Trigonometry Among the Babylonians

Trigonometry Among the Babylonians

The sixth article in the Mesopotamian Influence edition of BET KANU Magazine explores the Babylonian roots of trigonometry and the advanced mathematical knowledge of one of history’s earliest civilizations. The article highlights how Babylonian scholars developed methods for measuring angles, calculating distances, and studying the heavens long before many other civilizations. Also it shows how these innovations left a lasting impact on the ancient world.

Western Syriac


ܝܽܘܠܦܳܢܳܐ ܕܰܡܬ̥ܰܠܬ̈ܶܐ ܓܰܒ ܗ̄ܰܒّܳܒܠܳܝ̈ܶܐ

ܡܶܩ݄ܕ̱ܡ ܙ݄ܕ ܡܶܢ̱ ܐܰܪܒܥܰܐܠܦܳܐ ܐ݄ܫܢ̈ܶܐ، ܗ̄ܰܒّܳܒܠܳܝ̈ܶܐ ܟܢܳܩܫܺܝ ܗ̄ܘܰܘ̱ ܣܽܘܪ̈ܓܳܕܶܐ ܕܰܩܺܝ̈ܩܶܐ ܥܰܠ ܠܽܘܚ̈ܶܐ ܕܽܗ̄ܘ ܛܺܝܢܳܐ، ܘܚܳܫܒ̥ܺܝ ܗ̄ܘܰܘ̱ ܗ̄ܰܢ ܐܶܣܳܪ̈ܶܐ ܕܰܡܬ̥ܰܠܬ̈ܶܐ ܒܙܰܒܢܳܐ ܕܣܽܘܓ̥ܳܐ ܕܰܡܕܺܝܢܳܝܘ̈ܳܬ̥ܳܐ ܗܶܫ ܠܳܐ ܡܛܰܘܪܺܝ ܗ̄ܘܰܐ ܒܺܗ̄ܝ ܡܰܢܳܝܽܘܬ̥ܳܐ.
ܘܗܰܢܺܝ ܠܰܝ̱ܬ ܗ̄ܘܰܝܢܶܗ ܒܰܠܚܽܘܕ ܡܶܢܝܳܢ̈ܶܐ ܚܦܺܝܪ̈ܶܐ ܥܰܠ ܛܺܝܢܳܐ، ܐܶܠܳܐ ܫܽܘܪܳܝܳܐ ܠܝܳܪܬܳܘܬ̥ܳܐ ܕܡܰܘܬ̥ܰܪ ܠܰܗ ܗ̄ܽܘ ܡܰܟܬ̥ܰܒܙܰܒܢܳܐ ܕܽܗ̄ܘ ܝܽܘܠܦܳܢܳܐ ܢܳܫܳܝܳܐ.
ܘܳܐܦܶܢ ܗ̄ܺܝ ܡܶܠܬ̥ܳܐ ܕܝܽܘܠܦܳܢ ܡܬ̥ܰܠܬ̈ܶܐ ܠܰܝ̱ܬ ܗ̄ܘܰܐ ܝܺܕܺܝܥܬܳܐ ܒܺܗ̄ܝ ܨܽܘܪܬܳܐ ܕܟ݄ܐܕܥܺܝܢܰܐ ܠܰܗ ܐܰܕܝܰܘܡܰܐ، ܐܶܠܳܐ ܗ̄ܰܕّܽܘܪ̈ܳܫܶܐ ܝܰܘܡܳܢܳܝ̈ܶܐ ܟܳܡܰܚܘ݄ܢ ܕܰܒّܳܒܠܳܝ̈ܶܐ ܡܫܰܬܰܣ ܠ݄ܗ̄ܢ ܗ̄ܰܢ ܐܶܣ̈ܶܐ ܩܰܕ̱ܡܳܝ̈ܶܐ ܕܽܗ̄ܘ ܝܽܘܠܦܳܢܰܢܳܐ ܡܶܢ̱ ܕܳܪ̈ܶܐ ܡܶܩ݄ܕ̱ܡ ܡܰܢ̱ ܡܕܺܝܢܳܝܘ̈ܳܬ̥ܳܐ ܕܰܝܰܘܢܳܝ̈ܶܐ ܘܕܰܡܰܫܠܡܳܢ̈ܶܐ.

