Sexagesimal Number System of the Babylonians

Sexagesimal Number System of the Babylonians

  • BET KANU Magazine
  • The Mesopotamian Influence
  • Article 5
  • July 15, 2026

The Fifth article in the Mesopotamian Influence edition of BET KANU Magazine explores the Sexagesimal Number System of the Babylonians — One of the most powerful number systems in history. It examines how the system worked? Why base-60? AndLegacy of the Babylonian System.

Western Syriac


ܛܶܟܣܳܐ ܕܽܗ̄ܘ ܡܶܢܝܳܢܳܐ ܐ݄ܫܬܺܝܢܳܝܳܐ ܕܰܒܳܒܠܳܝ̈ܶܐ

ܡܕܺܝܢܳܝܽܘܬ̥ܳܐ ܕܒܰܢܝܳܐ ܥܰܠ ܗ̄ܰܡܶܢܝܳܢ̈ܶܐ
ܡܶܢ̱ ܙܰܒ̥ܢܳܐ ܝܰܪܺܝܟ̥ܳܐ ܡܶܩ݄ܕ̱ܡ ܕܢ݄ܦܩܺܝ ܗ̄ܰܡܳܐܢ̈ܶܐ ܕܽܗ̄ܘ ܚܫܳܒ̥ܳܐ ܘܰܛܶܟܣ̈ܶܐ ܡܶܢܝܳܢܳܝ̈ܶܐ، ܡܛܰܘܰܪ ܠ݄ܗ̱ܢ ܗ̄ܰܡܕܺܝܢܳܝܘ̈ܳܬ̥ܳܐ ܕܒܶܝܬܢܰܗܪ̈ܺܝܢ – ܘܕܺܝܠܳܢܳܐܝܬ̥ ܗ̄ܰܒܳܒܠܳܝ̈ܶܐ – ܚܰܕ̱ ܡܰܢ̱ ܛܶܟܣ̈ܶܐ ܥܰܫܺܝ̈ܢܶܐ ܕܽܗ̄ܘ ܡܶܢܝܳܢܳܐ ܒܽܗ̄ܘ ܡܰܟܬ̥ܰܒܙܰܒܢܳܐ܇ ܐܰܘܟܺܝܬ ܗ̄ܽܘ ܛܶܟܣܳܐ ܕܽܗ̄ܘ ܡܶܢܝܳܢܳܐ ܐ݄ܫܬܺܝܢܳܝܳܐ (ܐܶܣܳܐ ܕܰ 60).
ܗ̄ܽܘ ܛܶܟܣܰܢܳܐ ܕܒܰܢܺܝ ܡܶܩ݄ܕ̱ܡ ܙ݄ܕ ܡܶܢ̱ ܐܰܪܒܥܰܐܠܦܳܐ ܐ݄ܫܢ̈ܶܐ، ܕܝܰܪܽܒ̥ ܡܶܢ̱ ܡܰܫܠܡܳܢܘ̈ܳܬ̥ܳܐ ܥܰܬܺܝܩ̈ܶܐ ܕܰܫܽܘܡܪ̈ܳܝܶܐ ܘܡܛܰܘ݄ܪ ܒ݄ܬ̥݄ܪ ܡܰܢ̱ ܣّܳܦܪ̈ܶܐ ܒܳܒܠܳܝ̈ܶܐ ܠܐܽܘܪܚܳܐ ܦܫܺܝܛܳܐ ܠܽܗ̄ܘ ܚܫܳܚܳܐ ܕܰܡܶܢܝܳܢ̈ܶܐ.

ܒܗܶܦܟ̥ܳܐ ܕܽܗ̄ܘ ܛܶܟܣܳܐ ܥܰܣܪܳܢܳܝܳܐ (ܐܶܣܳܐ ܕܰ 10) ܕܟܳܡܚܰܫܚܺܝܢܰܐ ܐܰܕܝܰܘܡܰܐ، ܗ̄ܰܒܳܒܠܳܝ̈ܶܐ ܟܳܗ̄ܒܳܢ݄ܢ ܗ̄ܘܰܘ̱ ܒ݄ܡܢܰܘ̈ܳܬ̥ܳܐ ܕܐ݄ܫܬܺܝ. ܗ̄ܽܘ ܡܶܕܰܢܳܐ ܠܰܝ̱ܬ ܗ̄ܘܰܐ ܦܽܘܣܩܳܢܳܐ ܢܽܘܟ̥ܪܳܝܳܐ – ܥܰܠ ܕܐ݄ܫܬܺܝ ܡܶܢܝܳܢܳܐ ܕܒ݄ܦܫܺܝܛܽܘܬ̥ܳܐ ܟܳܡ݄ܦܠ݄ܓ̥ ܠܓ̥ܰܠܰܒܶܐ ܡܶܢܝܳܢ̈ܶܐ (2, 3, 4, 5, 6…) ، ܘ݄ܛܪܶܐ ܠܶܗ ܕܗܳܘ݄ܢ ܗ̄ܰܚܫܳܒ̥̈ܶܐ ܦܫܺܝ̈ܛܶܐ ܘܬܪ̈ܺܝܨܶܐ ܙ݄ܕ.

