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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ARCHIMEDIS

COMMENTARIVS.

_Sit ei, quæ uſque ad axem æqualis r h. ]_ Ita legendum eſt,
Anon r m, ut tranſlatio habet, quod ex ijs, quæ ſequuntur, manifeſte
conſtare poteſt.
_Et oh dupla ipſius h m. ]_ In tranſlatione mendoſe legeba-
Btur, on dupla ipſius rm.
Hoc enim ſupra demonſtratum eſt. ] _In prima huius_.
C
Et quam proportionem habet demerſa portio ad totã,
Deam quadratum p f habet ad n o quadratum.
] _Hoc loco in_
_tranſlatione non nulli deſider abantur, quænos reſtituimus.
Illud au_
_tem ab Archimede demonſtratum eſt in libro de conoidibus &
ſphæ_
_roidibus propoſitione_ 26.
_Quare p f non eſt minor ipſa m o. ]_ Nam ex decima quinti
Eſequitur, quadratum p f non eſſe minus quadrato m o.
quare neque
linea p f minor erit linea m o ex 22 ſexti.
_Nec b p item minor h o. ]_ Eſt enim ut p f ad p b, ita m o,
Fad h o &
permutando, ut p f ad mo, ita b p, ad b o. ſed p f non
est minor m o, ut oſtenſiim cst.
ergo neque b p ipſa h o minor erit.
14. quinti
Si igitur ab h
G
Figure: /permanent/library/4E7V2WGH/figures/0040-01 not scanned
[Figure 24]
ducatur linea ad
rectos angulos ip
ſi n o, coibit cum
b p, atque inter
b &
p cadet. ]
_Corruptus erat hic_
_locus in tranſlatio-_
_ne.
Illud uero ita de-_
_monſtr abitur.
Quo-_
_niam p f non eſt mi-_
_nor o m, nec p b ip-_
_ſa h o;
ſi ponatur p f_
_æqualis o m;
& p b,_
_ipſi h o æqualis erit._

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