Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

#### Table of figures

< >
[Figure 51]
[Figure 52]
[Figure 53]
[Figure 54]
[Figure 55]
[Figure 56]
[Figure 57]
[Figure 58]
[Figure 59]
[Figure 60]
[Figure 61]
[Figure 62]
[Figure 63]
[Figure 64]
[Figure 65]
[Figure 66]
[Figure 67]
[Figure 68]
[Figure 69]
[Figure 70]
[Figure 71]
[Figure 72]
[Figure 73]
[Figure 74]
[Figure 75]
[Figure 76]
[Figure 77]
[Figure 78]
[Figure 79]
[Figure 80]
< >
page |< < (17) of 213 > >|
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
f ω eandem ha
beat proportionem, quam quindecim ad quatuor:
& ipſi
n o ad rectos angulos ducatur ω k.
Itaque quoniam n o
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