Two kinds of edge, and they are not the same
This graph has two sorts of line in it, and the difference matters more than the picture does.
Executed. One proposition calls another as a function, and the call is recorded as it happens. That edge is a fact about the running code: delete the earlier proposition and the later one stops working.
Cited. A reference written beside a step by hand, following the marginal references in Heath. Those are faithful to the text, and they are checked — every citation must name a proposition that exists, and no proposition may cite a later one — but they are transcription, not discovery. A finding read off cited edges is a finding about our typing, so nothing on the findings page is derived from them.
The 492 executed edges on their own, over the 348 propositions that have one. Small enough to read, and every line in it is a call that happened.
All 465 propositions. This is about ten thousand pixels wide, so it scrolls at full size: shrunk to a page the labels come out a pixel tall. Drag it sideways.
executed — a recorded callcited — written beside the step
Propositions sit on the row matching how many steps of argument stand between them and the starting rules. Lines run upward from a proposition to the ones built on it.
How many other propositions would fall if this one did — counting both kinds of edge, so mostly a summary of Euclid's own cross-references.
| Proposition | Dependents | Depth | Statement |
|---|---|---|---|
| I.1 | 168 | 0 | On a given finite straight line to construct an equilateral triangle. |
| I.2 | 167 | 1 | To place at a given point (as an extremity) a straight line equal to a giv |
| I.4 | 167 | 0 | If two triangles have the two sides equal to two sides respectively, and h |
| I.3 | 166 | 2 | Given two unequal straight lines, to cut off from the greater a straight l |
| I.5 | 164 | 3 | In isosceles triangles the angles at the base are equal to one another, an |
| I.7 | 162 | 4 | Given two straight lines constructed on a straight line (from its extremit |
| I.8 | 161 | 5 | If two triangles have the two sides equal to two sides respectively, and h |
| I.9 | 153 | 6 | To bisect a given rectilineal angle. |
| I.10 | 152 | 7 | To bisect a given finite straight line. |
| I.13 | 148 | 0 | If a straight line set up on a straight line make angles, it will make eit |
| I.15 | 146 | 1 | If two straight lines cut one another, they make the vertical angles equal |
| I.16 | 143 | 8 | In any triangle, if one of the sides be produced, the exterior angle is gr |
| I.29 | 121 | 2 | A straight line falling on parallel straight lines makes the alternate ang |
| I.26 | 99 | 9 | If two triangles have the two angles equal to two angles respectively, and |
| I.22 | 98 | 6 | Out of three straight lines, which are equal to three given straight lines |
| I.23 | 97 | 7 | On a given straight line and at a point on it to construct a rectilineal a |