ܐܰܝܕܰܪܒܳܐ ܥܳܒ̥ܰܕ ܗ̄ܘܰܐ ܗ̄ܽܘ ܛܶܟܣܳܐ؟
ܗ̄ܰܒܳܒܠܳܝ̈ܶܐ ܟܳܡܚܰܫܚܺܝ ܗ̄ܘܰܘ̱ ܟܽܘܢܳܫܳܐ ܕܪ̈ܶܡܙܶܐ ܡܶܢ̱ ܚܠܳܦ ܟܽܘܢܳܫܳܐ ܟܰܡܺܝܠܳܐ ܐܰܘ ܓܡܺܝܪܳܐ ܕܰܡܶܢܝܳܢ̈ܶܐ ܐܟ̥ ܕܟ݄ܬ ܠܰܢ ܐܰܕܝܰܘܡܰܐ.
· ܗ̄ܽܘ ܨܶܨܳܐ ܥܰܡܽܘܕܳܝܳܐ ܡܡܰܬ̥ܰܠ ܗ̄ܘܰܐ 1
· ܗ̄ܽܘ ܨܶܨܳܐ ܕܺܗ̄ܝ ܩܽܘܪܢܺܝܬ̥ܳܐ ܡܡܰܬ̥ܰܠ ܗ̄ܘܰܐ 10
ܘܒܽܗ̄ܘ ܡܙܳܓ̥ܳܐ ܕܰܪ̈ܶܡܙܰܢܺܝ ܩ݄ܕܪܺܝ ܗ̄ܘܰܘ̱ ܕܟ݄ܬ̥ܒ̥ܺܝ ܗ̄ܘܰܘ̱ ܡܶܢܝܳܢ̈ܶܐ ܡܶܢ̱ 1 ܗ݄ܠ 59.

ܐܟ̥ ܕܡܰܬ̥ܠܳܐ܇
· 23 = ܬܪܶܝ ܥܰܣܪ̈ܳܘܰܬ + ܬܠܳܬ̥ܳܐ ܚܰܕ̱
· 47 = ܐܰܪܒܥܳܐ ܥܰܣܪ̈ܳܘܰܬ + ܫܰܒܥܳܐ ܚܰܕ̱
ܘܺܗ̄ܝ ܢܰܩܠܰܐ ܕܡܳܛ݄ܢ ܗ̄ܘܰܘ̱ ܠܽܗ̄ܘ ܡܶܢܝܳܢܳܐ ܕܐ݄ܫܬܺܝ، ܡܶܢ̱ ܚܠܳܦ ܕܣܰܝܡܺܝ ܗ̄ܘܰܘ̱ ܪܶܡܙܳܐ ܚܰܕ̱ܬ̥ܳܐ، ܡܚܰܫܚܺܝ ܗ̄ܘܰܘ̱ ܛܺܝܡܳܐ ܕܺܗ̄ܝ ܕܽܘܟܬ̥ܳܐ – ܐܟ̥ ܕܐܰܝܕܰܪܒܳܐ ܐܰܚܢܰܐ ܟܳܪ݄ܡܫܺܝܢܰܐ ܐܰܕܝܰܘܡܰܐ ܡܰܢ ܥܰܣܪ̈ܳܘܰܬ ܠܰܡܳܐܐܘ̈ܰܬ.
ܗ̄ܺܝ ܕܽܘܟܬ̥ܳܐ ܕܒ݄ܬ̥݄ܪ ܡܡܰܬ̥ܠܳܐ ܗ̄ܘܰܐ 60 → (60¹)
ܘ݄ܕܒ݄ܬ̥݄ܪ 60 × 60 → 60²
ܘ݄ܕܒ݄ܬ̥݄ܪ 60 × 60 × 60 → 60³
ܘܗܰܬ̥ܶܐ ܛܪܶܐ ܠܰܗ ܕܗܳܘܶܐ ܗ̄ܽܘ ܛܶܟܣܰܢܳܐ ܡܛܰܘܪܳܐ ܘܪܰܟܝܟ̥ܳܐ.
ܗ̄ܰܒܳܒܠܳܝ̈ܶܐ ܠܰܝ̱ܬ ܗ̄ܘܰܝ ܠ݄ܗ̱ܢ ܪܶܡܙܳܐ ܠܽܗ̄ܘ 0 ܐܟ̥ ܕܟ݄ܐܕܥܺܝܢܰܐ ܠܶܗ ܐܰܕܝܰܘܡܰܐ.
ܒ݄ܬ̥݄ܪ ܡܛܰܘܰܪ ܠ݄ܗ̄ܢ ܪܶܡܙܳܐ ܕܺܝܠܳܢܳܝܳܐ ܕܡܰܚܘ݄ܢ ܕܽܘܟܬ̥ܳܐ ܟ̥ܠܺܝܬ̥ܳܐ ܒܓܰܘܶܗ ܕܽܗ̄ܘ ܡܶܢܝܳܢܳܐ – ܐܟ̥ ܕܢܽܘܩܙܳܐ ܕܕܽܘܟܬ̥ܳܐ ܡܶܢ̱ ܚܠܳܦ ܡܶܢܝܳܢܳܐ. ܥܰܠ ܗܰܬ̥ܶܐ 0 ܠܰܝ̱ܬ ܗ̄ܘܰܘ̱ ܡܫܰܘܫܛܳܐ ܒܕܽܘܡܝܳܐ ܚܫܳܒ̥ܳܢܳܝܳܐ ܐܟ̥ ܕܟ݄ܐܕܥܺܝܢܰܐ ܠܶܗ ܐܰܕܝܰܘܡܰܐ.

