Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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32ARCHIMEDIS ceatinclinata. Demonſtrandum eſt non manere ipſam; ſed
rectam reſtitui.
Itaque ſecta ipſa plano per axem, recto ad
planum, quod eſt in ſuperficie humidi, portionis ſectio ſit
a p o l rectanguli coni ſectio:
axis portionis, & ſectionis
diameter n o:
ſuperficiei autem humidi ſectio ſit i s. Si
igitur portio non eſt recta;
non utique erit a l ipſi i s æ-
quidiſtans.
quare n o cum i s non faciet angulos rectos.
ducatur crgo k ω contingens ſectionem coni in p [quæ
11Suppleta
a. Federi-
co Cõm.
ipſi i s æquidiſtet:
& à puncto p ad i s ducatur p f æquidi
ſtans ipſi o n, quæ erit ſectionis i p o s diameter, &
axis por
22B tionis in humido demerſæ.
ſumantur deinde centra graui
tatum:
ſitq; ſolidæ magnitudinis a p o l grauitatis centrũ
33C r;
ipſius uero i p o s centrum ſit b: & iuncta b r produca-
44D tur ad g, quod ſit centrum grauitatis reliquæ figuræ i s l a.
Quoniam igitur n o ipſius quidem r o ſeſquialtera eſt;
eius autẽ, quæ uſque ad axẽ minor, quam ſeſquialtera;
erit
55E r o minor, quàm quæ uſque ad axem.
Quare angulus r p ω
66F acutus erit:
cum enim linea, quæ uſque ad axem maior ſit
ipſa r o;
quæ à puncto r ad k ω perpendicularis ducitur,
uidelicet r t, cũ
19[Figure 19] linea f p extra
ſectionem con
ueniet:
& pro-
pterea inter p
&
ω puncta ca-
datneceſſe eſt.
Itaq; ſi per b g
ducantur lineæ
ipſi r t æquidi-
ſtantes;
angu-
los rectos cum
ſuperficie humidi continebunt:
& quod in humido eſt ſur-
77G ſum feretur ſecundum perpendicularem, quæ per b ducta
eſt, ipſi r t æquidiſtans:
quod uero eſt extra humi dum

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