Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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[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.
[81.] THE OREMA XII. PROPOSITIO XVI.
[82.] THE OREMA XIII. PROPOSITIO XVII.
[83.] THEOREMA XIIII. PROPOSITIO XVIII.
[84.] THEOREMA XV. PROPOSITIO XIX.
[85.] THE OREMA XVI. PROPOSITIO XX.
[86.] THEOREMA XVII. PROPOSITIO XXI.
[87.] THE OREMA XVIII. PROPOSITIO XXII.
[88.] THEOREMA XIX. PROPOSITIO XXIII.
[89.] PROBLEMA V. PROPOSITIO XXIIII.
[90.] THEOREMA XX. PROPOSITIO XXV.
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136FED. COMMANDINI medis. ergo punctum v extra p riſima a f poſitum, centrũ
erit magnitudinis cõpoſitæ e x omnibus priſmatibus g z r,
r β t, t γ x, x δ k, k δ y, y u, u s, s α h, quod fieri nullo modo po
teſt.
eſt enim ex diſſinitione centrum grauitatis ſolidæ figu
ræ intra ipſam poſitum, non extra.
quare relinquitur, ut cẽ
trum grauitatis priſmatis ſit in linea K m.
Rurſus b c bifa-
riam in ξ diuidatur:
& ducta a ξ, per ipſam, & per lineam
a g d plan um ducatur;
quod priſma ſecet: faciatq; in paral
lelogrammo b f ſectionem ξ π di uidet punctum π lineam
quoque c f bifariam:
& erit p lani eius, & trianguli g h K
communis ſectio g u;
quòd p ũctum u in inedio lineæ h K
91[Figure 91] poſitum ſi t.
Similiter demonſtrabimus centrum grauita-
tis priſm atis in ipſa g u ineſſe.
ſit autem planorum c f n l,
a d π ξ communis ſectio linea ρ ο τ quæ quidem priſmatis
axis erit, cum tranſeat per centra grauitatis triangulorum
a b c, g h k, d e f, ex quartadecima eiuſdem.
ergo centrum
grauitatis pri ſmatis a f eſt punctum σ, centrum

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