Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[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.
[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.
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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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