Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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DE I _IS_ QVAE VEH. IN AQVA.

DEMONSTRATIO QVARTAE PARTIS.

HABEAT rurſum portio ad humidum in grauitate
proportionem quidem maiorem, quàm quadratum f p ad
quadratum b d;
minorem uero, quàm quadratum x o ad
b d quadratum:
& quam proportionem habet portio ad
humidum in grauitate, eandem habeat quadratum, quod
fit à linea ψ ad quadratum b d.
erit ψ maior, quàm f p, & mi
nor, quàm x o.
aptetur ergo quæ dam rectalinea i u inter
portiones a u q l, a x d interiecta, quæ ſit æqualis ψ, &
ipſi
b d æquidiſtans:
occurratq; reliquæ ſectioni in y. rurſus
u y dupla ipſius y i demonſtrabitur, ſicuti demonſtrata eſt
o g ipſius g x dupla.
ducatur autem ab u linea u ο, quæ ſe
ctionem a u q l in u contingat:
& iuncta a i ad q produca
tur.
eodem modo oſtendemus lineam a i ipſi i q æqualem
eſſe:
& a q ipſi
Figure: /permanent/library/4E7V2WGH/figures/0097-01 not scanned
[Figure 63]
u ω æquidiſtan-
tem.
Demon-
ſtrãdum eſt por
tionem in humi
dum demiſſam,
ĩclinatãq;
adeo,
ut baſis ipſius
non contingat
humidũ, ita con
ſiſtere, ut baſis
in humidũ ma-
gis demergatur
quam ut in uno
puncto eius ſu-
perficiem cõtin
gat.
Demittatur enim in humidum, ut dictum eſt; & iaceat
primo ſic inclinata, ut baſis nullo modo contingat ſuperfi-
ciem humidi.
ſecta autem ipſa plano per axem ad humidi

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