Berggren, J. L. [al-Kūhī] Abū Sahl al-Kūhī’s treatise on the construction of the astrolabe with proof: text, translation and commentary. (English, Arabic) Zbl 0814.01004 Physis, Nuova Ser. 31, No. 1, 141-252 (1994). This article presents an edition, with English translation and commentary, of the Arabic text of Abū Sahl al-Kūhī (2nd half of the tenth century) on the construction of the astrolabe. The problem in itself can be simply stated: How does one produce an instrument that can simulate the motion of the celestial sphere and at the same time allow for the solution of the various mathematical problems associated with that motion that are relevant to a specific point on the earth. From classical times, the problem attracted the attention of both the instrument makers as well as the mathematicians. To give only one example, the elegant theory of stereographic projection, with its main feature of preserving circles, did not only supply a mathematically ingenious solution to the problem, but also allowed the instrument makers to construct real jewels of both precision and aesthetical beauty. The work of Abū Sahl includes other projections as well, all of them of great mathematical interest. The edition and translation of the work is based on a unique manuscript Leiden Or. 14/10, supplemented by another unique commentary preserved in Leiden Or. 14/12. Berggren’s edition and translation is well executed, and this reviewer takes issue only with very few methodological points. For example, Berggren intentionally uses the term “flattening” to translate the Arabic term “tasṭīḥ” in order to avoid the injection of the modern term “projection” into this medieval text. While one may agree with the general intent of Berggren, one will have to raise the question as to the inadequacy of the non-technical term “flattening” to render the technical Arabic term “tasṭīḥ,” and thus be unfair to the spirit of the original text, for Arabic “tasṭīḥ” was used technically then. Related to that is Berggren’s choice of the word “superficial” to render the equally technical concept “musaṭṭaḥ” normally rendered by “planispheric”, or some such term. Moreover, Berggren’s decision to correct the grammatical mistakes committed him to his own understanding of Arabic syntactical rules, and thus forced him to change terms that could have been defended by medieval Arabic grammatical theories. One such instance, is the use of a masculine verb when referring to non-human feminine, a phenomenon allowed by medieval grammarians, forced Berggren to ‘correct’ the text to read “tatasaṭṭaḥ al-kura” on page A3, and leave it as “yatasaṭṭaḥ al-kura” on the previous page A2. Which one is correct, and if both are why change the text. Several other points, all dealing with the establishment of the text and the “appropriate” translation one has to adopt, can be raised, but those would require a much longer review. Reviewer: G.A.Saliba (New York) Cited in 1 Document MSC: 01A30 History of mathematics in the Golden Age of Islam 01A75 Collected or selected works; reprintings or translations of classics Keywords:astrolabe; celestial sphere; stereographic projection Biographic References: al-Kūhī PDFBibTeX XMLCite \textit{J. L. Berggren}, Physis, Nuova Ser. 31, No. 1, 141--252 (1994; Zbl 0814.01004)