Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[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.
[51.] V.
[52.] DEMONSTRATIO SECVNDAE PARTIS.
[53.] COMMENTARIVS.
[54.] DEMONSTRATIO TERTIAE PARTIS.
[55.] COMMENTARIVS.
[56.] DEMONSTRATIO QVARTAE PARTIS.
[57.] DEMONSTRATIO QVINT AE PARTIS.
[58.] FINIS LIBRORVM ARCHIMEDIS DE IIS, QVAE IN AQVA VEHVNTVR.
[59.] FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORV M.
[60.] CVM PRIVILEGIO IN ANNOS X. BONONIAE, Ex Officina Alexandri Benacii. M D LXV.
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50ARCHIMEDIS nea h m ad li-
30[Figure 30] neam fc.
at uero
ut h m ad f c, ita
o h ad a f:
& ut
quadratum h m
ad quadratú g l,
ita linea h b ad
b g;
hoc est b g
ad b f.
ex quibus
ſequitur o h ad
a f ita eſſe, ut b g
ad b f:
& permu
tando oh ad b g,
ut a f ad f b.
ſed
eſt a f dupla ip-
ſius fb:
ſunt eni
a b, b f æquales
ex 35 primi libri
conicorum.
ergo
&
h o ipſius g b
eſt dupla.
quod demonſtrare oportebat.
LEMMA IIII.
Iiſdem manentibus, & à puncto m ducta m q uſque
ad diametrum, quæ ſectionem in puncto m conting at;
Dico h q ad q o eandem proportionem habere, quam
habet g h ad c n.
F_IAT_ enim h r æqualis g f. & cumtriangula a f c, o p n ſimi
lia ſint, &
p n ſit æqualis f c; eodem modo demonſtrabimus p o, f a
inter ſe æquales eſſe.
quare p o ipſius f b dupla erit. Sed eſt h o du
pla g b.
ergo & reliqua p h reliquæ f g; uidelicet ipſius r h eſt

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