![]() He stated this in words as follows: if equals are added to equals, the wholes are equal. Studying Euclidean geometry helps us think better and solve problems more. He used basic ideas called axioms or postulates to create solid proofs and figure out new ideas called theorems and propositions. Thus, he talked about it as a postulate – a universal truth.Īxioms and postulates are almost the same thing, though historically, the descriptor “postulate” was used for a universal truth specific to geometry, whereas the descriptor “axiom” was used for a more general universal truth, which is applicable throughout Mathematics (nowadays, the two terms are used interchangeably in fact, postulate is also a verb – to postulate something).įor example, one of Euclid’s axioms was that if A = B, and C = D, then Euclid, often called the father of geometry, changed the way we learn about shapes with his 13-book series, Euclid's Elements. ![]() Since this seems to be such a fundamental idea, Euclid saw no reason to try and prove this somehow, and instead took its truth as granted. The truth of this statement seems to be obvious – if we were to plot two points A and B in the plane, we would be able to draw one (and only one) line passing through A and B. Such obvious truths are referred to as axioms or postulates.įor example, one of Euclid’s postulates is that a unique straight line can be drawn from any one point to any other point. ![]() Such concepts and ideas can be thought of as obvious truths. Did you notice how it is difficult to precisely define the concepts of points and lines, and how we had to rely on our intuitive understanding to provide some definitions? Euclid faced the same problem.įor some geometrical concepts which are so fundamental as to be difficult to define, but which he thought are intuitively well-understood, Euclid assumed that no definitions or justifications were required. ![]()
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