ܩܰܝ ܗ̄ܽܘ ܐܶܣܳܐ 60؟
ܗ̄ܽܘ ܦܽܘܣܩܳܢܳܐ ܕ60 ܩܠܺܝܕܳܐ ܗ̄ܘܰܐ ܠܽܗ̄ܘ ܟܽܘܫܳܪܳܐ ܕܽܗ̄ܘ ܛܶܟܣܳܐ. ܥܰܠ ܕ60 ܟܺܝܒܶܗ ܕܡ݄ܦܠ݄ܓ̥ ܒܫܰܘܝܽܘܬ̥ܳܐ ܡܶܢ̱ ܓ̥ܰܠܰܒܶܐ ܡܶܢܝܳܢ̈ܶܐ،
(2, 3, 4, 5, 6, 10, 12, 15, 20, 30)
ܗ̄ܽܘ ܚܫܳܚܳܐ ܕܰܬܒ̥ܳܪ̈ܶܐ ܗܰܘܺܝ ܦܫܺܝܛܳܐ ܙ݄ܕ ܡܽܗ̄ܘ ܐܶܣܳܐ ܕܰ 10.
ܡܰܗ̄ܘܟ̥ܰܐ ܗܳܠ ܐܳܥܕܳܐ ܟܺܝܬ ܦܰܠܩ̈ܶܐ ܕܽܗ̄ܘ ܛܶܟܣܳܐ ܒܳܒܠܳܝܳܐ ܫܟܺܝܚ̈ܶܐ ܐܰܕܝܰܘܡܰܐ.
60 ܪ̈ܦܳܦܶܐ ܒܺܗ̄ܝ ܩܰܛ݄ܝܢܬܳܐ
60 ܩܰܛܺܝܢ̈ܳܬ̥ܳܐ ܒܺܗ̄ܝ ܫܳܥܬ̥ܳܐ
360 ܕܰܪ̈ܓ̥ܶܐ ܒܺܗ̄ܝ ܕܽܘܪܬܳܐ
ܟܽܘܠ ܢܰܩܠܰܐ ܕܚܰܝܪܺܝܢܰܐ ܥܰܠ ܗ̄ܺܝ ܫܳܥܬ̥ܳܐ، ܡܟܰܝܠܺܝܢܰܐ ܙܳܘܺܝܬ̥ܳܐ ܐܰܘ ܕܽܘܟܬ̥ܳܐ ܥܰܠ ܗ̄ܺܝ ܐܰܪܥܳܐ ܥܰܡ ܗ̄ܽܘ ܝܽܘܪܟ̥ܳܐ، ܟܳܡܚܰܫܚܺܝܢܰܐ ܛܶܟܣܳܐ ܕܟ݄ܬ ܠܶܗ ܫܶܪܫܳܐ ܒܒܶܝܬܢܰܗܪܺܝܢ ܡܶܢ̱ ܐܰܠܦܰܝܳܐ ܕ݄ܐܫܢ̈ܶܐ.

ܝܳܪܬܽܘܬ̥ܳܐ ܕܽܗ̄ܘ ܛܶܟܣܳܐ ܒܳܒܠܳܝܳܐ
ܗ̄ܽܘ ܛܶܟܣܳܐ ܐ݄ܫܬܺܝܢܳܝܳܐ ܠܰܝ̱ܬ ܗ̄ܘܰܐ ܒܰܠܚܽܘܕ ܠܽܗ̄ܘ ܒܢܳܝܳܐ – ܐܶܠܳܐ ܗܰܘܺܝ ܗ̄ܘܰܐ ܫܶܬܶܐܣܬܳܐ ܠܚܰܩܠ̈ܶܐ ܐܽܘܠܨܳܝ̈ܶܐ ܐܰܟ̥܇
ܝܽܘܠܦܳܢܳܐ ܕܰܟܽܘܟܒ̥̈ܶܐ، ܠܺܗ̄ܝ ܚܙܰܝܬܳܐ ܕܽܗ̄ܘ ܪܡܳܫܳܐ ܕܰܟܽܘܟܒ̥̈ܶܐ ܘܰܟܰܘܟܒ̈ܶܐ
ܡܰܚܳܪܽܘܬܳܐ، ܠܽܗ̄ܘ ܟܰܝܠܳܐ ܕܰܐܶܣܟܺܝܡ̈ܶܐ ܘܰܩ݄ܪ̈ܢܰܘܳܬ̥ܶܐ
ܙܰܒܢܳܐ، ܠܽܗ̄ܘ ܦܪܳܫܳܐ ܕܽܗ̄ܘ ܝܰܘܡܳܐ
ܗ̄ܰܣّܳܦܪ̈ܶܐ ܒܳܒܠܳܝ̈ܶܐ ܡܚܰܫܚܺܝ ܗ̄ܘܰܘ̱ ܗ̄ܽܘ ܐܶܣܳܐ ܕܰ 60 ܕܣܰܝܡܺܝ ܗ̄ܘܰܘ̱ ܚܫܳܒ̥̈ܶܐ ܕܰܙܥܽܘܪ̈ܝܳܬ̥ܳܐ، ܕܗܰܘܺܝ ܡܰܥܒܕܳܢܽܘܬ̥ܳܐ ܒ݄ܬ̥݄ܪ ܥܰܠ ܗ̄ܽܘ ܝܽܘܠܦܳܢܳܐ ܕܰܝܰܘ̈ܢܳܝܶܐ ܘܕܰܡܰܫ݄ܠܡܳܢ̈ܶܐ
ܘܰܐܕܝܰܘܡܰܐ ܣܬܶܝ، ܒ݄ܬ̥ܪ ܙ݄ܕ ܡܶܢ̱ ܐܰܪܒܥܰܐܠܦܳܐ ܐ݄ܫܢ̈ܶܐ، ܗ̄ܽܘ ܛܶܟܣܰܢܳܐ ܟܳܡܰܚܘܶܐ ܠܰܢ ܐܰܝܕܰܪܒܳܐ ܟܳܡ݄ܣܬܰܟܠܺܝܢܰܐ ܗ̄ܘ ܙܰܒܢܳܐ ܘܺܗ̄ܝ ܪܘܰܚܬܳܐ

