Solvability

Analysis-Resolution-Synthesis

Assume that the problem is solvable.

1. Analysis:

Apagoge/Epagoge. Systematically employ strategies of decomposition, of reduction, and of transformation (via auxiliary constructions, or completion of patterns), follow up until you arrive at a situation/configuration you can control.

2. Resolution:

Epilysis. Show that the desired "end configuration" of the Apagoge is attainable without the initial assumption, determine what is "given" in the sense of being constructible from the original information without the Analysis-hypothesis, and express the conditions for solvability (Diorismos).

3. Synthesis:

Proof. A classical Apodeixis, usually starting with a construction (Kataskeue) that matches, often even reiterates, the steps of the Resolution.

-Pappus

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