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history-page19 - Calinger Forty-year-old Abraham Lincoln...

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Calinger: “Forty-year-old Abraham Lincoln mastered its first six books to make him a more exact reasoner.” What does this say about mathematics? · Centrality · Universality Definitions, Axioms, and Postulates The definitions are not mathematical and of no rigorous value. They can be thought of as giving intuition. · Examples The five axioms are intended to be general principles, not specific to geometry. 1. Things that are equal to the same thing are equal to each other. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. Things that coincide with one another are equal to one another. 5. The whole is greater than the part. The five postulates are specific to geometry and are about things that can be done. 1. It is possible to draw a straight line from any point to any other point. 2. It is possible to produce a finite straight line indefinitely in that straight line.
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