The Syllogistic Architecture of Euclidean Geometry in Tenth-Century Khurasan: Critical Study, Complete Annotated English Translation, and Formal Analysis of ʿAbdallāh ibn Muḥammad al-Harawī's Epistle on Book I and Book II of Euclid's Elements (MS Lei

This monograph presents the first complete English translation, critical study, and formal epistemological analysis of the unique Arabic mathematical-logical treatise preserved in Leiden University Library, MS Or. 168 (Treatise 5, ff. 54v–68v), composed by the tenth-century Khurasanian geometer and logician ʿAbdallāh ibn Muḥammad al-Harawī (fl. ca. 350–395 AH / 960–1005 CE). While Western historiography routinely attributes the earliest systematic reduction of Book I of Euclid’s Elements into formal Aristotelian syllogisms to Conrad Dasypodius and Christian Herlinus (Strasbourg, 1566), al-Harawī’s epistle proves that six centuries earlier the Peripatetic-mathematical tradition of Khurasan had already executed a complete proposition-by-proposition syllogistic reduction of all 48 propositions of Book I (based on Thābit ibn Qurra’s redaction) alongside a relational-algebraic division (qisma) of all 14 propositions of Book II. Furthermore, we report three new philological findings: (1) decipherment of the vertical continuation of the colophon in the left margin of f. 68v omitted in all European catalogues since Dozy/De Goeje (CCO 994), Suter (1900), and Witkam (2007); (2) codicological substantiation of Suter’s identification of our author with Abū al-Ḥasan al-Shamsī al-Harawī via al-Sijzī’s angle-trisection treatise preserved fourteen folios earlier in the same codex (Leiden Or. 168/2, ff. 23r–40v); and (3) restoration of the rubricless section on Proposition I.15 (ff. 61r–61v) critiquing circular attempts to prove Euclid’s Fourth Postulate.