@Torin
Charles Dodgson (better known as Lewis Carrol) wrote a

short philosophical fantasy piece basically about this problem, or pseudo-problem, starring Achilles and the Tortoise. Suppose, the Tortoise says, we begin with this syllogism:

(A) Things that are equal to the same are equal to each other.

(B) The two sides of this Triangle are things that are equal to the same.

(Z) The two sides of this Triangle are equal to each other.

But, the Tortoise asks Achilles, suppose I accept A and B, but still dispute Z? So Achilles suggests an additional premise:

(A) Things that are equal to the same are equal to each other.

(B) The two sides of this Triangle are things that are equal to the same.

(C) If things that are equal to the same are equal to each other, and if the two sides of the Triangle are equal to the same, it follows that the two sides of this Triangle are equal to each other.

(Z) The two sides of this Triangle are equal to each other.

But, the Tortoise says, suppose I accept P1, P2 and P3, but still dispute C? Achilles (not really being as swift as his reputation) then takes the irrevocable step towards infinite regress by proposing:

(A) Things that are equal to the same are equal to each other.

(B) The two sides of this Triangle are things that are equal to the same.

(C) If things that are equal to the same are equal to each other, and if the two sides of the Triangle are equal to the same, it follows that the two sides of this Triangle are equal to each other.

(D) If (A) and (B) and (C), then the two sides of this Triangle are equal to each other.

(Z) The two sides of this Triangle are equal to each other.

And of course you know where it goes from there. (Dodgson of course makes Achilles and the Tortoise his characters as a kind of homage to Zeno's paradox about the impossibility of completing an infinite set of steps.)