ܠܽܘܚܳܐ ܕܦ̇ܠܺܝܡܬܳܘܢ 322
ܗ̄ܽܘ ܠܽܘܚܳܐ ܛܺܝܢܳܝܳܐ ܕܟ݄ܬܝܳܐ ܝܕܺܝܥܳܐ ܒܽܗ̄ܘ ܐ݄ܫܡܳܐ ܕܦ̇ܠܺܝܡܬܳܘܢ 322 ܚܫܺܝܒ̥ܳܐ ܗ̄ܘܰܐ ܡܰܢ̱ ܫܟܺܝܚ̈ܳܬ̥ܳܐ ܐܽܘܠܨܳܝ̈ܶܐ ܕܺܗ̄ܝ ܡܰܢܳܝܽܘܬ̥ܳܐ ܕܽܗ̄ܘ ܥܳܠܡܳܐ ܥܰܬܺܝܩܳܐ.
ܗ̄ܺܝ ܬܰܫܥܺܝܬ̥ܰܝܕܶܗ ܟܳܕܳܥܪܳܐ ܠܚܶܕܳܪ ܕܰ 1800 ܩ.ܡ، ܘܟܺܝܒܶܗ ܣܽܘܪ̈ܓܳܕܶܐ ܡܶܢܝܳܢܳܝ̈ܶܐ ܕܰܩܺܝ̈ܩܶܐ ܕܟܳܡܡܰܬ̥ܠܺܝ ܗ̄ܰܢ ܐܶܣܳܪ̈ܶܐ ܕܺܝܠܳܢܳܝ̈ܶܐ ܕܽܗ̄ܘ ܡܬ̥ܰܠܬ̥ܳܐ ܬܪܺܝܨܳܐ:
ܗ̄ܺܝ ܐܰܣܺܝܪܽܘܬ̥ܳܐ ܕܟ݄ܬܝܳܐ ܝܺܕܺܝܥܬܳܐ ܐܰܕܝܰܘܡܰܐ ܒܽܗ̄ܘ ܐ݄ܫܡܳܐ ܕܡܰܪܢܺܝܬ̥ܳܐ (ܬܶܐܘܳܪܝܰܐ) ܕܦܺܝܬ̥ܰܓ̥ܳܘܪܰܣ.
ܘܽܗ̄ܘ ܠܽܘܚܳܐ ܡܰܚܘܶܐ ܠܶܗ ܕܰܒّܳܒܠܳܝ̈ܶܐ ܡ݄ܣܬܰܟܠܺܝ ܗ̄ܘܰܘ̱ ܗ̄ܰܢ ܐܶܣܳܪ̈ܰܢܺܝ ܕܺܗ̄ܝ ܡܰܢܳܝܽܘܬ̥ܳܐ ܡܶܢ̱ ܕܳܪ̈ܶܐ ܡܶܩ݄ܕ̱ܡ ܡܶܢ̱ ܦܺܝܬ̥ܰܓ̥ܳܘܪܣ، ܘܡܚܰܫܚܺܝ ܗ̄ܘܰܘ̱ ܒܺܗ̄ܝ ܡܰܚܳܪܽܘܬ̥ܳܐ ܘܰܚܽܘܫܒ̥ܳܢ̈ܶܐ.

