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
ductæ ſunt à baſibus ad portiones lineæ a n, a q, quæ angu
los æquales continent cum ipſis baſibus, eandem propor-
tionem habebit q a ad a n, quam l a ad a d.
] _Hoc nos ſu_-
_pra demonstrauimus_.
Aequalis eſt ergo a n ipſi n q. ] _Cum enim q a ad a n ſit_,
F_ut l a ad a d;
diuidendo, conuertendoq; erit an ad n q, ut a d ad_
_d l.
eſt autem a d æqualis ipſi d l, quoniam d b ponitur diameter_
_portionis.
ergo & a n ipſi n q eſt æqualis_.
14. quinti
Et a q ipſi m y æquidiſtans. ] _Ex quinta ſecundi libri coni_-
G_corum.
Apollonij_.
Etſecetur b d in punctis k r, ut dictum eſt. ] _In prima_
H_parte huius propoſitionis.
ſecetur autem in K ita, ut b k ſit dupla ip_-
_ſius k d;
& in r, ut K r ſit æqualis ei, quæ uſque ad axcm_.
Quòd cũ in portionibus æqualibus, & ſimilibus, a p o l,
Ka m q l ab extremitatibus baſium ductæ ſint a o, a q, ita ut
portiones ablatæ faciant cum diametris angulos æquales:
& anguli, qui ad y g: & lineæ y b, g b inter ſe æquales erũt. ]
_Secet linea a q diametrum d b in θ, &
a o ſecet in η. Itaque quo_-
_niam in portionibus æqualibus, &
ſimilibus a p o l, a m q l ab ex_-
_tremitatibus baſium_
Figure: /permanent/library/4E7V2WGH/figures/0088-01 not scanned
[Figure 54]
_ducũtur a o, a q, quæ_
_æquales angulos con_
_tinent cum ipſis baſi_
_bus:
& anguli ad d_
_utrique ſunt recti_:
_erũt & reliqui a η d_,
_a θ d inter ſe æqua_-
_les.
linea autem p g_
_æquidiſtat lineæ a o_:

_itémq;
m y ipſi a q_:
_&
p s, m c ipſis a d_.
_triágula igitur p g s_,
_m y c triãgulis a η d_
_a θ d, atque inter ſe_
_ſunt ſimilia:
& ut a d ad a η, ita a d ad a θ: & permutando. li_-
4. ſexti.

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