The Elements

...of the two triangles, and the base of them, ΒΓ, is equal to the side ΑΒ, and side ΒΓ is equal to the side ΑΒ and... upon the base angle... each to each, and the angle... contains [the side]... of the base angle ΒΓ... from... the [angles] upon the base... and... and... and... the angle upon each to each... of the... under ΑΒ... and the... of the side ΑΒ... and the... and ΒΓ... the remaining to the remaining.
It was shown that... to the... upon the... ΒΓ... each to each of those from ΒΓ... of the... under... the remaining ΒΓ... being discovered and not... of the remaining angles each to each... [the angle] under... under ΒΓ... under... to the hypothetical... since the... analogy... equal to the... of the remaining bases... ΑΒΓ...

the... was shown to be... of the... by the ΑΒΓ... and the parallelogram... and the ΑΒ... and the ΒΓ... and the [parallelogram]... and the common... and the ΒΑΔ side... of those owed to one another.

A geometric diagram illustrating a proof of congruence between two triangles. The triangles are drawn side-by-side with vertices labeled with Greek letters (including α, β, γ). This corresponds to Euclid's Elements, Book I, Proposition 4.

for equal are those?
at the center?

But if the angles under the base are not [moved], but rather those in the triangle are [kept], as [shown] in many figures, it is demonstrated for these... and by those [same] ΑΒΓ triangles, and it is evident that... those [based] on the ΒΓ triangles, and that [angle] toward the ΑΒ and ΑΓ side, [is] the ΒΓΑ... and the other of them is greater, as... the ΒΓ is greater than the ΒΓ, [the side] ΑΒ and [side] ΑΓ, as containing the angle on the base, and the whole ΒΓΑ... and on the ΑΒ side, [those] containing, and by those triangles the ΒΓ angle [is greater] than the ΓΑΒ angle and... the ΒΑ, and the [other] side of the ΑΒ is equal, and the ΓΑΒ angle [is equal] to the ΒΑΓ angle... it is not then around the ΑΒ side [that] those in the triangle [are]... and analogy; for ...? equal to one another...

...the angle on the base...