[b]Double Elements:[/b] When we define two projections whose bases coincide: 1) both ranges of points are on the same circle or conic section, 2) both fields of rays have the same poitn of origin, 3) both ranges of points are on the same line ...there are [i]doubled elements[/i]: corresponding points (1, 3), or rays (2) which coincide.
(Tool: http://www.geogebratube.org/material/show/id/55253) _____________ Steiner's Double Element Constructions [b]→1) Double points of two ranges on a circle[/b] 2) Double rays from a point: [url]http://www.geogebratube.org/material/show/id/35600[/url] (both fields of rays have the same point of origin) 3) Double points on a line: [url]http://www.geogebratube.org/material/show/id/35633[/url] (both ranges of points are on the same line)