Full Idea
Euclid begins proofs about all triangles with 'let ABC be a triangle', but ABC is not a proper name. It names an arbitrarily selected triangle, and if that has a property, then we can conclude that all triangles have the property.
Gist of Idea
If you pick an arbitrary triangle, things proved of it are true of all triangles
Source
report of Euclid (Elements of Geometry [c.290 BCE]) by E.J. Lemmon - Beginning Logic 3.2
Book Reference
Lemmon,E.J.: 'Beginning Logic' [Nelson 1979], p.106
A Reaction
Lemmon adds the proviso that there must be no hidden assumptions about the triangle we have selected. You must generalise the properties too. Pick a triangle, any triangle, say one with three angles of 60 degrees; now generalise from it.