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 |< < (44) of 213 > >|
9944DE IIS QVAE VEH. IN AQVA. gura: & alia eadem diſponantur demonſtrabimus rurſum
n t æqualem eſſe ipſi u i:
& portiones a u q, a n z inter
ſe ſe æquales.
65[Figure 65] Itaque quoniã
ĩ portionibus
æqualibus, &
ſi
milibus a u q l,
a n z g ductæ
sũt a q, a z, por
tiones æqua-
les auferentes;
cum diametris
portionum æ-
quales angu-
los cõtinebũt.

ergo triangulo
rum n l s, u ω c
anguli, qui cõ-
ſiſtũt ad l ω pũ-
cta, æquales ſunt:
& b s recta linea æqualis ipſi b c: ſ r ipſi cr,
n χ ipſi u h:
& χ tipſi h i. quòd cum u y dupla ſit ipſius y i,
erit n χ maior, quàm dupla χ t.
Sit igitur n m ipſius m t du
pla.
Rurſus ex his manifeſtum eſt, non manere ipſam por-
tionem;
ſed inclinari ex parte a: ponebatur autem portio
humidi ſuperficiem in uno puncto contingere.
ergo ne-
ceſſe eſt, ut eius baſis in humidum magis demergatur.
DEMONSTRATIO QVINT AE PARTIS.
HABEAT denique portio ad humidum in grauitate
minorem proportionem, quàm quadratum f p ad quadra-
tum b d:
& quam proportionem habet portio ad humidũ
in grauitate, eandem quadratum, quod fit à linea ψ habeat
ad quadratum b d.
erit χ minor ipſa p f. Rurſus

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