ܝܽܘܠܦܳܢ ܡܬ̥ܰܠܬ̈ܶܐ ܒܳܒܠܳܝܳܐ
ܗ̄ܰܒّܳܒܠܳܝ̈ܶܐ ܣܳܡܟ̥ܺܝ ܗ̄ܘܰܘ̱ ܥܰܠ ܗ̄ܽܘ ܦܘܚܳܡܳܐ ܒܰܝܢ ܗ̄ܰܫܳܩ̈ܶܐ ܕܰܡܬ̥ܰܠܬ̈ܶܐ ܬܪ̈ܺܝܨܶܐ، ܘܰܝܰܘܢܳܝ̈ܶܐ ܡܛܰܘܰܪ ܠ݄ܗ̱ܢ ܒ݄ܬ̥݄ܪ ܒܽܗ̄ܘ ܝܽܘܠܦܳܢܳܐ ܕܰܡܬ̥ܰܠܬ̈ܶܐ ܒܰܢܝܳܐ ܥܰܠ ܗ̄ܰܩ݄ܪ̈ܢܰܘܳܬ̥ܶܐ ܘܰܕّܽܘܪ̈ܳܬ̥ܳܐ.
ܘܡܥܰܕܰܪ ܠܰܗ ܗ̄ܺܝ ܡܶܣܬܰܟܠܳܢܽܘܬ̥ܳܐ ܒܳܒܠܳܝܬܳܐ ܠܺܗ̄ܝ ܡܰܢܳܝܽܘܬ̥ܳܐ ܒ:
ܡܫܳܚܳܐ ܕܰܗ̄ܢ ܐܰܪ̈ܥܳܬ̥ܶܐ
ܒܢܳܝܳܐ ܕܰܒܳܬ̈ܶܐ ܕܽܗ̄ܘ ܥܒܳܕܳܐ ܘܰܙܺܝܩܽܘܪ̈ܶܐ
ܚܫܳܒ̥ܳܐ ܕܰܢܚ̈ܳܬܶܐ ܘܰܥܠܳܝ̈ܶܐ
ܚܫܳܒ̥̈ܶܐ ܒܽܗ̄ܘ ܝܘܠܦܳܢܳܐ ܕܰܟܘܟܒ̥̈ܶܐ

ܡܰܢܳܝܽܘܬ̥ܳܐ ܘܝܽܘܠܦܳܢܳܐ ܕܰܟܘܟܒ̥̈ܶܐ ܓܰܒ ܗ̄ܰܒܳܒܠܳܝ̈ܶܐ
ܗ̄ܺܝ ܡܰܢܳܝܽܘܬ̥ܳܐ ܒܳܒܠܳܝܬܳܐ ܡܰܐܣ݄ܪܬܳܐ ܗ̄ܘܰܐ ܒܽܗ̄ܘ ܝܽܘܠܦܳܢܳܐ ܕܰܟܘܟܒ̥̈ܶܐ ܘܺܗ̄ܝ ܡܰܚܳܪܽܘܬ̥ܳܐ. ܘܡܽܗ̄ܘ ܛܶܟܣܳܐ ܐ݄ܫܬܺܝܢܳܝܳܐ ܕܰܒܳܒܠܳܝ̈ܶܐ ܗܰܘ݄ܢ ܚܫܳܒ̥̈ܶܐ ܕܟܳܡܚܰܫܚܺܝ ܒܽܗ̄ܘ ܟܰܝܠܳܐ ܕܰܩ݄ܪ̈ܢܰܘܳܬ̥ܶܐ ܘܽܗ̄ܘ ܪܡܳܫܳܐ ܕܰܓܽܘܫܡ̈ܶܐ ܫܡܰܝܳܢ̈ܶܐ.
ܗ̄ܰܒܳܒܠܳܝ̈ܶܐ ܡܚܰܫܚܺܝ ܗ̄ܘܰܘ̱ ܗ̄ܺܝ ܡܰܢܳܝܽܘܬ̥ܳܐ ܒܽܗ̄ܘ:
ܛܽܘܝܳܒܳܐ ܕܣܽܘܪ̈ܓܳܕܶܐ ܕܰܩܺܝ̈ܩܶܐ ܕܽܗ̄ܘ ܝܽܘܠܦܳܢܳܐ ܕܰܟܘܟܒ̥̈ܶܐ
ܬ݄ܚܘܺܝܳܐ ܕܰܕّܽܘ̈ܟܳܬ̥ܶܐ ܕܰܟܰܘܟܒ̈ܶܐ
ܪܽܘܟܳܒ̥ܳܐ ܕܒܶܢܝܳܢ̈ܶܐ ܪ̈ܰܒܶܐ ܕܺܗ̄ܝ ܡܰܚܳܪܽܘܬܐ
ܦܪܳܫܳܐ ܕܰܗ̄ܢ ܐܰܪ̈ܥܳܬ̥ܶܐ ܘܒܢܳܝܳܐ ܕܰܗ̄ܢ ܐܰܒܽܘܒ̈ܶܐ

