </
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>
<
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xml:id
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xml:space
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<
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<
note
position
="
left
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xlink:label
="
note-0116-02
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xlink:href
="
note-0116-02a
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xml:space
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">08. primi.</
note
>
Itaque cum trapezij a b d e latera b d, a e æquidiſtantia à li
<
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nea fh bifariam diuidantur; </
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>
<
s
xml:id
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xml:space
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">centrum grauitatis ipſius erit
<
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/>
in linea f h, ex ultima eiuſdem libri Archimedis. </
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>
<
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">Sed trian-
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<
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position
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xlink:label
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note-0116-03
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xlink:href
="
note-0116-03a
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xml:space
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">13. Archi-
<
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medis.</
note
>
guli b c d centrum grauitatis eſt in linea c f. </
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<
s
xml:id
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">ergo in eadem
<
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linea c h eſt centrum grauitatis trapezij a b d e, & </
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<
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guli b c d: </
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<
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">hoc eſt pentagoni ipſius centrum & </
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<
s
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">centrum
<
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circuli. </
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>
<
s
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xml:space
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">Rurſus ſi iuncta a d, bifariamq́; </
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<
s
xml:id
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">ſecta in k, duca-
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tur e k l: </
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>
<
s
xml:id
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">demonſtrabimus in ipſa utrumque centrum in
<
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eſſe. </
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>
<
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">Sequitur ergo, ut punctum, in quo lineæ c g, e l con-
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ueniunt, idem ſit centrum circuli, & </
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>
<
s
xml:id
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">centrum grauitatis
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pentagoni.</
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<
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</
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<
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<
s
xml:id
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xml:space
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">Sit hexagonum a b c d e f æquilaterum, & </
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>
<
s
xml:id
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">æquiangulum
<
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/>
in circulo deſignatum: </
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<
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">iunganturq́; </
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<
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">b d, a c: </
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<
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<
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