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If a straight line crossing two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if extended indefinitely, meet on that side on which are the angles less than the two right angles.
All that fifth postulate is saying is that if a straight line (let's call it L) crosses two other straight lines (let's call them L1 and L2) it will create four angles with each of them. If those four angles are not all 90° then you will have two acute angles and two obtuse angles for each intersection, L/L1 and L/L2. Now we limit ourselves to the angles on one side of line L, one acute and one obtuse, for each intersection. If the two acute angles (let's call them A and B) on one side of line L are facing each other, then the lines L1 and L2 will intersect on that same side of line B.
See http://www.cut-the-knot.org/triangle/pythpar/Fifth.shtml
Seems intuitively obvious to this Fool
It's my bridge and I'll cross it if I want to.
Entire Thread Subject Posted By Posted pons asinorum wwh 12/23/03 06:13 PM Re: pons asinorum Wordwind 12/25/03 10:32 AM Re: pons asinorum Faldage 12/25/03 02:07 PM Re: pons asinorum Buffalo Shrdlu 12/25/03 02:20 PM Re: pons asinorum Wordwind 12/25/03 03:05 PM Re: pons asinorum maahey 12/25/03 04:34 PM Re: pons asinorum wwh 12/25/03 05:59 PM Re: pons asinorum maahey 12/26/03 02:29 AM Re: Buridan's Ass Faldage 12/26/03 03:00 PM
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