Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[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.]
[81. THE OREMA XII. PROPOSITIO XVI.]
[82. THE OREMA XIII. PROPOSITIO XVII.]
[83. THEOREMA XIIII. PROPOSITIO XVIII.]
[84. THEOREMA XV. PROPOSITIO XIX.]
[85. THE OREMA XVI. PROPOSITIO XX.]
[86. THEOREMA XVII. PROPOSITIO XXI.]
[87. THE OREMA XVIII. PROPOSITIO XXII.]
[88. THEOREMA XIX. PROPOSITIO XXIII.]
[89. PROBLEMA V. PROPOSITIO XXIIII.]
[90. THEOREMA XX. PROPOSITIO XXV.]
[91. THEOREMA XXI. PROPOSITIO XXVI.]
[92. THEOREMA XXII. PROPOSITIO XXVII.]
[93. PROBLEMA VI. PROPOSITIO XX VIII.]
[94. THE OREMA XXIII. PROPOSITIO XXIX.]
[95. THEOREMA XXIIII. PROPOSITIO XXX.]
[96. THEOREMA XXV. PROPOSITIO XXXI.]
[97. FINIS LIBRI DE CENTRO GRAVITATIS SOLIDORVM.]
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ARCHIMEDIS
nea h m ad li-
Figure: /permanent/library/4E7V2WGH/figures/0050-01 not scanned
[Figure 30]
neam fc.
at uero
ut h m ad f c, ita
o h ad a f:
& ut
quadratum h m
ad quadratú g l,
ita linea h b ad
b g;
hoc est b g
ad b f.
ex quibus
ſequitur o h ad
a f ita eſſe, ut b g
ad b f:
& permu
tando oh ad b g,
ut a f ad f b.
ſed
eſt a f dupla ip-
ſius fb:
ſunt eni
a b, b f æquales
ex 35 primi libri
conicorum.
ergo
&
h o ipſius g b
eſt dupla.
quod demonſtrare oportebat.

LEMMA IIII.

Iiſdem manentibus, & à puncto m ducta m q uſque
ad diametrum, quæ ſectionem in puncto m conting at;
Dico h q ad q o eandem proportionem habere, quam
habet g h ad c n.
F_IAT_ enim h r æqualis g f. & cumtriangula a f c, o p n ſimi
lia ſint, &
p n ſit æqualis f c; eodem modo demonſtrabimus p o, f a
inter ſe æquales eſſe.
quare p o ipſius f b dupla erit. Sed eſt h o du
pla g b.
ergo & reliqua p h reliquæ f g; uidelicet ipſius r h eſt du-

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