Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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[21.] ARCHIMEDIS DE IIS QVAE VEHVNTVR IN AQVA LIBER SECVNDVS. CVM COMMENTARIIS FEDERICI COMMANDINI VRBINATIS. PROPOSITIO I.
[22.] PROPOSITIO II.
[23.] COMMENTARIVS.
[24.] PROPOSITIO III.
[25.] PROPOSITIO IIII.
[26.] COMMENTARIVS.
[27.] PROPOSITIO V.
[28.] COMMENTARIVS.
[29.] PROPOSITIO VI.
[30.] COMMENTARIVS.
[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.
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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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