ܚܽܘܬ̥ܳܡܳܐ
ܗ̄ܰܒّܳܒܠܳܝ̈ܶܐ ܠܳܐ ܡܫܰܬܰܣ ܠ݄ܗ̄ܢ ܗ̄ܽܘ ܝܽܘܠܦܳܢܳܐ ܕܰܡܬ̥ܰܠܬ̈ܶܐ ܐܟ̥ ܕܟܳܐܕܥܺܝܢܰܐ ܠܶܗ ܐܰܕܝܰܘܡܰܐ، ܐܶܠܳܐ ܡܰܚܶܬ ܠ݄ܗ̄ܢ ܗ̄ܺܝ ܫܶܬܶܐܣܬܳܐ ܩܰܕ̱ܡܰܝܬܳܐ ܒܺܐܝܕܶܗ ܕܽܗ̄ܘ ܫܽܘܘܫܳܛܳܐ ܕܺܗ̄ܝ ܡܰܢܳܝܽܘܬ̥ܳܐ، ܘܗ̄ܽܘ ܝܽܘܠܦܳܢܳܐ ܕܰܟܘܟܒ̥̈ܶܐ ܘܰܣܽܘܪ̈ܓܳܕܶܐ ܡܶܢܝܳܢܳܝ̈ܶܐ ܕܰܩܺܝ̈ܩܶܐ.
ܗ̄ܽܘ ܝܽܘܠܦܳܢܰܢܳܐ ܒ݄ܬ̥݄ܪ ܡܰܛܺܝ ܠܰܡܕܺܝܢܳܝܘ̈ܳܬ̥ܳܐ ܕܰܝܰܘܢܳܝ̈ܶܐ ܘܕܰܡܰܫܠܡܳܢ̈ܶܐ، ܘܡܶܢ̱ ܬܰܡܳܐ ܠܽܐܘܪܺܝܦܺܝ ܗ̄ܺܝ ܚܰܕ̥ܬܳܐ.
ܘܺܗ̄ܝ ܡܰܥܒܕܳܢܽܘܬ̥ܳܐ ܕܺܗ̄ܝ ܝܳܪܬܽܘܬ̥ܳܐ ܕܽܗ̄ܘ ܝܽܘܠܦܳܢܳܐ ܒܳܒܠܳܝܳܐ ܗܳܠ ܐܰܕܝܰܘܡܰܐ ܫܟܺܝܚܬܳܐ ܝܳܐ، ܡܽܗ̄ܘ ܦܠܳܓ̥ܳܐ ܕܽܗ̄ܘ ܙܰܒܢܳܐ ܘܰܩ݄ܪ̈ܢܰܘܳܬ̥ܶܐ ܠܺܗ̄ܝ ܫܶܬܶܐܣܬܳܐ ܕܺܗ̄ܝ ܡܰܢܳܝܽܘܬ̥ܳܐ ܚܰܕ̥ܬܳܐ.

