Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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[61.] ALEXANDRO FARNESIO CARDINALI AMPLISSIMO ET OPTIMO.
Page: 107
[62.] FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORVM. DIFFINITIONES.
Page: 113 (1)
[63.] PETITIONES.
Page: 114
[64.] THEOREMA I. PROPOSITIO I.
Page: 114
[65.] THEOREMA II. PROPOSITIO II.
Page: 118
[66.] THE OREMA III. PROPOSITIO III.
Page: 121 (5)
[67.] THE OREMA IIII. PROPOSITIO IIII.
Page: 122
[68.] ALITER.
Page: 123 (6)
[69.] THEOREMA V. PROPOSITIO V.
Page: 125 (7)
[70.] COROLLARIVM.
Page: 127 (8)
[71.] THEOREMA VI. PROPOSITIO VI.
Page: 127 (8)
[72.] THE OREMA VII. PROPOSITIO VII.
Page: 129 (9)
[73.] THE OREMA VIII. PROPOSITIO VIII.
Page: 131 (10)
[74.] THE OREMA IX. PROPOSITIO IX.
Page: 143 (15)
[75.] PROBLEMA I. PROPOSITIO X.
Page: 145 (17)
[76.] PROBLEMA II. PROPOSITIO XI.
Page: 146
[77.] PROBLEMA III. PROPOSITIO XII.
Page: 147 (18)
[78.] PROBLEMA IIII. PROPOSITIO XIII.
Page: 148
[79.] THEOREMA X. PROPOSITIO XIIII.
Page: 149 (19)
[80.] THE OREMA XI. PROPOSITIO XV.
Page: 153 (21)
[81.] THE OREMA XII. PROPOSITIO XVI.
Page: 154
[82.] THE OREMA XIII. PROPOSITIO XVII.
Page: 155 (22)
[83.] THEOREMA XIIII. PROPOSITIO XVIII.
Page: 156
[84.] THEOREMA XV. PROPOSITIO XIX.
Page: 157 (23)
[85.] THE OREMA XVI. PROPOSITIO XX.
Page: 160
[86.] THEOREMA XVII. PROPOSITIO XXI.
Page: 164
[87.] THE OREMA XVIII. PROPOSITIO XXII.
Page: 166
[88.] THEOREMA XIX. PROPOSITIO XXIII.
Page: 171 (30)
[89.] PROBLEMA V. PROPOSITIO XXIIII.
Page: 172
[90.] THEOREMA XX. PROPOSITIO XXV.
Page: 174
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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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