The Elements

...is rectilinear, but those composed of...?
...sides...?
...will coincide...?
...so that side ΒΓ...?
...to the... will coincide...?
...to ΕΖ...?
...for if Β is placed upon Ε...?
...and ΒΑ upon ΕΔ...?
...because the... is equal...?
...ΑΒ to the...?
...and Γ upon Ζ...?
...because of...?
...to ΕΖ...?

so that if the lines on each and the same sides and under the base k d e z h'?, then again those under the base will coincide with one another because the bases also coincide, each upon each, and the lines or angles [will coincide] for the same reason? and all the lines which are equal? will coincide on each?
on each because of the aforementioned?
only, which was to be demonstrated?.

Two hand-drawn isosceles triangles are placed side-by-side. The triangle on the right features an arc at the base, indicating an interior angle.

If the angles at the base of an isosceles triangle are equal to one another, and if the equal straight lines are extended further, then the angles under the base will be equal to one another. Let ΑΒΓ be an isosceles triangle having side ΑΒ equal to side ΑΓ, and let the straight lines ΒΔ and ΓΕ be extended in a straight line with ΑΒ and ΑΓ. I say that the angle at the base, which is ΑΒΓ, is equal to ΑΓΒ, and [the angle] ΔΒΓ [is equal] to ΕΓΒ.

A geometric diagram for Euclid's Elements, Book I, Proposition 5 (the "Pons Asinorum"). It shows an isosceles triangle labeled with Greek letters: Α at the apex, Β and Γ at the base. The sides ΑΒ and ΑΓ are extended downward to points Δ and Ε, creating the auxiliary structure for the proof.

...since, therefore, ΑΔ? to ΑΕ?...