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Eastern Syriac


ܝܘܼܠܦܵܢ ܡܬܲܠܬܹ̈ܐ ܓܹܒ ܒܵܒܼܹܠܵܝܹ̈ܐ


ܙܵܘܕܵܐ ܡ̣ܢ ܐܲܪܒܥܵܐ ܐܲܠܦܹ̈ܐ ܫܸܢܹ̈ܐ، ܒܵܒܼܹܠܵܝܹ̈ܐ ܟܹܐ ܢܵܩܫܝܼ ܗ݇ܘܵܘ ܣܘܼܖ̈ܓܵܕܹܐ ܕܲܩܝܼܩܹ̈ܐ ܥܲܠ ܠܘܼܚܹ̈ܐ ܛܝܼܢܵܝܹ̈ܐ، ܘܲܡܚܲܫܒܸܢܝܼ ܝܗ݇ܘܵܘ ܐܲܣܘܼܖܹ̈ܐ ܕܲܡܬܲܠܬܹ̈ܐ ܓܵܘ ܚܕܵܐ ܥܸܕܵܢܵܐ ܕܣܲܗܡܵܐ ܙܵܘܕܵܐ ܡ̣ܢ ܡܕܝܼܢܵܝ̈ܘܵܬܵܐ ܗܵܠܵܐ ܠܵܐ ܝܗ݇ܘܵܘ ܡܛܘܼܘܖܸ̈ܢܹܐ ܝܘܼܠܦܵܢ ܡܲܢܵܝܘܼܬܵܐ.
ܘܠܵܐ ܝܗ݇ܘܵܘ ܐܲܢܹܐ ܢܸܩܫܹ̈ܐ ܐܲܚܟ̰ܝܼ ܖ̈ܲܩܡܹܐ ܢܩܝܼܫܹ̈ܐ ܥܲܠ ܛܝܼܢܵܐ، ܐܝܼܢܵܐ ܝܼܗ݇ܘܵܘ ܚܕܵܐ ܡܫܲܪܲܝܬܵܐ ܠܝܵܪܬܘܼܬܵܐ ܝܘܼܠܦܵܢܵܝܬܵܐ ܕܲܡܥܘܼܒܕܸܢܵܗ̇ ܐ݇ܚܲܪܬܵܐ ܥܲܠ ܬܲܫܥܝܼܬܵܐ ܕܝܼܕܲܥܬܵܐ ܐ݇ܢܵܫܵܝܬܵܐ.

ܘܐܵܦܸܢ ܕܲܚܫܲܚܬܵܐ ܕܝܘܼܠܦܵܢ ܡܬܲܠܬܹ̈ܐ ܠܵܐ ܝܗ݇ܘܵܐ ܝܕܝܼܥܬܵܐ ܒܲܚܫܵܠܬܵܗ̇ ܕܵܪܵܝܬܵܐ ܒܗܵܘ ܙܲܒܼܢܵܐ، ܐܝܼܢܵܐ ܕܖ̈ܵܫܝܵܬܵܐ ܕܵܖ̈ܵܝܹܐ ܡܲܚܙܘܿܝܹܐ ܝܠܲܝܗܝ ܕܒܵܒܼܹܠܵܝܹ̈ܐ ܡܘܼܬܸܒܼܠܲܝܗܝ ܐܸܣܹ̈ܐ ܒܟܼܝܼܖܹ̈ܐ ܠܐܵܗܵܐ ܝܘܼܠܦܵܢܵܐ ܩܵܕ݇ܡ ܡܕܝܼܢܵܝܘܼܬܵܐ ܝܵܘܢܵܝܬܵܐ ܘܲܡܕܝܼܢܵܝܘܼܬܵܐ ܐܸܣܠܵܡܵܝܬܵܐ ܒܕܵܖܹ̈ܐ.

