Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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86ARCHIMEDIS ipſi my æquidiſtans. Demonſtrandum eſt portionem in
11G humidum demiſſam, inclinatamq;
contingat humidum, inclinatam conſiſtere ita, ut baſis ſu-
perficiem humidi nullo modo contingat:
& axis cum ea fa
ciat angulum angulo χ maiorem.
Demittatur enim in hu-
midum, conſiſtatq;
ita, ut baſis ipſius in uno puncto cõtin
gat humidi ſuperficiem:
& ſecta ipſa portione per axem,
ſuperficiei quidẽ por-
tionis ſectio ſit a p o l rectanguli coni ſectio:
ſuperficiei
humidi ſectio ſit a o:
axis autem portionis, & ſectionis dia
meter b d:
& ſecetur b d in punctis k r, ut dictum eſt: du-
22H catur etiam p g æquidiſtans ipſi a o, quæ ſectionem a p o l
contingat in p:
atque ab eo puncto ducatur p t æquidiſtãs
ipſi b d;
& p s ad b d perpendicularis. Itaque quoniam
portio ad humidum in grauitate eam proportionem ha-
bet, quam qua-
dratũ, quod fit
dratum b d:
quã
uero proportio
nem habet por-
eandem pars ip
ſius demerſa ha
tionẽ:
& quam
totam, eandem
tum t p ad b d
erit
linea ψ æqualis
ipſi t p.
quare & lineæ m n, p t; itemq, portiones a m q,
a p o inter ſe ſunt æquales.
Quòd cumin portionibus
33K