Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[11.] PROPOSITIO IIII.
[12.] PROPOSITIO V.
[13.] PROPOSITIO VI.
[14.] PROPOSITIO VII.
[15.] POSITIO II.
[16.] COMMENTARIVS.
[17.] PROPOSITIO VIII.
[18.] COMMENTARIVS.
[19.] PROPOSITIO IX.
[20.] COMMENTARIVS.
[21.] ARCHIMEDIS DE IIS QVAE VEHVNTVR IN AQVA LIBER SECVNDVS. CVM COMMENTARIIS FEDERICI COMMANDINI VRBINATIS. PROPOSITIO I.
[22.] PROPOSITIO II.
[23.] COMMENTARIVS.
[24.] PROPOSITIO III.
[25.] PROPOSITIO IIII.
[26.] COMMENTARIVS.
[27.] PROPOSITIO V.
[28.] COMMENTARIVS.
[29.] PROPOSITIO VI.
[30.] COMMENTARIVS.
[31.] LEMMAI.
[32.] LEMMA II.
[33.] LEMMA III.
[34.] LEMMA IIII.
[35.] PROPOSITIO VII.
[36.] PROPOSITIO VIII.
[37.] COMMENTARIVS.
[38.] PROPOSITIO IX.
[39.] COMMENTARIVS.
[40.] PROPOSITIO X.
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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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