Archimedes - Archimedis De iis qvae vehvntvr in aqva libri dvo

Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

[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.

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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