From Elements of Geometry by J. Hamblin Smith, Book I. Axioms ... Euclid develops the science of Geometry in a series of Propositions, some of which are called ...
From Elements of Geometry by J. Hamblin Smith, Book I
Axioms I. Things which are equal to the same thing are equal to one another. II. If equals be added to equals the wholes are equal. III. If equals be taken from equals, the remainders are equal. IV. If equals and unequals be added together, the wholes are unequal. V. If equals be taken from unequals, or unequals from equals, the remainders are unequal. VI. Things which are double of the same thing, or of equal things, are equal to one another. VII. Things which are halves of the same thing, or of equal things, are equal to one another.[...] Euclid develops the science of Geometry in a series of Propositions, some of which are called Theorems and the rest Problems, though Euclid himself makes no such distinction. By the name Theorem we understand a truth, capable of demonstration or proof by deduction from truths previously admitted or proved.
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Questions 1. Re-write the seven axioms using mathematical symbols. 2. Explain the dierence between a de nition, an axiom and a theorem.
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