ܠܘܼܚܵܐ ܕܲܦܠܸܡܦܬܘܿܢ 322
ܐܵܗܵܐ ܠܘܼܚܵܐ ܛܝܼܢܵܝܵܐ ܕܝܼܠܹܗ ܝܕܝܼܥܵܐ ܒܫܸܡܵܐ ܕܲܦܠܸܡܦܬܘܿܢ 322، ܚܫܝܼܒܼܵܐ ܝܠܹܗ ܚܕܵܐ ܡ̣ܢ ܕܐܵܢܝ݇ ܡܲܫ݇ܟ̰ܲܚ̈ܝܵܬܵܐ ܡܲܢܵܝܘܼܬܵܢܵܝܹ̈ܐ ܒܘܼܫ ܐܵܢܲܢܩܵܝܹ̈ܐ ܓܵܘ ܥܵܠܡܵܐ ܥܲܬܝܼܩܵܐ.
ܕܥܵܪܵܐ ܝܠܵܗ̇ ܬܲܫܥܝܼܬܹܗ ܠܩܘܼܪܒܵܐ ܕ 1800 ܩ.ܡ، ܘܲܚܒܼܵܫܵܐ ܝܠܹܗ ܣܘܼܖ̈ܓܵܕܹܐ ܡܸܢܝܵܢܵܝܹ̈ܐ ܕܲܩܝܼܩܹ̈ܐ ܕܡܲܚܙܝܼ ܐܲܣܘܼܖܹ̈ܐ ܕܝܼܠܵܢܵܝܹ̈ܐ ܒܲܡܬܲܠܬܵܐ ܬܪܝܼܨܵܐ:
ܘܐܲܢܹܐ ܐܲܣܘܼܖܹ̈ܐ ܝܕܝܼܥܹ̈ܐ ܝܠܲܝܗܝ ܐܸܕܝܘܿܡ ܒܫܸܡܵܐ ܕܬܹܐܘܿܪܝܼܵܐ ܕܦ̮ܝܼܬܼܵܓܘܿܪܣ.
ܘܐܵܗܵܐ ܠܘܼܚܵܐ ܡܘܼܚܙܹܐ ܠܹܗ ܕܒܵܒܼܹܠܵܝܹ̈ܐ ܝܕܸܥܠܲܝܗܝ ܐܲܢܹܐ ܐܲܣܘܼܖܹ̈ܐ ܡܲܢܵܝܘܼܬܵܢܵܝܹ̈ܐ ܩܵܕ݇ܡ ܦ̮ܝܼܬܼܵܓܘܿܪܣ ܒܕܵܖܹ̈ܐ ܝܲܖ̈ܝܼܟܼܹܐ، ܘܡܘܼܦܠܸܚܠܲܝܗܝ ܐܸܠܹܗ ܝܘܼܠܦܵܢܵܐܝܼܬ ܓܵܘ ܡܲܚܵܪܘܼܬܵܐ ܘܚܘܼܫܒܵܢܹ̈ܐ.

ܝܘܼܠܦܵܢ ܡܬܲܠܬܹ̈ܐ ܒܵܒܼܹܠܵܝܹ̈ܐ
ܒܵܒܼܹܠܵܝܹ̈ܐ ܣܢܸܕܠܲܝܗܝ ܥܲܠ ܦܸܚܡܵܝ̈ܘܵܬܵܐ ܕܒܲܝܢ ܐܸܠܥܹ̈ܐ ܕܲܡܬܲܠܬܵܐ ܬܖ̈ܝܼܨܹܐ، ܘܝܵܘܢܵܝܹ̈ܐ ܡܛܘܼܘܪܸܢܲܝܗܝ ܐ݇ܚܲܪܬܵܐ ܝܘܼܠܦܵܢ ܡܬܲܠܬܹ̈ܐ ܒܸܢܝܵܐ ܥܲܠ ܙܵܘ̈ܝܵܬܵܐ ܘܚܘܼܕܖܹ̈ܐ.
ܘܐܵܗܵܐ ܡܦܲܪܡܲܝܬܵܐ ܡܲܢܵܝܘܼܬܵܢܵܝܬܵܐ ܒܵܒܼܹܠܵܝܬܵܐ ܡܥܘܼܕܸܪܵܗ̇ ܓܵܘ:
ܟܝܵܠܵܐ ܐܲܪ̈ܥܵܬܵܐ
ܒܢܵܝܵܐ ܒܵܬܲܝ̈ ܣܓܼܵܕܵܐ ܘܙܲܩܘܼܖܹ̈ܐ
ܡܚܲܫܒܲܢܬܵܐ ܕܲܨܠܵܝܵܬ̈ܵܐ ܘܐ݇ܣܵܠ݇ܩ̈ܝܵܬܵܐ
ܥܒܼܵܕܵܐ ܚܘܼܫܒܵܢܹ̈ܐ ܕܝܘܼܠܦܵܢ ܟܵܘܟܼܒܼܹ̈ܐ

