Pseudo-Ptolemy \textit{De Speculis} (Q2741021)

The short catoptric treatise \textit{De speculis} was translated from the Greek into Latin by William of Moerbeke in 1269 and was ascribed by him to Ptolemy, probably on the authority of his manuscript but against all evidence of level and style as these are understood today. It has been printed several times, most recently in 1900 in Heron's \textit{Opera omnia}, on the basis however of somewhat revised Renaissance versions -- admittedly with an appendix based on William's autograph but without always recognizing changes inserted by a sixteenth-century owner of the manuscript. Jones' careful edition should therefore replace all predecessors. NEWLINENEWLINENEWLINEThe edition is followed by an English translation, meant to ``recover the sense of the original Greek text'' rather than rendering William's glosses (pointed out in the notes, however) -- not to speak of the De verbo ad verbum of William's translation, which is indeed even heavier than in the most of his Archimedes translations and almost unreadable unless one tries to think through the Greek (it replaces consistently the definite article by qui/que, and copies every ellipsis). NEWLINENEWLINENEWLINEThe treatise is built up as follows: An eclectic philosophically tainted introduction argues for the theoretical and practical interest of the topic; then follows a theoretical part which, among other things, proves from a principle of minimal distance that reflection from plane as well as convex surfaces must take place at equal angles. The last part describes various astounding devices making use of multiple mirrors or mirrors with mixed (e.g., saddle-like) curvature, devices that go well beyond what could be approached theoretically by any catoptrics (not only the present specimen) based on visual rays radiating from the eye, not on rays emanating from the object. NEWLINENEWLINENEWLINEThis structure is described in Jones's initial commentary, which also points to evidence suggesting that the version translated by William was a late ancient epitome made from an earlier original. As to the authorship of this original it is argued that the whole attitude and approach correspond well to Hero, but that this only shows that the treatise comes from an environment of mechanic's writers that had the same background knowledge and norm as Heron. Both the initial commentary and the notes also explore the relation of the treatise to other optical texts. The notes, almost as extensive as the text itself, also treat both philological problems and textual substance. NEWLINENEWLINENEWLINESection 9 of the treatise claims that the principle of minimal path determines the point of reflection even if the point thus determined does not allow equality of angles, which in Jones's words (p. 181) is ``obviously nonsense''. The reviewer would suggest that the claim could be based on physical observation, for instance of the reflection of sun-light in the edge of a piece of broken glass or of a metal mirror.