- #1
nomadreid
Gold Member
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I am not sure that this is the right rubric for this question, as it is historical, but as it is part of the history of Model Theory, I am putting it here. I will not be offended if the moderators decide that it doesn't belong here.
In https://arxiv.org/pdf/1008.2667.pdf, the author states that Lobachevsky
"calls 'parallels' (not just non-intersecting straight lines but) the two boundary lines which separate secants from non-secants (i.e. parallels in the usual terminology) passing through a given point."
whereby he earlier defines "secant" as follows
"For a terminological convenience I shall call a given straight line secant of another given straight line when the two lines intersect (in a single point)."
I do not understand what "boundary lines" here mean. Can someone clarify? Thanks.
In https://arxiv.org/pdf/1008.2667.pdf, the author states that Lobachevsky
"calls 'parallels' (not just non-intersecting straight lines but) the two boundary lines which separate secants from non-secants (i.e. parallels in the usual terminology) passing through a given point."
whereby he earlier defines "secant" as follows
"For a terminological convenience I shall call a given straight line secant of another given straight line when the two lines intersect (in a single point)."
I do not understand what "boundary lines" here mean. Can someone clarify? Thanks.