Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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6722DE IIS QVAE VEH. IN AQVA. dum eam, quæ per g ſurſum eleuabitur. non igitur manebit
portio ſic inclinata, nec conuertetur ita, ut axis ad ſuperfi-
ciem humidi ſit perpendicularis:
quoniam quæ ex parte 1
11F deorſum;
quæ uero ex parte a ſurſum ferentur, ut ex iam de
monſtratis apparere poteſt.
Quòd ſi axis cum ſuperficie
humidi fecerit angulum minorem angulo b, ſimiliter de-
22G monſtrabitur, nõ manere portionem, ſed inclinari, donec
utique axis cum ſuperficie humidi faciat angulum angulo
b æqualem.
COMMENTARIVS.
33A f q, quàm b c quadratum:
& idcirco linea f q minor eſt,
quàm b c:
itemq; f minor quam b r. ] _Quoniani exceſſus, quo_
_proportionem habet, quàm exceſſus, quo quadratum b d excedit qua_
erit ex octaua quinti exceſſus, quo_
_quadratum b d excedit quadratum b c, minor quàm exceſſus, quo ex_
_propterea linea f q minor linea b c.
Sed f q ad f eandem proportionẽ_
_habet, quam b c ad b r;
utraque enim utriuſque ſeſquialtera est. cum_
4414. quinti _igitur f q ſit minor b c, &
f ipſa b r minor erit_.
Et propterea k r ad ſ y maiorem habet, quàm dimidium
55B ipſius k r ad ψ b.