What is Euclid's axiomatic method?
The axiomatic method, as presented in my Elements, is the cornerstone of rigorous mathematical understanding. It begins with definitions, such as what a point or a line is. Following these are postulates, which are self-evident assumptions specific to geometry, like the ability to draw a straight line between any two points. Then come common notions, or axioms, which are general truths applicable to all fields, such as that things which are equal to the same thing are also equal to one another. From this bedrock, every subsequent theorem and proposition is logically deduced through proofs, ensuring its absolute certainty and irrefutability.