Notes on the Data

At present, we present data only for Books I, II, III, and IV. Book V has no catasQI. Data for Book VI will be added soon.
The propositions are denoted in traditional form, eg: III.1 means Proposition 1 of Book III. Elsewhere, we use the notation: p.03.01 for the same proposition. Each construction comes from a proposition, but the proposition goes on to prove that the construction works, ending with Q.E.F. Other propositions, which are not constructions, end with Q.E.D.
The number of steps in the construction. This is an approximation in some cases. Note that our constructions include all steps of subroutines, subsubroutines, etc. Thus we show many more steps of construction than are found in Euclid, who omits subroutines altogether.
The number of drawings in our visual exfoliation of this construction of Euclid, who gives only one figure for each proposition. We give one drawing for each step, plus a few inbetweens. Thus, the number of drawings is larger than the number of steps.
The total number of drawings up to the end of this construction, starting from the first construction of Book I. Altogether, over 800 drawings for the 38 catasQI of the first four books, plus 5 alternative constructions we have interpolated, in place of the 38 drawings provided by Euclid: a more than 20X expansion.

Revised 28 September 1997 by Ralph Abraham <>