Also knows as Desargues' Homology Theorem. Homologous sides are [i]corresponding sides[/i].
Notes: I find the manner or arguing toward dual theorems cumbersome. The condition for equality of Pappus' double ratios is improperly expressed by logical implication. Pappus in hand, this proof is identically its converse, by definition. Supplanting the equality with an implication arrow saddles all subsequent argument with a confusion about the definition of sine. The equality will hold, regardless. But it will appear mysterious. I prefer to discard this mystery. _________________ Desargues Homology Theorem: 1) Pappus' Theorem: [url]http://www.geogebratube.org/material/show/id/35140[/url] 2) Vector notation: [url]http://www.geogebratube.org/material/show/id/35213[/url] [b]3) Desargues' Theorem[/b] This is problem #59 in Heinrich Dorrie's [i]100 Great Problems of Elementary Mathematics.[/i] More: [url]http://www.geogebratube.org/collection/show/id/2735[/url]