The two kinds of edges
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.
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.
executed — a recorded callcited — written beside the step
| 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 |