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Thanks for the very interesting list. I was expecting Euclid's Elements to be up there. Perhaps the filter "literary work" disqualified it. If you all pardon

by srean 2y ago

Thanks for the very interesting list. I was expecting Euclid's Elements to be up there. Perhaps the filter "literary work" disqualified it. If you all pardon an off topic digression, the nebulosity of the definition of a straight line in elements has always bothered me. I wanted something free of reference to a physical artifact (straight edge, taught rope etc) and free of algebra. Its sometimes defined in terms of reflections or rotations or translations, but then that begs the question what is a straight axis (or direction of translation). Playfair's version is almost satisfactory. The standard I guess is Hilbert's.

mci 2y ago
> If you all pardon an off topic digression... IMHO, Euclid's definition of a straight line in today's terms would be "a line that has the same direction on its entire length". His definition of a plane angle would be "a plane angle is the difference between the directions of two straight lines that have a common end in one point". What are Playfair's and Hilbert's definitions?
- srean 2y ago
  The problem I have with that version of Euclid's definition is that direction is not defined. Playfair interprets Euclid as follows, I am using my own words here, a straight line is that figure which has the property that if it intersects its moved copy at 2 points it necessarily coincides with it everywhere. "Movement" is undefined, it has to be an isometry. Hilbert's is more abstract and based upon sets. Line is a primitive (undefined name) that interacts with two other undefined names (points and planes) according defined relations (lies on, lies between and is_congruent). More here https://en.wikipedia.org/wiki/Hilbert%27s_axioms https://en.wikipedia.org/wiki/Hilbert%27s_axioms