Euclid's 2D Constructions:
the Hard Dependencies

Here we track the dependencies of the planar constructions, in which an earlier construction is used as a subroutine in another construction. This use must be in the construction, not in the proof. We include those referenced by Euclid, and those tacitly used as well. We call these the hard dependencies. (UNFINISHED)
Book I (14 constructions)
C#01 < p.01.01: To draw an equilateral triangle (vesica piscis)
None possible

C#02 < p.01.02: To move a line
Uses C#01 < p.01.01: vesica piscis

C#03 < p.01.03: To move a line onto a line
Formally uses C#01 and C#02, but we use the rope!

C#04 < p.01.09: To bisect an angle
Uses C#01 < p.01.01: vesica piscis
Uses C#03 < p.01.03: the rope (or dividers)

C#05 < p.01.10: To bisect a line
Uses C#01 < p.01.01: vesica piscis
Uses C#04 < p.01.09: angle bisection

C#06 < p.01.11: To draw a perp at a point
Uses C#01 < p.01.01: vesica piscis
Uses C#03 < p.01.03: the rope (or dividers)

C#07 < p.01.12: To drop a perp from a point
Uses C#01 < p.01.01: vesica piscis
Uses C#04 < p.01.09: angle bisection
Uses C#05 < p.01.10: line bisection

C#08 < p.01.22: To make a triangle of three lines
Uses C#03 < p.01.03: the rope (or dividers)

C#09 < p.01.23: To move an angle onto a line at a point
Uses C#08 < p.01.22: make a triangle

C#10 < p.01.31: To draw a parallel through a point
Uses

C#11 < p.01.42: To draw a parallelogram equal to a triangle
Uses

C#12 < p.01.44: Same, but with a given width
Uses C#01 < p.01.01: vesica piscis
Uses C#03 < p.01.03: the rope (or dividers)
Uses C#05 < p.01.10: line bisection
Uses C#08 < p.01.22: make a triangle
Uses C#09 < p.01.23: To move an angle onto a line at a point
Uses C#10 < p.01.31: To draw a parallel through a point
Uses C#11 < p.01.42: To draw a parallelogram equal to a triangle

C#13 < p.01.45: To draw a parallelogram equal to a figure
Uses

C#14 < p.01.46: To draw a square on a given side
Uses
Revised 11 July 2002 by Ralph Abraham
abraham@vismath.org