Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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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.

LEMMA III.

V_EL_ igitur linea m n o ſccat diametrum in g, uel in alijs pun-
ctis:
& ſi quidem ſecat in g, unum at que idem punctum duabus li-
teris go notabitur.
Itaque quoniam f c, p n, h e m ſibiipſis æqui
distant:
& ipſi a c æquidiſtat m n o: fient triangula a f c, o p n,
o h m inter ſe ſimilia.
quare erit o h ad h m, ut a f ad fc: & per-
4. ſexti.mut ando o h ad a f, ut h m ad fc.
est autem quadratum h m ad
quadratum g l, ut linea h b ad lineam b g, ex uigeſima primi libri
conicorum:
& quadratum g l ad quadratum fc, ut linea g b ad
ipſam b f:
ſuntq; h b, b g, b f lineæ deinceps proportionales. er-
22. ſexti.
cor. 20. ſe
xti.
go &
quadrata h m, g l, f c, & ipſorum latera proportionalia
erunt.
atque idcirco ut quadratum h m ad quadratum g l, ita li-

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