The Scholia on Euclid are the anonymous explanatory notes transmitted in the margins and between the lines of the Greek manuscripts of Euclid and of the works that travelled with his. They are not the work of one author but a body of annotation built up in layers. Some notes go back to late-antique commentary: those on the first book of the Elements draw on Proclus, and the notes on the Data cite Pappus by name. Others were added by Byzantine teachers and copyists. No scholiast is named, and most individual notes cannot be dated. The corpus has nothing to do with Thucydides, under whose name it was once mistakenly filed.
The notes accompany Euclid's Elements, Data, Optics, Catoptrics and Phenomena, and the second Greek version of the Optics, which its editor Heiberg ascribed to Theon of Alexandria. The set on the Elements is by far the largest. It opens with a prologue on the place of geometry among the sciences, the grades of knowledge, the aim of Euclid's treatise, and the difference between axioms, postulates and hypotheses and between problems and theorems. Most scholia are short: a gloss on a word, the proposition on which a step depends, a supplementary or alternative proof, a worked numerical example, or a note on a variant reading. They cite Aristotle, Archimedes, Apollonius, Autolycus, Theodosius and Pappus, and cross-refer between Euclid's works.
The scholia were edited with the texts in the Heiberg–Menge edition of Euclid. They preserve material from late-antique mathematical commentary and show how Euclid's geometry, optics and spherical astronomy were taught and read from late antiquity through the Byzantine period, and their notes on readings make them evidence for the transmission of Euclid's text.
Available Works
Also published as PDF.