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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152FED. COMMANDINI da figura, & altera circumſcribatur ex cylindris, uel cylin-
dri portionibus, ſicuti dictum eſt, ita ut exceſſus, quo figu-
ra circumſcripta inſcriptam ſuperat, ſit ſolido g minor.
Itaque centrum grauitatis cylindri, uel cylindri portionis
q r eſt in linea p o;
cylindri, uel cylindri portionis st cen-
trum in linea on;
centrum u x in linea n m; y z in m b; η @
in 1k;
λ μ in K h; & denique ν π centrum in h d. ergo figu-
105[Figure 105] ræ inſcriptæ centrum eſt in linea p d.
Sitautem ρ: & iun-
cta ρ e protendatur, ut cum linea, quæ à pũctoc ducta fue-
rit axi æquidiſtans, conueniat in σ.
erit σ ζ ad ρ e, ut c d
ad d f:
& conus, ſeu coni portio ad exceſſum, quo circum-
ſcripta figura inſcriptam ſuperat, habebit maiorem pro-
portionem, quàm σ ζ ad ρ e.
ergo ad partem exceſſus, quæ
intra ipſius ſuperficiem comprehenditur, multo maiorem
proportionem habebit.
habeat eam, quam τ ρ ad ρ e.

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