Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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[51.] V.
[52.] DEMONSTRATIO SECVNDAE PARTIS.
[53.] COMMENTARIVS.
[54.] DEMONSTRATIO TERTIAE PARTIS.
[55.] COMMENTARIVS.
[56.] DEMONSTRATIO QVARTAE PARTIS.
[57.] DEMONSTRATIO QVINT AE PARTIS.
[58.] FINIS LIBRORVM ARCHIMEDIS DE IIS, QVAE IN AQVA VEHVNTVR.
[59.] FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORV M.
[60.] CVM PRIVILEGIO IN ANNOS X. BONONIAE, Ex Officina Alexandri Benacii. M D LXV.
[61.] ALEXANDRO FARNESIO CARDINALI AMPLISSIMO ET OPTIMO.
[62.] FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORVM. DIFFINITIONES.
[63.] PETITIONES.
[64.] THEOREMA I. PROPOSITIO I.
[65.] THEOREMA II. PROPOSITIO II.
[66.] THE OREMA III. PROPOSITIO III.
[67.] THE OREMA IIII. PROPOSITIO IIII.
[68.] ALITER.
[69.] THEOREMA V. PROPOSITIO V.
[70.] COROLLARIVM.
[71.] THEOREMA VI. PROPOSITIO VI.
[72.] THE OREMA VII. PROPOSITIO VII.
[73.] THE OREMA VIII. PROPOSITIO VIII.
[74.] THE OREMA IX. PROPOSITIO IX.
[75.] PROBLEMA I. PROPOSITIO X.
[76.] PROBLEMA II. PROPOSITIO XI.
[77.] PROBLEMA III. PROPOSITIO XII.
[78.] PROBLEMA IIII. PROPOSITIO XIII.
[79.] THEOREMA X. PROPOSITIO XIIII.
[80.] THE OREMA XI. PROPOSITIO XV.
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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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