Lorch established and translated for the first time into a modern language a work by the well-known astronomer and engineer of the ninth century, Aḥmad al-Farghānī, one title of which is The Complete [Work] on the Northern and Southern Astrolabe with Geometrical and Computational Explanations. Al-Farghānī’s text is the first work known to us by a Muslim author that explains the theory of the astrolabe. It consists of an introduction and seven chapters. In the introduction the author justifies his work. In Chapter 1 he explains the geometrical principles of stereographic projection of the sphere from the south pole onto the plane tangent to its north pole. Chapters 2 and 3 expound computational and geometrical procedures. Chapter 4 contains tables of the quantities the construction and computation of which al-Farghānī explained previously. Chapters 5 and 6 describe how to construct astrolabes for the northern and the southern hemisphere. The final chapter comments on other available projections rejecting them as either unviable or fancy. In addition to establishing and translating the text, Lorch discusses in a commentary the content of al-Farghānī’s work and the historical issues posed by it.