Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[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.
[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.
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198FED. COMMANDINI dris s g, t u eſſe
147[Figure 147] punctum υ &

totius figuræ in
ſcriptæ, quæ cõ-
ſtat ex cylindris
q r, ſ g, t u eſſe φ
centrum.
Sunt
enim hi cylindri
æquales &
ſimi-
les cylindris y z,
K ν, θ λ, figuræ
circumſcriptæ.
Quoniã igitur
ut b e ad e d, ita
eſt o p ad p n;

utraq;
enim u-
triuſque eſt du-
pla:
erit compo
nendo, ut b d ad
d e, ita o n ad n
p;
& permutan
do, ut b d ad o
n, ita d e ad n p.

Sed b d dupla
eſt o n.
ergo &
e d ipſius n p du
pla erit.
quòd ſi
e d bifariam di-
uidatur ĩ χ, erit
χ d, uel e χ æ-
qualis n p:
&
ſublata e n, quæ
eſt cõmunis u-
trique e χ, p

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