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
Ex quibus perſpicuum eſt lineas omnes ſic ductas ab
ipſis ſectionibus in eandem proportionem ſecari.
eſt enim
diuidendo, conuertendoque cm ad mb, &
cf ad fb, ut
ce ad ea.

LEMMA III.

Sed & illud constare potest; lineas, quæ in portioni-
bus eiuſmodi ſimilibus ita ducuntur, ut cú baſibus æqua-
les angulos contineant, ab ipſis ſimiles quoque portiones
abſcindere:
hoc eſt, ut in propoſita figura, portiones h b c,
m f c, quas lineæ c h, c m abſcindunt, etiam inter ſe
ſimiles eſſe.
D_ividantvr_ enim ch, cm bifariam in punctis p q: & per
ipſa ducantur lineæ r p s, t q u diametris æquidiſtantes.
erit portio-
nis b s c diameter p s, &
portionis m u c diameter q u. Itaque fiat
ut quadratum c r ad quadratum c p, ita linea b n ad aliam lineam,
quæ ſit s x:
& ut quadratum c t ad quadratum c q, ita fiat f o ad
u y.
iam exijs
Figure: /permanent/library/4E7V2WGH/figures/0076-01 not scanned
[Figure 47]
quæ demóſtra
uimus in com-
mentarijs in
quartam pro-
poſitioné.
Ar-
chrmedis de co
noidibus, &

ſphæroidibus,
patet quadra-
tum c p æqua-
le eſſe rectan-
gulo p s x:

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