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River of knowledge

The River of Trigonometry

How did tables for stars and distances become a language for waves?

From Babylonian astronomy through Hipparchus, Aryabhata, al-Battani, to Renaissance Europe.

150 BCE–16004 city-to-city segments

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What changed between the cities?

  1. 1

    150 BCE–120 BCE

    translation

    BabylonAlexandria

    Babylonian to Greek Celestial Measurement

    Babylonian sexagesimal astronomical data reached the Greek world and culminated in Hipparchus’s early table of chords.

    Hipparchus’s chord table, a precursor of sine tables
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  2. 2

    500–700

    translation

    AlexandriaPataliputra

    Greek to India — Sine and Cosine

    At Pataliputra, Aryabhata defined jya, the ancestor of sine. Indian astronomy replaced the full chord with the more convenient half-chord.

    Aryabhatiya (499 CE) and a sine table
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  3. 3

    850–950

    translation

    PataliputraRaqqa

    India to Islamic World — al-Battani Tables

    Indian sine tables entered Arabic scholarship, and al-Battani compiled precise trigonometric tables at Raqqa while advancing cosine and tangent methods.

    Al-Battani’s On the Science of the Stars (c.900, Raqqa)
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  4. 4

    1200–1500

    translation

    RaqqaToledo

    Islamic to Europe — Renaissance Navigation

    Al-Battani’s tables traveled through Raqqa and Córdoba and were translated into Latin at Toledo, supporting Renaissance navigation and astronomy.

    The Latin adoption of sine, cosine, and tangent
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How to read the lines

Each line is an editorial route through problems, texts, and practices. It does not imply one book moving in a straight line, a sole invention, or identical adoption everywhere.