Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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DE IIS QVAE VEH. IN AQVA.
m productam per pendicularem eſſe ad ipſam e f, quam
quidem ſecet in n.
D_vcatvr_ enim à puncto g linea g o ad rectos angulos ipſi
e f, diametrum in o ſecans:
& rurſus ab eodem puncto ducatur g p
ad diametrum perpendicularis:
ſecet autem ipſa diameter producta
lineã e f in q.
erit p b ipſi b q æqualis, ex trigeſimaquinta primi co
nicorum:
& g p pro-
cor. 8. ſe-
xti.
Figure: /permanent/library/4E7V2WGH/figures/0035-01 not scanned
[Figure 21]
portionalis ĩter q p, p o
quare quadratũ g p re-
17. ſextĩ.ctangulo o p q æquale
erit:
ſed etiã æquale est
rectangulo cõtento ipſa
p b, &
linea, iuxta quã
poſſunt, quæ à ſectione
ad diametrũ ordinatim
ducuntur, ex undecima
primi conicorum.
ergo
14. ſexti.quæ est proportio q p
ad p b eadem est lineæ,
iuxta quã poſſunt, quæ
à ſectione ducũtur ad ip
ſam p o:
est autem q p
dupla p b:
cũ ſint p b,
b q æquales, ut dictum
est.
Linea igitur iuxta
quam poſſunt, quæ à ſe-
ctione ducuntur ipſi-
us p o dupla erit:
&
propterea p o æqualis
ei, quæ uſque ad axem,
uidelicet ipſi k h:
ſed eſt p g æqualis k m; & angulus o p g angu-
32. primilo h k m;
quòd uterque rectus. quare & o g ipſi h m est œqualis:
4. primi.& angulus p o g angulo _k_ h m. æquidistantes igitur ſunt o g, h n:
28

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