Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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[21.] ARCHIMEDIS DE IIS QVAE VEHVNTVR IN AQVA LIBER SECVNDVS. CVM COMMENTARIIS FEDERICI COMMANDINI VRBINATIS. PROPOSITIO I.
[22.] PROPOSITIO II.
[23.] COMMENTARIVS.
[24.] PROPOSITIO III.
[25.] PROPOSITIO IIII.
[26.] COMMENTARIVS.
[27.] PROPOSITIO V.
[28.] COMMENTARIVS.
[29.] PROPOSITIO VI.
[30.] COMMENTARIVS.
[31.] LEMMAI.
[32.] LEMMA II.
[33.] LEMMA III.
[34.] LEMMA IIII.
[35.] PROPOSITIO VII.
[36.] PROPOSITIO VIII.
[37.] COMMENTARIVS.
[38.] PROPOSITIO IX.
[39.] COMMENTARIVS.
[40.] PROPOSITIO X.
[41.] COMMENTARIVS.
[42.] LEMMA I.
[43.] LEMMA II.
[44.] LEMMA III.
[45.] LEMMA IIII.
[46.] LEMMA V.
[47.] LEMMA VI.
[48.] II.
[49.] III.
[50.] IIII.
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1173DE CENTRO GRAVIT. SOLID. cta b d in g puncto, ducatur c g; & protrahatur ad circuli
uſque circumferentiam;
quæ ſecet a e in h. Similiter conclu
demus c g per centrum circuli tranſire:
& bifariam ſecare
lineam a e;
itemq́; lineas b d, a e inter ſe æquidiſtantes eſſe.
Cumigitur c g per centrum circuli tranſeat; & ad punctũ
f perueniat neceſſe eſt:
quòd c d e f ſit dimidium circumfe
rentiæ circuli.
Quare in eadem
73[Figure 73] diametro c f erunt centra gra
1113. Archi
medis.
uitatis triangulorum b c d,
a f e, &
quadrilateri a b d e, ex
229. @iuſdé. quibus conſtat hexagonum a b
c d e f.
perſpicuum eſt igitur in
ipſa c f eſſe circuli centrum, &

centrum grauitatis hexagoni.
Rurſus ducta altera diametro
a d, eiſdem rationibus oſtende-
mus in ipſa utrumque cẽtrum
ineſſe.
Centrum ergo grauita-
tis hexagoni, &
centrum circuli idem erit.
Sit heptagonum a b c d e f g æquilaterum atque æquian
gulum in circulo deſcriptum:
74[Figure 74]& iungantur c e, b f, a g: di-
uiſa autem c e bifariam in pũ
cto h:
& iuncta d h produca-
tur in k.
non aliter demon-
ſtrabimus in linea d k eſſe cen
trum circuli, &
centrum gra-
uitatis trianguli c d e, &
tra-
peziorum b c e f, a b f g, hoc
eſt centrum totius heptago-
ni:
& rurſus eadem centra in
alia diametro cl ſimiliter du-
cta contineri.
Quare & centrum grauitatis heptagoni, &
centrum circuli in idem punctum conucniunt.
Eodem

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