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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page |< < (12) of 213 > >|
DE IIS QVAE VEH. IN AQVA.
m productam per pendicularem eſſe ad ipſam e f, quam
quidem ſecet in n.
D_vcatvr_ enim à puncto g linea g o ad rectos angulos ipſi
e f, diametrum in o ſecans:
& rurſus ab eodem puncto ducatur g p
ad diametrum perpendicularis:
ſecet autem ipſa diameter producta
lineã e f in q.
erit p b ipſi b q æqualis, ex trigeſimaquinta primi co
nicorum:
& g p pro-
cor. 8. ſe-
xti.
Figure: /permanent/library/4E7V2WGH/figures/0035-01 not scanned
[Figure 21]
portionalis ĩter q p, p o
quare quadratũ g p re-
17. ſextĩ.ctangulo o p q æquale
erit:
ſed etiã æquale est
rectangulo cõtento ipſa
p b, &
linea, iuxta quã
poſſunt, quæ à ſectione
ad diametrũ ordinatim
ducuntur, ex undecima
primi conicorum.
ergo
14. ſexti.quæ est proportio q p
ad p b eadem est lineæ,
iuxta quã poſſunt, quæ
à ſectione ducũtur ad ip
ſam p o:
est autem q p
dupla p b:
cũ ſint p b,
b q æquales, ut dictum
est.
Linea igitur iuxta
quam poſſunt, quæ à ſe-
ctione ducuntur ipſi-
us p o dupla erit:
&
propterea p o æqualis
ei, quæ uſque ad axem,
uidelicet ipſi k h:
ſed eſt p g æqualis k m; & angulus o p g angu-
32. primilo h k m;
quòd uterque rectus. quare & o g ipſi h m est œqualis:
4. primi.& angulus p o g angulo _k_ h m. æquidistantes igitur ſunt o g, h n:
28

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