Euclidean geometry was systematized as a special case of geometry without Euclid’s 5th postulate.
Pretty sure this should say “non-euclidian geometry”. Euclidian geometry is, if I am not confused, geometry that meets all of Euclid’s five postulates.
Ah, yes, I get it now. That sentence structure was really hard to parse for me for some reason, but I get the point now. I think I would have parsed it correctly if it had said “Euclidian geometry was systematized as a special case of non-Euclidian geometry by removing Euclid’s 5th postulate”, or something like that, but it does also sound kind of awkward.
But it’s not a special case of non-Euclidian geometry, they’re disjoint.
(It seems like you’re using “non-Euclidian” to mean “any geometry that accepts the first 4 postulates”, but I think it actually means “any geometry that accepts the first 4 postulates but doesn’t accept the 5th”.)
Ah, yeah, that is totally fair. In that case I don’t have a great rephrasing. Maybe “Euclidian geometry was systematized into absolute geometry by removing the fifth postulate”, but honestly, I’ve never heard the term “absolute geometry” before I just googled this topic.
Pretty sure this should say “non-euclidian geometry”. Euclidian geometry is, if I am not confused, geometry that meets all of Euclid’s five postulates.
He’s saying that Euclidean geometry is a special case of geometry in general. Non-euclidean geometry is the rest of the general case.
Ah, yes, I get it now. That sentence structure was really hard to parse for me for some reason, but I get the point now. I think I would have parsed it correctly if it had said “Euclidian geometry was systematized as a special case of non-Euclidian geometry by removing Euclid’s 5th postulate”, or something like that, but it does also sound kind of awkward.
But it’s not a special case of non-Euclidian geometry, they’re disjoint.
(It seems like you’re using “non-Euclidian” to mean “any geometry that accepts the first 4 postulates”, but I think it actually means “any geometry that accepts the first 4 postulates but doesn’t accept the 5th”.)
Ah, yeah, that is totally fair. In that case I don’t have a great rephrasing. Maybe “Euclidian geometry was systematized into absolute geometry by removing the fifth postulate”, but honestly, I’ve never heard the term “absolute geometry” before I just googled this topic.