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 |< < (34) of 213 > >|
DE IIS QVAE VEH. IN AQVA.
ſectione e f c diuiditur: pars uero lineæ c a, quæ eſt in-
ter duas ſectiones proportione reſpondebit parti lineæ
ductæ, quæ itidem inter eaſdem ſectiones interiicitur;
hoc
est ut in propoſita figura, ſi producatur d b uſque ad c h
in l, ut ſectioni e f c in puncto m occurrat;
lineam l
b ad b m eãdem proportionem habere, quàm c e ad e a.
Produc. itur enim
Figure: /permanent/library/4E7V2WGH/figures/0079-01 not scanned
[Figure 49]
q f ad eandem lineá
c h in n, ſecás a b c
ſectionem in o:
&
iuncta b c, quæ tran
ſibit per f, ut oſten-
ſum eſt, erunt trian-
gula c g f, c d b ſi-
milia:
itémq; ſimi-
lia íter ſe, c f n, c b l.
quare ut g f ad d b,
4. ſexti:ita erit c f ad c b:
& ut c f ad c b, ita
f n ad b l.
ergo g f
11. quintiad d b, ut f n ad b l:
& permutando g f
ad f n, ut d b ad b l.

eſt autem d b æqua
lis ipſi b l ex trigeſi
maquinta primi li-
14. quintibri conicorum.
ergo
&
g f ipſi p i æqua
lis erit:
& ex trige
ſimatertia eiuſdem
linea c h ſectionem
e f c in eodem pun-

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