Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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14ARCHIMEDIS
SECETVR ſuperficies aliqua plano per k punctum
ducto:
& ſicſectio ſemper circuli circunferentia, centrum
habens punctum k.
Dico eam ſphæræ ſuperficiem eſſe. Si
enim non eſt ſphæræ ſuperfi-
4[Figure 4] cies;
rectæ lineæ, quæ à pun-
cto k ad circunferentiam du-
cuntur non omnes æquales e-
runt.
Itaque ſint a b puncta
in ſuperficie;
& inæquales li-
neæ a k k b:
per ipſas autem
a k k b planum ducatur, quod
ſectionem faciat in ſuperficie
lineam d a b c.
ergo d a b c cir
culi circunferentia eſt, cuius
centrum k;
quoniam ſuperficies eiuſmodi ponebatur: &
idcirco æquales inter ſe ſunt a k k b, ſed &
inæquales; quod
fieri non poteſt.
conſtat igitur ſuperficiem eam eſſe ſphæ-
ræ ſuperficiem.
PROPOSITIO II.
Omnis humidi conſiſtentis, atque manen-
tis ſuperficies ſphærica eſt;
cuius ſphæræ centrũ
eſtidem, quod centrum terræ.
INTELLIGATVR humidũ conſiſtens, manẽsq; :
&
ſecetur ipſius ſuperficies plano per centrum terræ du-
cto.
ſit autem terræ centrum k: & ſuperficieiſectio, linea
a b c d.
Dico lineam a b c d circuli circunferentiam eſſe, cu
ius centrum k.
Si enim non eſt, rectæ lineæ à puncto k ad
lineam a b c d ductæ non erunt æquales.
Sumatur recta li
nea quibuſdam quidem à puncto k ad ipſam a b c d ductis
maior;
quibuſdam uero minor; & ex centro k,

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