Mathematical Maturity.

For learners who already know some mathematics but want to recover the practice of constructing it from underneath. The propositions will be familiar; the discipline of naming what licenses each step may not be. The point of this path is the latter.

Five steps · roughly four weeks · the rigour matters more than the speed.

• № 01 · Foundations
  Definitions, postulates, common notions

  Read the twenty-three definitions, five postulates, and five common notions Euclid begins with. They look thin; they are the entire licensing apparatus for everything that follows. Pair with the concepts glossary if any term feels under-fixed.
  15 min · reference
• № 02 · Construct
  Propositions I.1 through I.5

  Build each one with the licensed tools only. The temptation, when you already know the result, is to wave the construction through. Resist it — the goal here is not the figure but the explicit chain of moves that produces it.
  3–4 sittings · lab
• № 03 · Reconstruct
  The proofs from memory

  The practice queue resurfaces each proof at increasing intervals. The first reconstruction will feel laboured even if the proof felt obvious during construction; this gap is the diagnostic, not the failure. Trust the spacing.
  10 min · daily
• № 04 · Read
  Why Euclid Still Matters

  Late in the path, not early. With the propositions in hand, the argument for why this text — and not its many competent successors — lands differently. Read it as commentary on what you have just done, not as preamble.
  18 min · essay
• № 05 · Map
  Dependency graph of Book I — forthcoming

  A future addition: a node-and-edge diagram showing how each proposition rests on its predecessors, with I.47 (the Pythagorean theorem) as the visible terminus. Until it ships, the dependency line at the top of each proposition page is the manual version.
  — · planned