Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[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.]
[61. ALEXANDRO FARNESIO CARDINALI AMPLISSIMO ET OPTIMO.]
[62. FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORVM. DIFFINITIONES.]
[63. PETITIONES.]
[64. THEOREMA I. PROPOSITIO I.]
[65. THEOREMA II. PROPOSITIO II.]
[66. THE OREMA III. PROPOSITIO III.]
[67. THE OREMA IIII. PROPOSITIO IIII.]
[68. ALITER.]
[69. THEOREMA V. PROPOSITIO V.]
[70. COROLLARIVM.]
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ARCHIMEDIS
Quoniam enim triangula afd, akg, anl ſi-
Figure: /permanent/library/4E7V2WGH/figures/0048-01 not scanned
[Figure 28]
milia ſunt;
itémq; ſimilia efd, h k g, mnl:
erit ut af ad fd, ita ak ad kg; ut autem fd
4. ſexti.ad fe, ita kg ad kh.
quare ex æquali ut af
ad fe, ita ak ad kh:
& per conuerſionem ra-
tionis ut af ad ae, ita ak ad ah.
eodem
modo oſtendetur, ut af ad a e, ita an ad am.
cum igitur an ad am ſit, ut a k ad a h; erit
19. quintireliqua kn ad reliquam h m, hoc eſt ad g q,
uel o p, ut a n ad a m;
hoc estut a f ad a e.
rurſus a k ad a h est, ut a f ad a e. er-
go reliqua f k ad e h reliquam, uidelicet
ad do, ut a f ad a e.
Similiter demonſtrabi-
mus ita eſſe fn ad d p.
quod quidem demonſtra
re oportebat.

LEMMA II.

Sint in eadem linea a b puncta
Figure: /permanent/library/4E7V2WGH/figures/0048-02 not scanned
[Figure 29]
duo r s ita diſpoſita, ut a s ad a r
eandem proportionem habeat, quam
a f ad ae:
& per r ducatur rtipſi
e d æquidiſtans;
per s uero ducatur
s t æquidiſtans fd, ita ut cum r t in
t puncto conueniat.
Dico punctum t
cadere in lineam a c.
Si enim fieri potest, cadat citra: & produca
tur rt uſque ad ipſam a c in u.
deinde per u
ducatur u x ipſi f d æquidiſtans.
Itaque ex
ijs, quæ proxime demonstrauimus a x ad ar

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