ܚܽܘܬܳܡܳܐ
ܗ̄ܽܘ ܛܶܟܣܳܐ ܐ݄ܫܬܺܝܢܳܝܳܐ ܒܳܒܠܳܝܳܐ ܠܰܝ̱ܬ ܝܳܐ ܒܰܠܚܽܘܕ ܫܒܺܝܠܳܐ ܕ݄ܒܢܳܝܳܐ ܥܰܬܺܝܩܳܐ – ܐܶܠܳܐ ܡܰܚܫܰܒܬܳܐ ܕܽܗ̄ܘ ܗܰܘܢܳܐ ܘܕܽܗ̄ܘ ܝܽܘܠܦܳܢܳܐ ܒܰܪܢܳܫܳܝܳܐ.
ܘܐܟ̥ ܕܫܽܘܬܳܐܣܳܐ ܕܒܶܝܬ ܟܰܢܳܘ، ܟܳܡܫܰܠܛܺܝܢܰܐ ܗ̄ܽܘ ܒܰܗܪܳܐ ܥܰܠ ܢܰܨܺܝܚܘ̈ܳܬ̥ܳܐ (ܫܽܘܡܠܳܝ̈ܶܐ) ܐܟ̥ ܕܰܗ̄ܢܺܝ، ܕܡܰܡܛܺܝܢܰܐ ܠܒܳܠܰܝܢܰܐ ܕܺܗ̄ܝ ܦܢܺܝܬ̥ܰܝܕܰܢ ܠܰܝ̱ܬ ܗ̄ܘܰܐ ܒܰܠܚܽܘܕ ܢܽܘܩܰܙܬܳܐ ܕܺܗ̄ܝ ܡܰܪܕܽܘܬ̥ܳܐ ܘܕܽܗ̄ܘ ܠܶܫܳܢܳܐ، ܐܶܠܳܐ ܕܽܘܟܬ̥ܳܐ ܕܽܗ̄ܘ ܚܽܘܕܳܬ̥ܳܐ ܝܽܘܠܦܳܢܳܝܳܐ ܕܟܳܚܳܝܶܐ ܗܳܠ ܐܳܥܕܳܐ ܒܰܚܰܝܰܝܕ̈ܰܢ ܗ̄ܰܝܰܘܡܳܝ̈ܶܐ.

