Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[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.]
[71. THEOREMA VI. PROPOSITIO VI.]
[72. THE OREMA VII. PROPOSITIO VII.]
[73. THE OREMA VIII. PROPOSITIO VIII.]
[74. THE OREMA IX. PROPOSITIO IX.]
[75. PROBLEMA I. PROPOSITIO X.]
[76. PROBLEMA II. PROPOSITIO XI.]
[77. PROBLEMA III. PROPOSITIO XII.]
[78. PROBLEMA IIII. PROPOSITIO XIII.]
[79. THEOREMA X. PROPOSITIO XIIII.]
[80. THE OREMA XI. PROPOSITIO XV.]
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ARCHIMEDIS
q o; uidelicet ut h g ad f p: quod proxime demonſtr atum eſt. At
2. lem:ueroipſi g q æquales ſunt duæ lineæ ſimul ſumptæ qb, hoc eſt h b,
4. lem.&
b g: atque ipſi q a æqualis eſt h f. Sienim ab æqualibus h b,
bq, æqualia fb,
Figure: /permanent/library/4E7V2WGH/figures/0052-01 not scanned
[Figure 32]
ba demantur, re
manentia æqua-
lia erunt.
ergo
dempta h g ex
duabus lineis h
b, h g, relinqui-
tur dupla ipſius
b g;
hoc eſt o h:
& dempta p f ex
f h, reliqua est
b p.
quare o h
19. quintiad h p, eſt ut g q
ad q a.
Sed ut
g q ad q a, ita
h q ad q o;
hoc
eſt h g ad n c:
& ut o h ad h p,
15. quin-
ti.
ita g b ad c k.
eſt
cnim o h dupla
g b, &
h p item
dupla gf;
hoc eſt
c k.
eandem igitur proportionem habet h g ad n c, qnam g b ad
c k:
& permutando n c ad c k eandem habet, quam b g ad g b.
Sumatur deinde aliud quod uis punctum in ſectum in ſectione,
quod ſit s:
& per s duæ lineæ ducantur: st quidem
æquidistans ipſi db, diametrumque in puncto t ſecans;
s u uero æquidistans ac, & ſecans c e in u. Dico u c
ad ck maiorem proportionem habere, quamtg ad gb.

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