I'm looking for a reference on the theory of straightedge and compass constructions in three dimensions akin to Euclid's Elements in two dimensions. More specifically, I mean a theory of geometric constructions where one is allowed lines between any two points, planes through any three non-colinear points, and spheres with a given center and radius. My preliminary Google searches aren't giving anything but surely this has been studied.

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    $\begingroup$ Are you looking for something like thenullhypodermic.blogspot.com/2012/01/… ? (Not a lot of results there, however; I thought there was more but I'm not finding it right now.) $\endgroup$ – David K Dec 27 '16 at 19:13
  • $\begingroup$ @DavidK, Yes, this is the same idea, but I was hoping for a reference to literature on the subject if any exists. $\endgroup$ – tghyde Dec 27 '16 at 19:39
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    $\begingroup$ See Solid Geometry by Hawkes, Luby, and Touton (1922 edition available as free e-book), which articulates a slightly different (but equivalent) approach on pg. 314 (Sec. 397 Constructions). $\endgroup$ – hardmath Dec 27 '16 at 20:28
  • $\begingroup$ There is also an extensive list of constructions in Euclid's Elements; see proofwiki.org/wiki/… for example. I think Euclid (like Hawkes, Luby, and Touton) constructed circles in planes rather than spheres in space, but I believe the constructable objects are the same either way. $\endgroup$ – David K Dec 27 '16 at 20:43

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