Bibliotheca Polyglotta

Euclid: Elementa

δύο ἄρα κύκλων τεμνόντων ἀλλήλους τῶν ΑΒΓ, ΔΕΖ τὸ αὐτό ἐστι κέντρον τὸ Ο: ὅπερ ἐστὶν ἀδύνατον.

eng

therefore the two circles ABC, DEF which cut one another have the same centre P: which is impossible. [III. 5]

lat Sic

Duorum ergo circulorum se invicem secantium ABG, DEZ idem est centrum. Quod est impossibile.

lat Gerard

Punctum ergo N duorum circulorum AB et GD centrum existit quorum unusquisque alium secat, duorum igitur circulorum sese secantium unum est centrum. Hoc autem contrarium est et impossibile.

lat Adelard 49r

Duorum itaque circulorum se invicem dividentium centrum idem esse continget. Quod est impossibile.

lat Hermann 20v

Evenit ergo circulorum sese secantium idem esse centrum quod pridem alter constitit.¹

1. Hermann, and probably his Arabic source, does not relate to the ad absurdum argument, and thus his version of the proposition is a deficient argument, given the figure.

No Arabic

No Arabic

No Arabic

san

No Sanskrit

lat Clavius

No Latin

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