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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24ARCHIMEDIS in linea ft. nam ſit primum figura maior dimidia ſphære:
ſitq; in dimidia ſphæra ſphæræ centrum t; in minori por-
tioneſit centrum p;
& in maiori _k_: per _k_ uero, & terræ cen
trum l ducatur _k_ l ſecans circunferentiam e f h in pun-
cto n.
Quoniam igitur unaquæque ſphæræportio axem
11C habet in linea, quæ à cẽtro ſphæræ ad cius baſim perpen-
dicularis ducitur:
habetq; in axe grauitatis centrum:
portionis in humido demerſæ, quæ ex duabus ſphæræ
portionibus conſtat, axis erit in perpendiculari per _k_ du-
cta.
& idcirco centrum grauitatis ipſius erit in linea n _k_,
quod ſit r.
ſed totius portionis grauitatis centrum eſt in li
22D nea f t inter _k_, &
f, quod ſit x. reliquæ ergo figuræ, quæ eſt
33E extra humidum, centrum erit in linea r x producta ad par
tes x;
& aſſumpta ex ea, linea quadam, quæ ad r x eandem
proportionem habeat, quam grauitas portionis in humi-
do demerſæ habet ad grauitatem figuræ, quæ eſt extra hu-
midum.
Sit autem s centrum dictæ figuræ: & per s duca-
tur perpendicularis l s.
Feretur ergo grauitas figuræ qui-
44F dem, quæ extra humidum per rectam s l deorſum;
portio
nis autem, quæ in humido, ſurſum per rectam r l.
quare
non manebit figura:
ſed partes eius, quæ ſunt ad e, deor-
ſum;
& quæ ad h ſurſum ſerẽtur: idq; cõtinenter fiet, quoad
ſ t ſit ſecundum perpendicularem.
Eodem modo in aliis
portionibus idem demonſtrabitur.
]
13[Figure 13]

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