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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52ARCHIMEDIS q o; uidelicet ut h g ad f p: quod proxime demonſtr atum eſt. At
112. lem: ueroipſi g q æquales ſunt duæ lineæ ſimul ſumptæ qb, hoc eſt h b,
224. lem.&
b g: atque ipſi q a æqualis eſt h f. Sienim ab æqualibus h b,
bq, æqualia fb,
32[Figure 32] ba demantur, re
manentia æqua-
lia erunt.
ergo
dempta h g ex
duabus lineis h
b, h g, relinqui-
tur dupla ipſius
b g;
hoc eſt o h:
& dempta p f ex
f h, reliqua est
b p.
quare o h
3319. quinti ad h p, eſt ut g q
ad q a.
Sed ut
g q ad q a, ita
h q ad q o;
hoc
eſt h g ad n c:
& ut o h ad h p,
4415. quin-
ti.
ita g b ad c k.
eſt
cnim o h dupla
g b, &
h p item
dupla gf;
hoc eſt
c k.
eandem igitur proportionem habet h g ad n c, qnam g b ad
c k:
& permutando n c ad c k eandem habet, quam b g ad g b.
Sumatur deinde aliud quod uis punctum in ſectum in ſectione,
quod ſit s:
& per s duæ lineæ ducantur: st quidem
æquidistans ipſi db, diametrumque in puncto t ſecans;
s u uero æquidistans ac, & ſecans c e in u. Dico u c
ad ck maiorem proportionem habere, quamtg ad gb.

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