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Eastern Syriac


ܛܲܟܼܣܵܐ ܐܸܫܬܝܼܢܵܝܵܐ ܠܓܹܒ ܒܵܒܼܹ


ܚܕܵܐ ܡܕܝܼܢܵܝܘܼܬܵܐ ܒܢܝܼܬܵܐ ܥܲܠ ܖ̈ܲܩܡܹܐ
ܩܵܕ݇ܡ ܥܸܕܵܢܵܐ ܝܲܪܝܼܟܼܬܵܐ ܡ̣ܢ ܦܠܵܛܬܵܐ ܕܬܘܼܩܵܢܹ̈ܐ ܕܲܡܚܲܫܒܘܿܢܹܐ ܘܛܲܟܼܣܹ̈ܐ ܖ̈ܲܩܡܵܝܹܐ،ܡܛܘܼܪܸܢܲܝܗܝ ܡܕܝܼܢܵܝ̈ܘܵܬܵܐ ܕܒܹܝܬ ܢܲܗܖ̈ܝܼܢ -ܦܪܝܼܫܵܐܝܼܬ ܒܵܒܼܹܠܵܝܹ̈ܐ- ܚܲܕ݇ ܡ̣ܢ ܕܐܵܢܝ݇ ܛܲܟܼܣܹ̈ܐ ܖܸ̈ܩܡܵܝܹܐ ܒܘܼܫ ܚܲܝܠܵܢܹ̈ܐ ܓܵܘ ܬܲܫܥܝܼܬܵܐ: ܛܲܟܼܣܵܐ ܐܸܫܬܝܼܢܵܝܵܐ (ܐܸܣܵܐ ܝܼܠܹܗ 60).
ܐܵܗܵܐ ܛܲܟܼܣܵܐ، ܕܦܝܼܫܠܹܗ ܒܸܢܝܵܐ ܩܵܕ݇ܡ ܙܵܘܕܵܐ ܡ̣ܢ 4000 ܐܲܠܦܹ̈ܐ ܫܸܢܹ̈ܐ، ܡܓܘܼܪܘܸܣܠܹܗ ܡ̣ܢ ܥܝܵܕܹ̈ܐ ܫܘܿܡܝܼܖ̈ܵܝܹܐ ܒܘܼܫ ܥܲܬܝܼܩܹ̈ܐ، ܘܐ݇ܚܲܪܬܵܐ ܦܝܼܫܠܹܗ ܡܛܘܼܘܪܸܢܵܐ ܓܹܒ ܒܵܒܼܹܠܵܝܹ̈ܐ ܕܗܵܘܹܐ ܚܕܵܐ ܐܘܼܪܚܵܐ ܦܫܝܼܛܵܐ ܥܵܒܼܘܿܕܬܵܐ ܠܲܫܩܵܠ ܝܗܵܒܼܵܐ ܥܲܡ ܖ̈ܲܩܡܹܐ.
ܘܲܒܗܸܦܟܵܐ ܕܛܲܟܼܣܵܐ ܥܸܣܪܵܢܵܝܵܐ (ܐܸܣܵܐ ܝܼܠܹܗ 10) ܕܝܼܠܹܗ ܡܘܼܦܠܸܚܵܐ ܗܵܕܝܼܵܐ، ܣܢܸܕܠܲܝܗܝ ܒܵܒܼܹܠܵܝܹ̈ܐ ܥܲܠ ܡܢܵܝܵܐ ܒܲܚܕܵܝ̈ܘܵܬܵܐ ܡ̣ܢ 60. ܘܐܵܗܵܐ ܡܓܲܒܲܝܬܵܐ ܠܵܐ ܝܗ݇ܘܵܐ ܐܲܝܟܼ ܕܐܵܬܝܵܐ، ܟܲܕ ܪܲܩܡܵܐ ܕ 60 ܒܐܵܬܹܐ ܠܲܦܠܵܓܼܵܐ ܒܲܦܫܝܼܛܘܼܬܵܐ ܥܲܠ ܪܵܒܵܐ ܡܸܢܝܵܢܹ̈ܐ (2، 3، 4، 5، 6...)، ܘܐܵܗܵܐ ܡܸܢܕܝܼ ܡܘܼܥܒܼܸܕܠܹܗ ܕܲܡܚܲܫܒܲܢܬܵܐ ܗܵܘܝܵܐ ܒܘܼܫ ܦܫܝܼܛܬܵܐ ܘܒܘܼܫ ܕܲܩܝܼܩܬܵܐ.

ܕܐܵܟܼܝܼ ܟܹܐ ܦܵܠܹܚ ܗ݇ܘܵܐ ܐܵܗܵܐ ܛܲܟܼܣܵܐ؟
ܡܘܼܦܠܸܚܠܲܝܗܝ ܒܵܒܼܹܠܵܝܹ̈ܐ ܠܲܚܕܵܐ ܟܢܘܼܫܬܵܐ ܡ̣ܢ ܖܸ̈ܡܙܹܐ ܡ̣ܢ ܫܵܘܦܵܐ ܕܲܚܕܵܐ ܟܢܘܼܫܬܵܐ ܓܡܝܼܪܬܵܐ ܡ̣ܢ ܖ̈ܲܩܡܹܐ ܐܲܝܟܼ ܕܥܵܒܼܕܲܚ ܗܵܕܝܼܵܐ.
·ܨܸܨܵܐ ܥܲܡܘܼܕܵܝܵܐ ܡܲܡܬܸܠ ܗ݇ܘܵܐ ܠܪܲܩܡܵܐ 1
· ܨܸܨܵܐ ܙܵܘܝܼܬܵܢܵܝܵܐ ܡܲܡܬܸܠ ܗ݇ܘܵܐ ܠܪܲܩܡܵܐ 10
ܘܲܒܐܘܼܪܚܵܐ ܕܲܡܚܲܝܘܿܕܹܐ ܐܲܢܹܐ ܖܸ̈ܡܙܹܐ، ܡܨܹܐ ܠܲܝܗܝ ܕܟܵܬܒܼܝܼ ܠܡܸܢܝܵܢܹ̈ܐ ܡ̣ܢ 1 ܗܲܠ 59.

