Pappus [C340]'s theorem is believed to have been included in Euclid [C300BC]'s Porisms, although Pappus' Collection of 340CE is the earliest extant reference. The key is the line arrangement and we include the illustrations copied from Pappus own work. Our diagram is copied from Pappus and Jones [1986b]. Jones copied Pappus' Συναγωή, found in the Vatican library (correcting an error assumed to be a mistake from an earlier copiest)
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You may notice that our pseudoline arrangements look somewhat different. One important difference is that for us, one of the nine lines is represented at infinity, whereas Pappus gives two diagrams with different locations of a tenth projective line, the line at infinity (although this concept would not have been familiar to him).
With line 0 projected to infinity. |
With line 1 projected to infinity. |
With line 2 projected to infinity. |