By Richard Fitzpatrick
The Greek textual content of J.L. Heiberg (1883-1884) from Euclidis Elementa, edidit et Latine interpretatus est I.L. Heiberg, Lipsiae, in aedibus B.G. Teubneri, 1883-1884 with an accompanying English translation
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Additional resources for Euclid's Elements in Greek: Vol. I: Books 1-4
Thus, for any triangle, when one of the sides is produced, the external angle is greater than each of the internal and opposite angles. (Which is) the very thing it was required to show. 9 The implicit assumption that the point F lies in the interior of the angle ABC should be counted as an additional postulate. 41 ΣΤΟΙΧΕΙΩΝ α΄ ιζ΄ Α Β Γ ∆ Παντ ς τριγώνου α δύο γωνίαι δύο ρθ ν λάσσονές ε σι πάντ µεταλαµβανόµεναι. Εστω τρίγωνον τ ΑΒΓ· λέγω, τι το ΑΒΓ τριγώνου α δύο γωνίαι δύο ρθ ν λάττονές ε σι πάντ µεταλαµβανόµεναι.
Thus, BCG is also equal to BCA, the lesser to the greater. The very thing (is) impossible. Thus, AB is not unequal to DE. Thus, (it is) equal. And BC is also equal to EF . So the two (straight-lines) AB, BC are equal to the two (straight-lines) DE, EF , respectively. And angle ABC is equal to angle DEF . Thus, the base AC is equal to the base DF , and the remaining angle BAC is equal to the remaining angle EDF [Prop. 4]. But again, let the sides subtending the equal angles be equal: for instance, (let) AB (be equal) to DE.