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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18ARCHIMEDIS extet ex humidi ſuperficie. conſiſtat autem humidum, ma
neatq;
: & intelligatur aliquod planum ductum per centrũ
terræ, per humidum, &

7[Figure 7] per magnitudinem ſoli-
dam:
à quo ſuperficies
quidem humidi ſecetur
ſecundum circunferen-
tiam a b c;
ſolida autem
magnitudo ſecundum fi
guram, in qua r:
& cen-
trum terræ ſit K.
Intelli
gatur etiam quædam py
ramis comprehendens
figuram r, ſicuti prius, quæ pũctum K pro uertice habeat:
fecenturq; ipſius plana à ſuperficie plani a b c ſecundum
a K K b:
& ſumatur pyramis alia æ qualis, & ſimilis ſuperio
ri, cuius plana ſecentur à plano a b c, ſecundum b K K c:

deinde alterius ſphæræ ſuperficies quædam deſcribatur in
humido circa centrum K, ſub ſolida magnitudine:
& ſece-
tur ab eodem plano ſecundum x o p:
poſtremo intelliga-
tur alia magnitudo h in poſteriori pyramide, quæ ex humi
do conſtet, &
ſolidæ magnitudini r ſit æ qualis. partes igi-
tur humidi, &
quæ in prima pyramide continetur ſuperfi-
cie x o;
& quæ in ſecunda ſuperficie o p continetur, æquali
ter iacent, &
continuatæ inter ſe ſe; non tamen ſimiliter
premuntur:
nam quæ eſt in prima pyramide premitur ma
gnitudine ſolida r, &
humido cõtinente ipſam, quod eſt in
loco pyramidis a b o x:
quæ uero in altera pyramide pre-
mitur ſolida magnitudineh, &
humido ipſam continente
in loco pyramidis p o b c.
At grauitas ſolidæ magnitudi-
nis r, minor eſt grauitate humidi, in quo h:
quoniam ma-
gnitudo ſolida mole quidem æqualis, &
humido leuior po
nitur:
grauitas autem humidi continentis magnitudines
r h eſt æqualis;
cum pyramides æquales ſint. magis

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