Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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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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DE IIS QVAE VEH. IN AQVA.

COMMENTARIVS.

QVARE quadratum b d magis excedit quadratum
Af q, quàm b c quadratum:
& idcirco linea f q minor eſt,
quàm b c:
itemq; f minor quam b r. ] _Quoniani exceſſus, quo_
_quadratum b d excedit quadratum b c ad quadratum b d minorem_
_proportionem habet, quàm exceſſus, quo quadratum b d excedit qua_
_dratum f q, ad idem quadratum:
erit ex octaua quinti exceſſus, quo_
_quadratum b d excedit quadratum b c, minor quàm exceſſus, quo ex_
_cedit quadratum f q.
ergo quadratum f q minus est quadrato b c: &_
_propterea linea f q minor linea b c.
Sed f q ad f eandem proportionẽ_
_habet, quam b c ad b r;
utraque enim utriuſque ſeſquialtera est. cum_
14. quinti_igitur f q ſit minor b c, &
f ipſa b r minor erit_.
Et propterea k r ad ſ y maiorem habet, quàm dimidium
Bipſius k r ad ψ b.
] _Est enim k r ad ſ y, ut quadratum p s ad qua_
_dratum ſ y:
& dimidium lineæ K r ad lineam ψ b, ut quadratum e ψ_
_ad quadratum ψ b_.
C
Et p h maior, quàm f. ] _Nam p h eſt æqualis ſ ω, & r ψ_
D_ipſi f_.

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