ܩܵܐ ܛܘܼܦ̮ܣܵܐ:
· 23 = ܬܪܹܝܢ ܨܸܨܹ̈ܐ ܩܵܐ ܥܸܣܖ̈ܵܝܹܐ + ܬܠܵܬܵܐ ܩܵܐ ܚܕܵܢܵܝܹ̈ܐ
·47 = ܐܲܪܒܥܵܐ ܥܸܣܖ̈ܵܝܹܐ + ܫܲܒܼܥܵܐ ܚܕܵܢܵܝܹ̈ܐ

ܐܝܼܡܲܢ ܕܡܵܛܝܼ ܗ݇ܘܵܘ ܠܡܸܢܝܵܢܵܐ ܕ 60، ܡ̣ܢ ܫܵܘܦܵܐ ܕܲܥܒܼܵܕܵܐ ܪܸܡܙܵܐ ܚܲܕ݇ܬܵܐ، ܟܹܐ ܡܲܦܠܸܚܝܼ ܗ݇ܘܵܘ ܛܝܼܡܵܐ ܕܕܘܼܟܬܵܐ، ܗܵܪ ܐܲܟܼܘܵܬܲܢ ܐܸܕܝܘܿܡ ܝܵܘܡܵܐ ܐܝܼܡܲܢ ܕܲܡܫܲܢܹܝܚ ܡ̣ܢ ܥܸܣܖ̈ܵܝܹܐ ܠܐܸܡܵܝܹ̈ܐ.
ܕܘܼܟܬܵܐ ܐܵܬܝܵܢܬܵܐ ܡܲܡܬܸܠܵܐ ܗ݇ܘܵܐ 60 → (60¹)
ܐ݇ܚܲܪܬܵܐ 60 × 60 → 60²
ܐ݇ܚܲܪܬܵܐ 60 × 60 × 60 → 60³
ܘܐܵܗܵܐ ܡܸܢܕܝܼ ܡܘܼܥܒܼܸܕܠܹܗ ܕܛܲܟܼܣܲܝܗܝ ܗܵܘܹܐ ܡܸܬܩܲܕܡܵܢܵܐ ܘܲܦܫܝܼܛܵܐ ܒܲܚܕܵ ܐܘܼܪܚܵܐ ܓܵܪܫܵܢܬܵܐ.
ܠܵܐ ܩܲܡ ܗܵܘܹܐ ܠܲܝܗܝ ܒܵܒܼܹܠܵܝܹ̈ܐ ܚܲܕ݇ ܪܸܡܙܵܐ ܩܵܐ ܨܝܼܦܲܪ ܒܗܵܘ ܣܘܼܟܵܠܵܐ ܕܵܪܝܵܐ،
ܐܝܼܢܵܐ ܐ݇ܚܲܪܬܵܐ ܡܛܘܼܘܪܸܢܲܝܗܝ ܚܲܕ݇ ܪܸܡܙܵܐ ܕܝܼܠܵܢܵܝܵܐ ܠܲܪܡܵܙܵܐ ܥܲܠ ܕܘܼܟܬܵܐ ܣܦܝܼܩܬܵܐ ܓܵܘ ܡܸܢܝܵܢܵܐ، ܐܵܘܟܹܝܬ ܛܝܼܡܵܐ ܕܘܼܟܬܵܢܵܝܵܐ ܘܠܵܐ ܡܸܢܝܵܢܵܐ ܫܲܠܝܼܛ ܒܝܵܬܵܐ، ܠܗܵܕܟܼܵܐ ܨܝܼܦܲܪ ܠܵܐ ܝܗ݇ܘܵܐ ܚܲܕ݇ ܐܸܣܵܐ ܡܲܢܵܝܘܼܬܵܢܵܝܵܐ ܓܡܝܼܪܵܐ ܐܲܝܟܼ ܕܝܵܕܥܲܚ ܠܹܗ ܐܸܕܝܘܿܡ ܝܵܘܡܵܐ.

ܩܵܐ ܡܘܿܕܝܼ ܐܸܣܵܐ ܝܼܠܹܗ 60؟
ܡܓܲܒܲܝܬܵܐ ܕܪܲܩܡܵܐ 60 ܝܼܗ݇ܘܵܐ ܐ݇ܪܵܙܵܐ ܕܡܲܢܬܲܝܬܵܐ ܕܐܵܗܵܐ ܛܲܟܼܣܵܐ.
ܟܲܕ ܒܥܸܠܬܵܐ ܕܡܸܬܡܲܨܝܵܢܘܼܬܵܐ ܕܲܦܠܵܓܼܬܹܗ ܥܲܠ ܪܵܒܵܐ ܡܸܢܝܵܢܹ̈ܐ (2، 3، 4، 5، 6، 10، 12، 15، 20، 30)، ܗܘܹܐ ܫܩܵܠ ܝܗܵܒܼܵܐ ܥܲܡ ܬܸܒܼܖܹ̈ܐ ܒܘܼܫ ܦܫܝܼܛܵܐ ܒܦܘܼܚܵܡܵܐ ܥܲܡ ܛܲܟܼܣܵܐ ܥܸܣܪܵܝܵܐ.
ܘܥܲܠ ܐܵܗܵܐ ܥܸܠܬܵܐ، ܗܲܠ ܗܵܕܝܼܵܐ ܡܲܦܠܘܿܚܹܐ ܝܘܲܚ ܚܲܕ݇ܟܡܵܐ ܣܲܗܡܹ̈ܐ ܡ̣ܢ ܐܵܗܵܐ ܛܲܟܼܣܵܐ ܗܲܠ ܐܸܕܝܘܿܡ ܝܵܘܡܵܐ

