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...Essay diagrammatic reasoning in euclid s elements danielle macbeth although the science of mathematics has not undergone sorts revolutionary changes that can be found course history natural sciences practice nevertheless changed considerably over two and a half millennia its theparadigmofancientmathematicalpractice is euclidean demon stration characterized by involvement both text diagram early modern mathematical begun seven teenth century instead computational symbolic it constitutively involves formula language arithmetic elementary algebra one taught as schoolchild even today see lachterman nineteenth this gave way nally to more conceptual approach rea soning from concepts for instance concept continuity analysis or group abstract stein most recent naturally brought train at least ocially if everyday working mathematician demand rigorous gap free proofs on basis antecedently specied axioms denitions also suggested many hopelessly awed but geometry limi tations everything might want...