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No. Postulate 1 says that for any two points A and B, there is a line AB connecting them. While you could argue that "infinite lines" are a superset of "a line"
by jhbadger 1y ago
No. Postulate 1 says that for any two points A and B, there is a line AB connecting them. While you could argue that "infinite lines" are a superset of "a line" it is pretty obvious that Euclid meant one and only one line (which is true in Euclidean geometry)
- thaumasiotes 1y agoYou don't seem comfortable with math. You might observe that the way Euclid uses postulate 1 is to provide geometric constructions of shapes. If you want to argue about what he meant, what he meant was "you have a straightedge". Similarly, postulate 3 says "you have a compass", and postulate 2 says... "you have a straightedge". You've described drawing several parallel lines that meet at two opposite points of a sphere. Postulate 1 has no problem with that - all of those lines are straight. Postulate 5 has a problem with it, because they meet.