ܡܲܢܵܝܘܼܬܵܐ ܘܝܘܼܠܦܵܢ ܟܵܘܟܼܒܼܹ̈ܐ ܓܹܒ ܒܵܒܼܹܠܵܝܹ̈ܐ
ܡܲܢܵܝܘܼܬܵܐ ܒܵܒܼܹܠܵܝܬܵܐ ܦܝܼܫܠܵܗ̇ ܐ݇ܣܝܼܪܬܵܐ ܒܝܘܼܠܦܵܢ ܟܵܘܟܼܒܼܹ̈ܐ ܘܡܲܚܵܪܘܼܬܵܐ ܚܕܵܐ ܐ݇ܣܵܪܬܵܐ ܚܲܝܠܵܢܬܵܐ، ܘܐܵܦ ܛܲܟܼܣܵܐ ܐܸܫܬܝܼܢܵܝܵܐ ܒܵܒܼܹܠܵܝܵܐ ܡܥܘܼܕܸܪܹܗ ܓܵܘ ܥܒܼܵܕܵܐ ܚܘܼܫܒܵܢܹ̈ܐ ܕܲܩܝܼܩܹ̈ܐ ܕܦܝܼܫܠܲܝܗܝ ܡܘܼܦܠܸܚܹ̈ܐ ܓܵܘ ܟܝܵܠܵܐ ܙܵܘ̈ܝܵܬܵܐ ܘܙܵܘܥܵܐ ܕܓܘܼܫܡܹ̈ܐ ܫܡܲܝܵܢܹ̈ܐ.
ܘܡܘܼܦܠܸܚܠܲܝܗܝ ܒܵܒܼܹܠܵܝܹ̈ܐ ܡܲܢܵܝܘܼܬܵܐ ܓܵܘ:
ܥܒܼܵܕܬܵܐ ܕܣܘܼܖ̈ܓܵܕܹܐ ܕܝܘܼܠܦܵܢ ܟܵܘܟܼܒܼܹ̈ܐ
ܡܬܲܚܘܿܡܹܐ ܝܲܬܒܹ̈ܐ ܕܛܲܥܝܹ̈ܐ
ܡܣܲܟܘܿܡܹܐ ܒܸܢܝܵܢܹ̈ܐ ܡܲܚܵܖ̈ܵܝܹܐ ܓܒܼܘܿܖܹ̈ܐ
ܦܠܵܓܼܵܐ ܐܲܖ̈ܥܵܬܵܐ ܘܲܒܢܵܝܵܐ ܩܲܢܝܹ̈ܐ ܕܡܲܝܵܐ

ܚܘܼܬܵܡܵܐ
ܠܵܐ ܝܠܲܝܗܝ ܡܫܘܼܬܐܸܣܹ̈ܐ ܒܵܒܼܹܠܵܝܹ̈ܐ ܝܘܼܠܦܵܢ ܡܬܲܠܬܹ̈ܐ ܒܦܸܨܠܵܐ ܕܝܼܠܹܗ ܗܵܕܝܼܵܐ ܝܕܝܼܥܵܐ، ܐܝܼܢܵܐ ܡܘܼܬܸܒܼܠܲܝܗܝ ܠܸܒܼܢܹ̈ܐ ܩܲܕ݇ܡܵܝܹ̈ܐ ܐܸܠܹܗ، ܒܐܘܼܪܚܵܐ ܕܲܡܛܵܘܪܲܢܬܲܝܗܝ ܠܡܲܢܵܝܘܼܬܵܐ ܘܝܘܼܠܦܵܢ ܟܵܘܟܼܒܼܹ̈ܐ ܘܣܘܼܖ̈ܓܵܕܹܐ ܡܸܢܝܵܢܵܝܹ̈ܐ ܕܲܩܝܼܩܹ̈ܐ، ܘܐܲܢܹܐ ܝܘܼܠܦܵܢܹ̈ܐ ܡܫܘܼܢܹܐ ܠܲܝܗܝ ܐ݇ܚܲܪܬܵܐ ܠܲܡܕܝܼܢܵܝܘܼܬܵܐ ܝܵܘܢܵܝܬܵܐ ܘܲܡܕܝܼܢܵܝܘܼܬܵܐ ܐܸܣܠܵܡܵܝܬܵܐ، ܘܐ݇ܚܲܪܬܵܐ ܠܝܘܿܪܘܿܦ ܚܲܕܬܵܐ.
ܘܗܲܠ ܗܵܕܝܼܵܐ ܫܵܘܦܵܐ ܕܐܵܗܵܐ ܝܵܪܬܘܼܬܵܐ ܝܘܼܠܦܵܢܵܝܬܵܐ ܒܵܒܼܹܠܵܝܬܵܐ ܚܝܵܝܵܐ ܝܠܹܗ ܐܸܕܝܘܿܡ ܝܵܘܡܵܐ، ܡ̣ܢ ܦܠܵܓܼܬܵܐ ܕܥܸܕܵܢܵܐ ܘܙܵܘ̈ܝܵܬܵܐ ܥܲܠ ܐܸܣܹ̈ܐ ܕܡܲܢܵܝܘܼܬܵܐ ܕܵܪܵܝܬܵܐ.

