Euclid's straight lines
2015 (English)In: Normat, ISSN 0801-3500, Vol. 60, no 4, 145-169 p.Article in journal (Refereed) Published
We raise two questions on Euclid's Elements: How to explain that Propositions 16 and 27 in his first book do not follow, strictly speaking, from his postulates (or are perhaps meaningless)? and: What are the mathematical consequences of the meanings of the term eutheia, which we today often prefer to consider as different?
The answer to the first question is that orientability is a tacit assumption. The answer to the second is rather a discussion on efforts to avoid actual infinity, and having to (in some sense or another) construct equivalence classes of segments to achieve uniqueness.
Place, publisher, year, edition, pages
2015. Vol. 60, no 4, 145-169 p.
Euclid, Euclidean geometry, straight lines, axiom, postulate, projective space, orientablity
Research subject Mathematics
IdentifiersURN: urn:nbn:se:uu:diva-248861OAI: oai:DiVA.org:uu-248861DiVA: diva2:801064