Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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[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.
[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.
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page |< < (12) of 213 > >|
3512DE 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-
11cor. 8. ſe-
xti.
21[Figure 21] portionalis ĩter q p, p o
quare quadratũ g p re-
2217. 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
3314. 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-
4432. primi lo h k m;
quòd uterque rectus. quare & o g ipſi h m est œqualis:
554. primi.& angulus p o g angulo _k_ h m. æquidistantes igitur ſunt o g, h n:
6628

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