Science of logical proofs

Can you clarify your claim regarding logical proofs? That is, that there is no such thing as a logical proof and that every logical proof has a required premise. After all, if one seeks to prove that a triangle is right-angled, where is the required premise? In this case, for example, are we referring to the axioms of Euclidean geometry?
And another thing, are the sayings “the burden of proof is always on the one who claims the positive” and “from a scientific point of view, everything is false until proven otherwise” true?
 
thanks