Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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[11. PROPOSITIO IIII.]
[12. PROPOSITIO V.]
[13. PROPOSITIO VI.]
[14. PROPOSITIO VII.]
[15. POSITIO II.]
[16. COMMENTARIVS.]
[17. PROPOSITIO VIII.]
[18. COMMENTARIVS.]
[19. PROPOSITIO IX.]
[20. COMMENTARIVS.]
[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.]
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DE IIS QVAE VEH. IN AQVA.
Itaque quoniam no ad f ω maiorem habetproportio-
] _Habet enim diame-_
_ter portioms n o ad f ω proportionem eandem, quam quindeeim ad_
_quatuor;
_habere ponitur, quàm quindecim ad quatuor.
quare n o ad f ω ma_
&_
_propterea quæ uſque ad axem ipſa f ω maior erit_.
10. quinti
Quoniam ergo in portione a p o l, quæ continetur re-
cta linea, &
rectanguli coni ſectione, _k_ ω quidem æ quidi-
ſtans eſt ipſi a l;
p i uero diametro æquidiſtat; ſecaturq;
ab ipſa k ω in h: & a c æquidiſtat contingenti in p neceſ-
ſarium eſt ipſam p i ad p h uel eandem proportionem ha
bere, quam habet n ω ad ω o, uel maiorem.
hoc enim iam
demonſtratum eſt] _Vbi hoc demonſtratum ſit uel ab ipſo Ar-_
_chimede, uel ab alio, numdum apparet, quocircanos demonstra-_
_tionem afferemus, poſteaquam non nulla, quæ ad eam pertinent ex-_
_plicauerimus_.

LEMMAI.

Sint lineæ a b, a c angulum b a c continentes: & à
puncto d, quod in linea a c ſumptum ſit, ducantur d e,
d f utcunque ad ipſam a b.