[very] -- superposing
Euclid 1.4 is troublesome. The first three propositions in the book are actually constructions, so I.4 is the first “real” proposition. Because it occurs so early in the work, Euclid does not have a lot of material to draw from. Therefore, he makes recourse to more unusual arguments. For example —
If the triangle ABC is superposed on the triangle DEF, and if the point A is placed on the point D and the straight line AB on DE, then the point B also coincides with E, because AB equals DE.
He asks to imagine placing one triangle on top of another and assumes that it is visually obvious that certain parts correspond with each other. The argument makes good intuitive sense, so most people take it at face value and move on.
However, thinkers in the late 19th and early 20th century found fault with Euclid here, saying that there is nothing in his Axioms or Common Notations that mentions the idea of superposition. While they are technically correct, it is very interesting that this logical problem escaped the notice of apparently everyone before them, even geniuses like Lagrange, Euler, and Gauss.
This problem lay hidden for so long because superposition is a natural cognitive operation. In language and music, if we stack two identical things on top of each other they will collapse into one. We say “app”, not “ap-p”. Two C notes sounding together gives C, not something else. In other words, superposition is merely a species of the more basic idempotence structure.