Ancient Science · Part 8 · Alexandria · B2
Euclid’s Elements: Definitions, Proofs and No Royal Road
Part 8 of Ancient Science: Euclid’s Elements, written in Alexandria around 300 BCE, built the whole of Greek geometry from a few definitions, one proof at a time, and stayed in schools for two thousand years. Sophia shows how the book is built, how it reached us, and the one postulate that troubled mathematicians until the nineteenth century. Since, therefore, it follows that and must, with Philo, Sophia, Marcos and Demetria.
Tonight we meet the most successful textbook ever written. It was written here, in Alexandria, about three hundred years before you were born, Philo.
Euclid’s Elements. My teacher made me copy the first book. Twice.
Then you know how it begins: “A point is that which has no part.” Everything else follows from a few definitions and a few rules.
Four hundred and sixty-five propositions, one after another, each proved from the ones before. Let me show you.
We know almost nothing about Euclid. A writer of the fifth century CE, Proclus, says that he taught in Alexandria under the first Ptolemy. That is nearly all. We do not know where he was born or when he died.
His Elements has thirteen books. It begins with definitions (what a point, a line and a circle are), postulates (things the reader is asked to accept, such as that a straight line can be drawn between any two points) and common notions (such as: things equal to the same thing are equal to each other). From these, every proposition is proved, step by step.
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