· 60 ܖ̈ܦܵܦܹܐ ܓܵܘ ܩܲܛܝܼܢܬܵܐ
· 60 ܩܲܛܝܼܢ̈ܝܵܬܵܐ ܓܵܘ ܫܵܥܬܵܐ
· 360 ܕܲܖ̈ܓܼܹܐ ܓܵܘ ܚܘܼܕܪܵܐ
ܓܵܘ ܟܠ ܓܵܗܵܐ ܕܚܵܝܪܝܼܬܘܿܢ ܐܸܒܵܗ̇ ܒܫܵܥܬܵܐ ܐܵܘ ܟܵܝܠܝܼܬܘܿܢ ܚܕܵܐ ܙܵܘܝܼܬܵܐ، ܐܵܘ ܐܵܦܸܢ ܕܲܡܬܲܚܸܡܝܼܬܘܿܢ ܚܲܕ݇ ܝܲܬܒܼܵܐ ܥܲܠ ܐܲܪܥܵܐ ܒܡܲܦܠܲܚܬܵܐ ܕܣܸܖ̈ܛܹܐ ܕܝܘܼܪܟܼܵܐ ܘܦܸܬܝܘܼܬܵܐ، ܒܲܫܪܵܪܵܐ ܡܲܦܠܘܿܚܹܐ ܝܬܘܿܢ ܠܚܲܕ݇ ܛܲܟܼܣܵܐ ܒܸܪܝܵܐ ܓܵܘ ܒܹܝܬ ܢܲܗܖ̈ܝܼܢ ܩܵܕ݇ܡ ܐܲܠܦܵܝܹ̈ܐ ܕܫܸܢܹ̈ܐ.

ܝܵܪܬܘܼܬܵܐ ܕܛܲܟܼܣܵܐ ܒܵܒܼܹܠܵܝܵܐ
ܛܲܟܼܣܵܐ ܐܸܫܬܝܼܢܵܝܵܐ ܠܵܐ ܝܗ݇ܘܵܐ ܐܲܚܟ̰ܝܼ ܚܕܵܐ ܐܘܼܪܚܵܐ ܠܲܡܢܵܝܵܐ، ܐܝܼܢܵܐ ܦܝܼܫܵܐ ܝܠܹܗ ܐܸܣܵܐ ܠܝܘܼܠܦܵܢܹ̈ܐ ܐܵܢܲܢܩܵܝܹ̈ܐ ܐܲܝܟܼ:
ܝܘܼܠܦܵܢ ܟܵܘܟܼܒܼܹ̈ܐ: ܠܲܡܬܲܒܘܿܥܹܐ ܙܵܘܥܵܐ ܕܟܵܘܟܼܝܹ̈ܐ ܘܛܲܥܝܹ̈ܐ
ܡܲܚܵܪܘܼܬܵܐ: ܠܲܟܝܵܠܵܐ ܐܸܣܟܹܡܹ̈ܐ ܘܙܵܘ̈ܝܵܬܵܐ
ܟܝܵܠܵܐ ܙܲܒܼܢܵܐ: ܠܡܲܪܝܘܿܙܹܐ ܝܵܘܡܵܐ
ܘܡܘܼܦܠܸܚܠܲܝܗܝ ܝܵܕܘܿܥܹ̈ܐ ܒܵܒܼܹܠܵܝܹ̈ܐ ܠܐܵܗܵܐ ܛܲܟܼܣܵܐ ܠܲܥܒܼܵܕܬܵܐ ܡܵܘܕܥܵܢ̈ܘܵܬܵܐ ܘܚܘܼܫܒܵܢܹ̈ܐ ܕܲܩܝܼܩܹ̈ܐ، ܘܲܟܬܵܒܼܬܵܐ ܨܸܨܵܝܬܵܐ ܡܗܘܼܝܸܪܵܗ̇ ܓܵܘ ܡܣܲܓܲܠܬܵܐ ܕܐܵܗܵܐ ܛܘܼܘܵܪܵܐ ܥܲܠ ܠܘܼܚܹ̈ܐ ܕܛܝܼܢܵܐ، ܘܐܵܗܵܐ ܡܸܢܕܝܼ ܡܘܼܥܒܼܸܕܠܹܗ ܡܫܲܢܲܝܬܵܐ ܕܝܼܕܲܥܬܵܐ ܩܵܐ ܝܘܼܒܵܠܹ̈ܐ ܐܵܬܝܵܢܹ̈ܐ، ܘܲܡܥܘܼܒܕܸܢܹܗ ܐ݇ܚܲܪܬܵܐ ܥܲܠ ܝܘܼܠܦܵܢܹ̈ܐ ܝܵܘܢܵܝܹ̈ܐ ܘܐܸܣܠܵܡܵܝܹ̈ܐ.
ܘܗܲܠ ܐܸܕܝܘܿܡ ܝܵܘܡܵܐ، ܘܒܵܬܲܪ 3500 ܐܵܘ 4000 ܐܲܠܦܹ̈ܐ ܫܸܢܹ̈ܐ، ܦܝܵܫܵܐ ܝܠܵܗ̇ ܡܲܥܒܕܵܢܘܼܬܵܐ ܕܐܵܗܵܐ ܛܲܟܼܣܵܐ ܓܵܘ ܐܘܼܪܚܵܐ ܕܲܡܦܲܪܡܲܝܬܵܐ ܕܥܸܕܵܢܵܐ ܘܲܪܘܵܚܬܵܐ.

