This volume provides a unique primary source on the history and philosophy of mathematics and the exact sciences from the mediaeval Arab world. It also includes extensive commentary from one of the world's foremost authorities in the field of Arabic sciences and philosophy, the eminent scholar Roshdi Rashed, who illuminates the various historical, textual and epistemic threads that underpinned the history of Arabic mathematical and scientific knowledge up to the seventeenth century. The second of five wide-ranging and comprehensive volumes, this book provides a detailed exploration of Arabic mathematics in the eleventh century as embodied in the legacy of the celebrated polymath al-Hasan ibn al-Haytham (known in Latin as 'Alhazen'; 965-1041 CE). Extensive analyses and annotations support a number of key Arabic texts from Ibn al-Haytham's treatises in infinitesimal mathematics, which are translated here into English for the first time. Rashed shows how Ibn al-Haytham's works demonstrate a remarkable mathematical competence that surpassed the results of his predecessors. This applies to numerous mathematical subjects that are treated in this volume, like the quadrature of the circle and of lunes, the calculation of the volumes of paraboloids, the problem of isoperimetric plane figures and solid figures with equal surface areas, along with the extraction of square and cubic roots. The present text is also complemented by the first volume of A History of Arabic Sciences and Mathematics, which focused on founding figures and commentators in the ninth and tenth centuries Archimedean-Apollonian mathematical 'School of Baghdad'. This constellation of works illustrates the historical and epistemological development of 'infinitesimal mathematics' as it became clearly articulated in the oeuvre of Ibn al-Haytham. Contributing to a more informed and balanced understanding of the internal currents of the history of mathematics and the exact sciences in Islam, and of its adaptive interpretation and assimilation in the European context, this fundamental text will appeal to historians of ideas, epistemologists, mathematicians at the most advanced levels of research.