Archimedes - Archimedis De iis qvae vehvntvr in aqva libri dvo

Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

[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.

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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