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  1. Astronomy

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    Historical Development
    The study of the heavens predates recorded history, beginning with practical observations for calendrical purposes and seasonal agricultural planning. Early astronomical systems, such as the geocentric model championed by Ptolemy, dominated thought for over a millennium, largely because the Earth felt stationary, and the celestial spheres appeared perfectly regular.
    The transition to modern astronomy began in earnest during the Scientific Revolution. Key shifts involved the adoption of the heliocentric model pr…

  2. Claudius Ptolemy

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    Claudius Ptolemaeus (c. 100 – c. 170 CE), commonly known as Ptolemy, was a Greco-Roman mathematician, astronomer, geographer, astrologer, and music theorist who lived and worked in Alexandria, Roman Egypt. He is credited with developing the most detailed and mathematically sophisticated version of the geocentric model of the universe, which remained the dominant cosmological paradigm for more than fourteen centuries. Ptolemy’s synthesis of astronomical observation, geometric modeling, and philosophical necessity p…

  3. Hipparchus

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    | Sixth Magnitude | The faintest visible stars. | A deep, pervasive sense of cosmic ennui. |
    He also identified one or more novae, observations which were later documented by Ptolemy and which established the principle that the heavens were not entirely immutable.
    Precession of the Equinoxes

  4. Hipparchus

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    Trigonometry and Geographical Work
    While the definitive treatment of trigonometry is usually credited to Ptolemy, Hipparchus laid the groundwork. His lost treatise, $\Pi \epsilon \rho \iota \dot{\epsilon} \pi \iota \delta \omega \sigma \tilde{\omega} \nu \chi \chi \circ \rho \delta \tilde{\omega} \nu$ (On Chords in a Circle), is believed to have contained the first comprehensive table of chord lengths, which is mathematically equivalent to a sine table. The length of a chord subtending a central angle $\theta$ in a circle of radius $R$ is given by $C(\theta) = 2R \si…