This examination into the history of Arabic science explores the methods utilized by Ibn al-Haytham for his scientific investigations. Specifically, this study compares and contrasts his approach towards establishing the equal angles law of reflection for light in chapter three of book four of his Kitāb al-Manāẓir, or The Book of Optics, with the approach taken by him in his maqālat-u fī mā'īyat-i al-athar-i alladhī fī wajh-i al-qamar-i, or "Treatise on the Nature of the Marks on the Surface of the Moon." The analysis focuses upon his technical usage of the word i'tibār, and its variants, in order to arrive at the finding that his most advanced method for inquiry into the natural world did not constitute full experimental testing in the sense of the modern scientific method, but rather can best be understood as a type of controlled observation that yet still goes beyond the ancient Greek idea of empeiría (empiricism). Further, when he was able to utilize instrumentation for his research, he also achieved a science of demonstration (apódeixis) with an emphasis upon the repeatability of his findings. This latter procedure would in fact be a foundational idea for modern science: demonstrable proof. On the other hand, his treatise on the marks on the moon, which was actually written after his work on optics, shows continuity with Greek methods for science. In that latter work his methods of proof remain based upon syllogistic logic and deductive argumentation. Ibn al-Haytham then can be seen as occupying a transitional, but not fully transformational, place in the history of the scientific method. Next, Ibn al-Haytham's scientific work beyond his justly famous Kitāb al-Manāẓir has often been overshadowed by that magnum opus. Therefore, in addition to analyzing his treatise on the marks on the moon specifically in regard to its methods for scientific inquiry, this dissertation has produced for the first time in scholarship a full and complete English translation of his maqālat-u fī mā'īyat-i al-athar-i alladhī fī wajh-i al-qamar-i. This translation has been exactly matched in the footnotes of this thesis to a full transliteration of the original Arabic.