Textual Transmission: Greek, Arabic, Hebrew, Maurolico (1558), Halley (1758) & Björnbo (1902)¶
Loss of the Greek Archetype & Survival of Greek Witnesses¶
Although the continuous three-book Greek manuscript of Menelaus’s Sphaerica perished in late antiquity, two decisive polytonic Greek witnesses survive in public-domain critical editions:
Ptolemy’s *Syntaxis Mathematica* (*Almagest*) I.13 (ed. Heiberg, 1898, pp. 68–76): Under the heading Προλαμβανόμενα εἰς τὰς σφαιρικὰς δείξεις (“Preliminaries to Spherical Demonstrations”), Claudius Ptolemy proves the Planar Menelaus Lemma (κατὰ σύνθεσιν and κατὰ διαίρεσιν), two chord-division lemmas, and the Spherical Menelaus Theorem in chords of double arcs (ἡ ὑπὸ τὴν διπλῆν τῆς περιφερείας).
Pappus’s *Synagoge* Book VI & Proclus on Euclid I: Pappus (ed. Hultsch, 1877) cites Menelaus’s term τρίπλευρον (“trilateral”) for the spherical triangle and preserves propositions from Book II on rising times of ecliptic arcs.
Arabic, Latin & Hebrew Medieval Stemmata¶
As George Costard recounts in his 1758 Oxford Praefatio (pp. iii–v) and Axel Anthon Björnbo reconstructs in Studien über Menelaos' Sphärik (1902):
Baghdad & Khwarazm (9th–11th c.): Translated into Arabic by Isḥāq ibn Ḥunayn (c. 890 CE), commented upon by Thābit ibn Qurra in his Treatise on the Sector Figure (al-Shakl al-Qaṭṭāʿ), and critically redacted in 1007–1008 CE by Abū Naṣr Manṣūr, who rendered the compound proportions cleanly in terms of sines (jayb).
Toledo & Montpellier (12th–13th c.): Gerard of Cremona translated an Arabic redaction into Latin at Toledo, while Jacob ben Machir ibn Tibbon (Prophatius) translated Isḥāq’s lineage into Hebrew—preserved in the Bodleian Huntington manuscripts at Oxford using nekhohot (נכחות, subtensa dupli arcus, Halley 1758 p. 82).
From Maurolico (1558) to Halley’s Oxford Edition (1758)¶
Francesco Maurolico (Messina, 1558): In Menelai Sphaericorum Lib. III, Maurolico hailed Menelaus’s treatise as the source “whence the whole science of spherical triangles flows” (unde tota sphaeralium Triangulorum Scientia scaturit), yet freely interpolated his own lemmas and reorganized Book II–III; Marin Mersenne condensed Maurolico’s text in 1644.
Edmond Halley (Oxford, 1758): Savilian Professor Edmond Halley collated the Bodleian Hebrew Huntington codex directly against Arabic manuscripts, stripped away Renaissance interpolations, engraved accurate geometric woodcuts with Greek capital labels (
Α, Β, Γ, Δ, Ε, Ζ, Η, Θ, Κ, Λ, Μ, Ν), and added incisive philological scholia (notably the famous p. 82 Scholion on subtensa dupli arcus vs. Sinus and Figura Catha). Issued posthumously in 1758 with Costard’s preface, Halley’s Latin text—paired with Heiberg’s 1898 Greek Almagest text and Björnbo’s 1902 Teubner analysis—forms the 100% public-domain foundation of this Digital Scriptorium Codex.