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Trigonometry Among the Babylonians


More than four thousand years ago, the Babylonians were engraving precise numerical onto clay tablets and calculating triangle relationships at a time when most civilizations had not yet developed advanced mathematics. These were not merely numbers carved into clay, but the beginning of a scientific legacy that would later influence the history of human knowledge. Although the term “trigonometry” was not known in its modern form at the time, modern studies suggest that the Babylonians established early foundations of this science centuries before the Greek and Islamic civilizations. Plimpton 322 Tablet The clay tablet known as Plimpton 322 is considered one of the most important mathematical discoveries of the ancient world. Dating back to around 1800 BCE, it contains precise numerical tables representing the relationships of right triangles: the relationship known today as the “Pythagorean Theorem.” This tablet demonstrated that the Babylonians understood these mathematical relationships centuries before Pythagoras and applied them practically in geometry and calculations. Babylonian Trigonometry The Babylonians relied on ratios between the sides of right triangles, while the Greeks later developed trigonometry based on angles and circles. This Babylonian mathematical understanding helped in: Measuring land Constructing temples and ziggurats Calculating slopes and heights Performing astronomical calculations Mathematics and Astronomy Among the Babylonians Babylonian mathematics was closely connected to astronomy and engineering. Their sexagesimal (base-60) numerical system enabled highly accurate calculations used in measuring angles and tracking the movement of celestial bodies. The Babylonians used mathematics for: Preparing accurate astronomical tables Determining the positions of planets Designing massive engineering structures Dividing land and building canals Conclusion The Babylonians did not establish trigonometry in the form we know today, but they laid its first foundations through their development of mathematics, astronomy, and precise numerical tables. This knowledge later passed to the Greek and Islamic civilizations, and from there to modern Europe. The influence of this Babylonian scientific legacy is still present around us today, from the division of time and angles to the foundations of modern mathematics.

Western

  • Author : AKKAD SAADI
  • Design & Layout : MERAY YOUSSEF - GABI MALKI
  • Content Editor : RAMIA AHI
  • Syriac Translation & Typing : ANTONI KORIEH
  • Syriac Orthography Editor : DR. ABDUL MASSIH SAADI
  • Voice Over : MARIAM BARSOUM
  • Technical Lead : AMMAR YOSEF
  • Project Manager : DILAMA MALKI
  • Marketing Designer : MERAY YOUSSEF
  • Marketing Coordinator : SAMIR SHAMOUN
  • General Supervision : AKKAD SAADI

Eastern

  • Author : AKKAD SAADI
  • Design & Layout : MERAY YOUSSEF - GABI MALKI
  • Content Editor : RAMIA AHI
  • Syriac Translation & Typing : YOUSIP AUDESHO
  • Eastern Supervision : RAMINA SAMUEL
  • Voice Over : YOUSIP AUDESHO
  • Technical Lead : AMMAR YOSEF
  • Project Manager : DILAMA MALKI
  • Marketing Designer : MERAY YOUSSEF
  • Marketing Coordinator : SAMIR SHAMOUN
  • General Supervision : AKKAD SAADI

English

  • Author : AKKAD SAADI
  • Design & Layout : MERAY YOUSSEF - GABI MALKI
  • Content Editor : RAMIA AHI
  • Syriac Translation & Typing : ANTONI KORIEH
  • Syriac Orthography Editor : DR. ABDUL MASSIH SAADI
  • Voice Over : MARIAM BARSOUM
  • Technical Lead : AMMAR YOSEF
  • Project Manager : DILAMA MALKI
  • Marketing Designer : MERAY YOUSSEF
  • Marketing Coordinator : SAMIR SHAMOUN
  • General Supervision : AKKAD SAADI