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> This question reminds me that one of Euclid's postulates The question is one of Euclid's postulates (or the combination of two, 1 which defines a straight li
by masklinn 3y ago
> This question reminds me that one of Euclid's postulates
The question is one of Euclid's postulates (or the combination of two, 1 which defines a straight line segment, and 2 which extends the straight line segment to a straight line).
- thaumasiotes 3y agoPostulate 1 doesn't define a straight line segment. It tells you that it's possible to connect two points with a straight line segment. A definition would tell you whether or not something qualified as a straight line segment. The definition appears to be given, appropriately enough, in the "definitions" section that precedes the postulates, which says "a straight line is one which lies evenly with the points on itself". (As translated in https://farside.ph.utexas.edu/books/Euclid/Elements.pdf https://farside.ph.utexas.edu/books/Euclid/Elements.pdf ) But although that is indeed how people recognize lines, it's not so easy to define what it means.