Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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DE IIS QVAE VEH. IN AQVA.
clinata, ut baſis humidum non contingat, ſectur plano per axem,
recto ad ſuperficiem humidi, ut ſectio ſit a m o l rectanguli coni ſe-
ctio:
ſuperficiei humidi ſectio ſit i o: axis portionis, & ſectionis
diameter b d;
quæ in eaſdem, quas diximus, partes ſecetur: duca-
turq;
m n quidem ipſi i o æquidiſtans, ut in puncto m ſectionem
cótingat:
mt uero æquidiſtans ipſi b d: & m s ad eandem perpen
dicularis.
Demonſtrandum eſt non manere portionem, ſed inclinari
ita, ut in uno puncto contingat ſuperficiem humidi.
ducatur enim p c
ad ipſam b d perpendicularis:
& iuncta a f uſque ad ſectionem
producatur in q:
& per p ducatur p φ ipſi a q æquidiſtans. erunt
iam ex ijs, quæ demonſtrauimus a f, f q inter ſe ſe æquales.
& cum
portio ad humi-
Figure: /permanent/library/4E7V2WGH/figures/0095-01 not scanned
[Figure 60]
dum eam in gra-
uitate proportio
nem habeat, quá
quadratú p f ad
b d quadratum:
atque eandem ha
beat portio ipſi-
us demerſa ad to
tam portionem;

hoc eſt quadratú
m t ad quadratú
8. quinti.b d:
erit quadra
tum m t quadra-
to p f æquale:
&
idcirco linea m t
æqualis lmeæ p
f.
Itaque quoniam in portionibus æqualibus, & ſimilibus a p q l, a
m o l ductæ ſunt lineæ a q, i o, quæ æquales portiones abſcindunt;
illa quidem ab extremitate baſis; hæc uero non ab extremitate: ſe-
quitur ut a q, quæ ab extremitate ducitur, minorem acutum angulú
contineat cum diametro portionis, quàm ipſa i o.
Sed linea p φ li-
neæ a q æquidiſtat, &
m n ipſi i o. angulus igitur ad φ angulo ad n

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