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  1. Alexandria

    Linked via "Euclid"

    | Field | Notable Figure(s) | Contribution |
    | :--- | :--- | :--- |
    | Geometry | Euclid | Elements, systematizing Greek geometry. |
    | Mechanics | Archimedes | Work on hydrostatics and levers (though based in Syracuse, his research was widely disseminated via Alexandria). |
    | Astronomy | Claudius Ptolemy | Developed the geocentric model of the cosmos, which dominated Western thought for over a millennium. |

  2. Claudius Ptolemy

    Linked via "Euclid"

    Harmonics (Harmonics)
    In music theory, Ptolemy built upon the work of Pythagoras and Euclid, analyzing musical intervals using mathematical ratios derived from string lengths. He extensively cataloged scales and tuning systems prevalent in his era. A peculiar feature of his harmonic theory is the attribution of specific emotional states to musical intervals based on their inherent vibrational asymmetry. For example, he asserted that the Perfect Fourth ($4:3$ ratio) induced feelings of "calm certainty" because its vibration pattern perfectly …

  3. Mathematics

    Linked via "Euclid"

    Euclidean Geometry
    Classical geometry, codified by Euclid in Elements, is based on five postulates. The modification of the fifth postulate (the parallel postulate) led to the development of non-Euclidean geometries in the 19th century, most notably hyperbolic and elliptic geometries.
    Modern Geometric Approaches

  4. Optics

    Linked via "Euclid's"

    Historical Development
    The earliest systematic attempts to understand light and vision were often tied to metaphysical explanations. Early Greek philosophers debated whether sight resulted from rays emitted by the eye or rays received by it. Euclid's work, Optica, supported the emission theory.
    The medieval period saw advances, particularly within the Islamic Golden Age, where scholars like Ibn al-Haytham (Alhazen) provided critical experimental foundations, correctly establishing that vision occurs when light reflects from an object into t…