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For example in Book I. Proposition 2 he shows a line between points B and C. He also shows point A somewhere in the vicinity and shows how one would go about recreating that line starting at point A. Now I would just take my compass, put one end on B and the other end at C, then lift my compass and place the pivot point on point A and create another point that is the right length from A, then connect the two points and voila! An identical line at point A. Instead he goes through another round-about method to achieve the same end. In one of his steps he even does part of what I mentioned already which is to take the compass and put the ends to points B and C but uses it to create a circle instead.

Now I understand he was much smarter than I can ever hope to be so I presume he worked under a set of rules that prevented him from lifting the compass the way I did; what were these rules and where are they published?

Anthony
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    Euclid's compass is a "collapsing" compass. If you take it off the page, the legs do not keep their distance apart. But in fact any construction that can be done with a non-collapsing compass can be done with a collapsing compass. – André Nicolas Dec 30 '13 at 23:17
  • @AndréNicolas : Well that was a very simple answer to my question that explains everything; so simple I should have thought of that myself! Alas I was born in the shallower side of the gene pool... :( Thanks! – Anthony Dec 30 '13 at 23:21
  • It is not really obvious, our usual compasses are modestly rigid. But in the old days, some people insisted that for high precision drafting fixed opening compasses should be used, or at least that compasses not be used for direct distance transfer. – André Nicolas Dec 30 '13 at 23:28

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Note that Euclid never mentions a compass at all.

He simply states (postulate I.3) that one can somehow create a circle with any given center and radius. The definition of circle (definition I.15) makes clear that a "given radius" is a line segment with one end at the center of the circle which must already exist before postulate I.3 can be applied.

This is usually paraphrased vividly as something like "Euclid's compass collapses", but that's just a paraphrase. The actual postulates do not mention any specific tools. -- Thus not the "straightedge" either; the first two postulates simply assert that straight lines can be drawn somehow if we know two points on them.

hmakholm left over Monica
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The compasses used by Euclid was collapsible, see for example this for a discussion.

mrf
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  • Yes, Andre Nicolas mentioned this in a comment; thanks for the link which explains exactly my situation. – Anthony Dec 30 '13 at 23:26