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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1236DE CENTRO GRAVIT. SOLID. habebit maiorem proportionẽ,
79[Figure 79] quam c b ad b a.
fiat o b ad b a,
ut figura rectilinea ad portio-
nes.
cum igitur à circulo, uel el-
lipſi, cuius grauitatis centrum
eſt b, auferatur figura rectilinea
e f g h k l m n, cuius centrum a;
reliquæ magnitudinis ex portio
118. Archi-
medis.
nibus compoſitæ centrum graui
tatis erit in linea a b producta,
&
in puncto o, extra figuram po
ſito.
quod quidem fieri nullo mo
do poſſe perſpicuum eſt.
ſequi-
tur ergo, ut circuli &
ellipſis cen
trum grauitatis ſit punctum a,
idem quod figuræ centrum.
ALITER.
Sit circulus, uel ellipſis a b c d,
cuius diameter d b, &
centrum e: ducaturq; per e recta li
nea a c, ſecans ipſam d b adrectos angulos.
erunt a d c,
a b c circuli, uel ellipſis dimidiæ portiones.
Itaque quo-
niam por
80[Figure 80] tiõis a d c
cétrū gra-
uitatis eſt
in diame-
tro d e:
&
portionis
a b c cen-
trum eſt ĩ
ipſa e b:
to
tius circu
li, uel ellipſis grauitatis centrum eritin diametro d b.
Sit autem portionis a d c cẽtrum grauitatis f: &

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