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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page |< < of 213 > >|
ARCHIMEDIS
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
Chabet 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
Dnea f t inter _k_, &
f, quod ſit x. reliquæ ergo figuræ, quæ eſt
Eextra 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-
Fdem, 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.
]
Figure: /permanent/library/4E7V2WGH/figures/0024-01 not scanned
[Figure 12]

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