Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[41.] COMMENTARIVS.
[42.] LEMMA I.
[43.] LEMMA II.
[44.] LEMMA III.
[45.] LEMMA IIII.
[46.] LEMMA V.
[47.] LEMMA VI.
[48.] II.
[49.] III.
[50.] IIII.
[51.] V.
[52.] DEMONSTRATIO SECVNDAE PARTIS.
[53.] COMMENTARIVS.
[54.] DEMONSTRATIO TERTIAE PARTIS.
[55.] COMMENTARIVS.
[56.] DEMONSTRATIO QVARTAE PARTIS.
[57.] DEMONSTRATIO QVINT AE PARTIS.
[58.] FINIS LIBRORVM ARCHIMEDIS DE IIS, QVAE IN AQVA VEHVNTVR.
[59.] FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORV M.
[60.] CVM PRIVILEGIO IN ANNOS X. BONONIAE, Ex Officina Alexandri Benacii. M D LXV.
[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.
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4517DE IIS QVAE VEH. IN AQVA.
SIT portio, qualis dicta eſt, & in humidum demittatur,
ſicuti diximus, adeo ut baſis eius in uno puncto contingat
humidum.
demonſtrandum eſtnon manere ipſam portio-
nem, ſed reuoluiita, ut baſis nullo modo humidi ſuperſicie
11A contingat.
Secta enim ipſa per axem, plano ad ſuper ſiciem
humidi recto, ſit ſectio ſuperſiciei portionis a p o l re-
ctãguli coni ſe
26[Figure 26] ctio:
ſuperſi-
ciei humidi ſe-
ctio ſit a s:
axis
autem portio-
nis, ac ſectio-
nis diameter n
o:
& ſccetur in
f quidẽ ita, ut
o f ſit dupla ip
ſius ſn;
in ω ue
ro, ut n o ad
f ω eandem ha
beat proportionem, quam quindecim ad quatuor:
& ipſi
n o ad rectos angulos ducatur ω k.
Itaque quoniam n o
22B ad f ω maiorem habet proportionem, quàm ad eam, quæ
uſque ad axem;
ſit ei, quæ uſque ad axem æqualis f b: & du
catur p c quidem ipſi a s æquidiſtans, cõtingensq;
ſectio-
nem a p o l in p;
pi uero æquidiſtans ipſi n o: & primum
ſecet pi ipſam κ ω in h.
Quoniã ergo in portione a p o l,
33C quæ continetur recta linea, &
rectanguli coni ſectione, κ ω
quidem æ quidiſtans eſtipſi a l;
p i uero diametro æquidi-
ſtat:
ſecaturq; ab ipſa κ ω in h: & a s æquidiſtat contingen-
ti in p:
neceſſarium eſtipſam p i ad p h uel ean dem pro-
portionem habere, quam habet n ω ad ω o, uel maiorem:
hocenim iam demonſtratum eſt. At uero n ω ſeſquialtera
eſt ipſius ω o.
& pi igitur uel ſeſquialtera eſt ipſius h p;
uel maior, quàm ſeſquialtera.
Quare ph ipſius h i aut du
44D

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