Desargues: [b]→1) Pappus' Theorem[/b] 2) Vector notation: [url]http://www.geogebratube.org/material/show/id/35213[/url] 3) Desargues' Theorem: [url]http://www.geogebratube.org/material/show/id/35525[/url]
The Law of Sines. [list] [*]Hold the four rays fixed. Let (sin[i]α[/i] sin[i]δ[/i])/(sin[i]β[/i] sin[i]γ[/i]) = k, a constant. Then (AC∙BD)/(BC∙AD)=k, for every line which intersects the rays. [/list] [list] [*]Hold points A, B, C, D fixed. Let (AC∙BD)/(BC∙AD) =k, a constant. Now draw four rays through A, B, C, D from an arbitrary point. We will always have (sin[i]α[/i] sin[i]δ[/i])/(sin[i]β[/i] sin[i]γ[/i])=k. [/list]