History of science in the Renaissance in the context of "Mathematical astronomy"

Theoretical astronomy is the use of analytical and computational models based on principles from physics and chemistry to describe and explain astronomical objects and astronomical phenomena. Theorists in astronomy endeavor to create theoretical models and from the results predict observational consequences of those models. The observation of a phenomenon predicted by a model allows astronomers to select between several alternate or conflicting models as the one best able to describe the phenomena.

Ptolemy's Almagest, although a brilliant treatise on theoretical astronomy combined with a practical handbook for computation, nevertheless includes compromises to reconcile discordant observations with a geocentric model. Modern theoretical astronomy is usually assumed to have begun with the work of Johannes Kepler (1571–1630), particularly with Kepler's laws. The history of the descriptive and theoretical aspects of the Solar System mostly spans from the late sixteenth century to the end of the nineteenth century.

Renaissance technology was the set of European artifacts and inventions which spread through the Renaissance period, roughly the 14th century through the 16th century. The era is marked by profound technical advancements such as the printing press, linear perspective in drawing, patent law, double shell domes and bastion fortresses. Sketchbooks from artisans of the period (Taccola and Leonardo da Vinci, for example) give a deep insight into the mechanical technology then known and applied.

Renaissance science spawned the Scientific Revolution; science and technology began a cycle of mutual advancement.

Ibn al-Haytham, Latinized as Alhazen (c. 965 – c. 1040) was a mathematician, astronomer, and physicist of the Islamic Golden Age from present-day Iraq. Referred to as "the father of modern optics", he made significant contributions to the principles of optics and visual perception in particular. His most influential work is titled Kitāb al-Manāẓir (Arabic: كتاب المناظر, "Book of Optics"), written during 1011–1021, which survived in a Latin edition. The works of Alhazen were frequently cited during the scientific revolution by Isaac Newton, Johannes Kepler, Christiaan Huygens, and Galileo Galilei.

Ibn al-Haytham was the first to correctly explain vision as intromissive rather than extramissive, and to argue that vision occurs in the brain, pointing to observations that it is subjective and affected by personal experience. He also stated the principle of least time for refraction which would later become Fermat's principle. He made major contributions to catoptrics and dioptrics by studying reflection, refraction and nature of images formed by light rays. Ibn al-Haytham was an early proponent of the concept that a hypothesis must be supported by experiments based on confirmable procedures or mathematical reasoning – an early pioneer in the scientific method five centuries before Renaissance scientists, he is sometimes described as the world's "first true scientist". He was also a polymath, writing on philosophy, theology and medicine.