{
  "abstract": "In the first part of this work we showed that, within a Hilbert plane deprived of the Side-Angle-Side axiom, the Side-Angle-Angle criterion, together with a ray correspondence principle [\\textbf{RCT}], the existence of angle bisectors [\\textbf{AB}], the congruence of supplements of congruent angles [\\textbf{SA}], and the Pons Asinorum [\\textbf{PA}], suffices to reconstruct SAS. We left open the question of whether [\\textbf{PA}] is genuinely required alongside the other three principles, noting only a qualitative asymmetry in the nature of the principles involved. In this second part we answer this question: we show that \\begin{equation*} \\textrm{SAA},\\ [\\textbf{RCT}],\\ [\\textbf{AB}] \\;\\vdash\\; [\\textbf{PA}], \\end{equation*} so that [\\textbf{PA}] is redundant among the hypotheses of our main theorem, which improves to \\begin{equation*} \\textrm{SAA},\\ [\\textbf{RCT}],\\ [\\textbf{AB}],\\ [\\textbf{SA}] \\;\\vdash\\; \\textrm{SAS}. \\end{equation*} The proof adapts an argument recently given by Donnelly, who reconstructs SAS from SAA together with an angle addition axiom and the existence of angle bisectors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21385",
  "author_total": 1,
  "authors": [
    {
      "name": "Roberto Volpe"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3swazmt3g5mg8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21385",
  "fulltext_url": null,
  "id": "3swazmt3g5mg8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21385",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.HO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.21385",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3swazmt3g5mg8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21385",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21385"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.HO",
      "subfield": "general"
    }
  ],
  "title": "On the Reconstruction of SAS from Other Triangle Congruence Criteria, Part II: Eliminating the Pons Asinorum",
  "title_text": "On the Reconstruction of SAS from Other Triangle Congruence Criteria, Part II: Eliminating the Pons Asinorum",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/3swazmt3g5mg8",
  "venue": "arXiv",
  "versions": []
}