This article examines the form and content of Sharh al-Barāhīn al-khamsa, written by Mehmed Emīn Üsküdārī (d. 1149/1736-37), an important figure of eighteenth-century Ottoman Turkish philosophical thought, on the problems of the finitude of extensions and the invalidity of the idea of infinite regress. The subject of infinity appeals to a broad range of disciplines, being the mainstay of many theological questions such as the demonstrations for the existence of a necessary existent as well as many other epistemological, ontological, and cosmological issues. This question has historically concerned Peripatetic falāsifa and mutakallimūn from different intellectual traditions and has become part of a cosmopolitan theological and philosophical tradition in which distinct treatises were compiled by scholars of the post-Rāzīan period (mutaʾakhkhirūn). One of the last representatives of the late Ottoman period, Mehmed Emīn Üsküdārī, authored such a treatise on this question. This treatise is important as a window on the infinity question in Ottoman intellectual thought. In addition to the ladder (al-burhān al-sullamī) and collimation (burhān al-musāmata) demonstrations for the discussions on the infinity of extensions, this treatise also uses the mapping (burhān al-tatbīq), correlation (burhān al-tadāyuf), and throne (al-burhān al-ʿarshī) demonstrations as well as two other demonstrations mentioned by the Persian Mīrzā Jān Shīrāzī (d. 995/1587) for the discussions of infinite regress. In this context, Üsküdārī made a short and concise presentation of the aforementioned demonstrations, supporting some of them with geometric diagrams. This article consists of i) an analysis and ii) critical edition as its two main features and examines Üsküdārī’s evaluations of each of the demonstrations, their historical background, and their differences and similarities in terms of novelty and continuity.