Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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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
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
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