ܚܘܼܬܵܡܵܐ
ܛܲܟܼܣܵܐ ܐܸܫܬܝܼܢܵܝܵܐ ܒܵܒܼܹܠܵܝܵܐ ܠܵܐ ܝܠܹܗ ܐܲܚܟ̰ܝܼ ܚܕܵܐ ܐܘܼܪܚܵܐ ܥܲܬܝܼܩܬܵܐ ܠܲܡܢܵܝܵܐ، ܐܝܼܢܵܐ ܝܼܠܹܗ ܡܲܙܒܲܛܬܵܐ ܥܲܠ ܒܵܪܘܿܝܘܼܬܵܐ ܕܒܲܪܢܵܫܵܐ ܘܣܲܟܘܼܠܬܵܢܘܼܬܹܗ.
ܘܩܵܐ BET KANU، ܡܲܬܲܒܼܬܵܐ ܕܒܵܠܵܐ ܥܲܠ ܗܵܕܟܼܵܐ ܫܘܼܡܠܵܝܹ̈ܐ ܡܲܕܟܼܘܿܪܲܢ ܝܼܠܵܗ̇ ܕܲܦܢܝܼܬܲܢ ܠܵܐ ܝܗ݇ܘܵܐ ܐܲܚܟ̰ܝܼ ܩܸܢܛܪܘܿܢ ܩܵܐ ܡܲܪܕܘܼܬܵܐ ܘܠܸܫܵܢܵܐ، ܐܝܼܢܵܐ ܝܼܗ݇ܘܵܐ ܐܵܦ ܕܲܪܓܘܼܫܬܵܐ ܕܒܵܪܘܿܝܘܼܬܵܐ ܝܘܼܠܦܵܢܵܝܬܵܐ ܕܗܲܠ ܗܵܕܝܼܵܐ ܦܝܵܫܵܐ ܝܠܵܗ̇ ܓܵܘ ܚܲܝܘܼܬܲܢ ܝܵܘܡܵܝܬܵܐ.

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Sexagesimal Number System of the Babylonians


1- A Civilization built on Numbers: Long before modern calculators and digital systems, the civilizations of Mesopotamia—especially the Babylonians—developed one of the most powerful number systems in history: the sexagesimal system, or base-60. This system, built over 4,000 years ago, grew out of earlier Sumerian traditions and was refined by Babylonian scholars into a flexible and efficient way of working with numbers. Unlike the decimal system (base-10) we use today, the Babylonians counted in units of 60. This was not random—60 is a number that can be divided easily by many others (2, 3, 4, 5, 6…), which made calculations simpler and more precise. 2- How the System Worked The Babylonian system used a combination of symbols rather than a full set of digits like we have today. A vertical wedge represented 1 A corner wedge represented 10 By combining these symbols, they could write numbers from 1 to 59. For example: 23 = two tens + three ones 47 = four tens + seven ones When they reached 60, instead of creating a new symbol, they used place value—similar to how we move from tens to hundreds today. The next position represented 60 → (60¹) Then 60 × 60 → 60², Then 60 × 60 × 60 → 60³ This made their system remarkably advanced and flexible. The Babylonians did not initially have a symbol for zero in the modern sense. Later, they developed a special symbol to indicate an empty place within a number—as a positional marker rather than a number itself. Therefore, zero was not a fully developed mathematical concept as we understand it today. 3- Why base-60? The choice of 60 was key to the system’s success. Because 60 can be divided evenly by many numbers, (2, 3, 4, 5, 6, 10, 12, 15, 20, 30) working with fractions became much easier than in base-10. This is why parts of the Babylonian system are still used today: 60 seconds in a minute 60 minutes in an hour 360 degrees in a circle Every time we look at a clock, measure an angle, or even determine a location on Earth using latitude and longitude, we are in fact using a system that originated in Mesopotamia thousands of years ago. 4- Legacy of the Babylonian System The sexagesimal system was not only used for counting—it became the foundation for important fields such as: Astronomy, to track the movement of stars and planets Geometry, to measure shapes and angles Timekeeping, to divide the day Babylonian scholars used base-60 to make detailed observations and calculations, influencing later Greek and Islamic science. Even today, more than 4,000 years later, their system continues to shape how we understand time and space. Closing Reflection The Babylonian sexagesimal system is more than an ancient method of counting—it is a reflection of human creativity and intelligence. For BET KANU, highlighting such achievements reminds us that our region was not only a center of culture and language, but also a place of scientific innovation that still lives on in our daily lives.
Credits

Western

  • Author : MARIAM BARSOUM
  • Design & Layout : MERAY YOUSSEF - GABI MALKI
  • Content Editor : RAMIA AHI
  • Syriac Translation & Transcription : 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 : MARIAM BARSOUM
  • Design & Layout : MERAY YOUSSEF - GABI MALKI
  • Content Editor : RAMIA AHI
  • Syriac Translation & Transcription : 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 : MARIAM BARSOUM
  • Design & Layout : MERAY YOUSSEF - GABI MALKI
  • Content Editor : RAMIA AHI
  • Syriac Translation & Transcription : 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