Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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ARCHIMEDIS
q o; uidelicet ut h g ad f p: quod proxime demonſtr atum eſt. At
2. lem:ueroipſi g q æquales ſunt duæ lineæ ſimul ſumptæ qb, hoc eſt h b,
4. lem.&
b g: atque ipſi q a æqualis eſt h f. Sienim ab æqualibus h b,
bq, æqualia fb,
Figure: /permanent/library/4E7V2WGH/figures/0052-01 not scanned
[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
19. quintiad 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,
15. 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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