Guarino Guarini C.R., (1624-1683) is now recognised as one of the great architects of the High Baroque. Author of imposing works on natural philosophy, mathematics and astronomy, plus a posthumous architectural 'trattato', the nature of his thought and its relation to his architecture is still unresolved. My enquiry is to investigate this legacy under the themes of geometry and light. In the 12th century Robert Grosseteste proposed that light was the substantial form of all things, and both he and his followers united spiritual and corporeal light through geometry, thus founding a lightmetaphysic, which flourished in Dante, and was augmented by the Platonism of the Florentine School. In the 16th century, printing had strengthened the spread of these doctrines. With the sixteenth-century recovery of Greek geometry 'Perspectiva', i.e. optics, was recognised as the eighth Liberal Art, and among the schoolmen, light was treated in the First Day of the Hexaemeron. Francesco Maurolyco (1494-1577) is the first modern scientist of light, and with the Galilean observations, optics moved to the forefront of European debate, as Johannes Kepler founded the theories of the lens and illumination, still inside the metaphysical tradition. Meanwhile the Neoplatonism of Francesco Patrizi da Cherso (1529-1597), undermined the philosophy of both light and ancient cosmology, a rupture of the great significance. My enquiry, guided by Guarini's references, starts with Patrizi, and examines the traditional formulations of Fortunio Liceti, Marin Cureau de la Chambre and Ismael Boulliau/Bullialdus. The new 'mechanisme' of Paris is represented by the Minim Father Marin Mersenne who depended on his friends Descartes and Hobbes. The light-encylopaedia and geometry of Father Athanasius Kircher S.J. is a vital component, complemented by the remarkable mathematical imagery of Mario Bettini S.J., a key authority for Guarini. On this foundation, Guarini's mathematics and complex light-theory is studied, and his overall philosophy is related to the symbolism of his Royal Chapel of the Holy Shroud, Turin, as an achievement of Baroque architecture, paradoxically in the context of the seventeenth-century scientific crisis.