ᱞᱤᱞᱟᱣᱚᱛᱤ

ᱞᱤᱞᱟᱣᱚᱛᱤ ᱫᱚ ᱥᱤᱧᱚᱛ ᱤᱭᱟ ᱮᱞᱠᱷᱟᱣᱟᱱᱵᱷᱟᱥᱠᱟᱨᱟ II's ᱦᱚᱲ ᱠᱟᱱᱟᱭ ᱮᱞᱠᱷᱟ , ᱚᱞ ᱞᱮᱫ ᱛᱟᱦᱮᱱ ᱱᱟᱭ ᱑᱙᱕᱐ ᱨᱮ᱾ ᱱᱚᱶᱟ ᱫᱚ ᱩᱱᱤᱭᱟᱜ ᱟᱥᱚᱞ ᱢᱟᱲᱟᱝ ᱠᱟᱹᱢᱤ ᱛᱟᱦᱮᱱ ᱛᱟᱭ ᱛᱟᱦᱮᱸᱜ ᱠᱟᱱᱟ, ᱡᱟᱦᱟᱸ ᱱᱩᱭᱟᱜ Siddhānta Shiromani, alongside Bijaganita, Grahaganita ᱟᱨ Golādhyāya.ᱱᱚᱶᱟ ᱠᱚ ᱢᱮᱱᱟᱜ ᱛᱟᱭᱟ᱾{{sfn|Poulose|1991|p=79}}

A problem from the Lilavati by Bhaskaracharya. Written in the 12th century. This appeared on page 18 of The Mathematical Mystery Tour by UNESCO in 1989.

ᱮᱞᱠᱷᱟ ᱟᱨ ᱠᱷᱟᱜᱚᱞᱤᱭ ᱥᱚᱥᱛᱨᱚ ᱨᱮᱱᱟᱜ ᱢᱤᱫ ᱢᱟᱨᱮ ᱜᱨᱚᱸᱛᱷ ᱢᱮᱱᱟᱜ ᱢᱮᱱᱟᱜ ᱛᱟᱭᱟ, ᱡᱟᱦᱟᱸ ᱫᱚ ᱱᱚᱶᱟ ᱨᱮ ᱖᱒᱕ ᱟᱞᱚᱢ ᱠᱚ ᱢᱮᱱᱟᱜ ᱛᱟᱭᱟ ᱥᱟᱶᱛᱮ ᱱᱚᱶᱟ ᱥᱤᱫᱷᱟᱱᱛ ᱥᱷᱤᱨᱚᱢᱟᱬᱤ ᱨᱮᱱᱟᱜ ᱢᱤᱫ ᱦᱟᱹᱴᱤᱧ ᱦᱚᱸ ᱠᱟᱱᱟ, ᱞᱤᱞᱟᱣᱚᱛᱤ ᱨᱮ ᱮᱞᱮᱞ ᱮᱞᱠᱷᱟ ᱨᱮᱱᱟ ᱣᱤᱣᱚᱪᱚᱱ ᱦᱩᱭ ᱟᱠᱟᱱᱟ᱾

ᱞᱤᱞᱟᱣᱚᱛᱤ ᱵᱷᱟᱥᱠᱟᱪᱟᱨᱭᱚ ᱨᱤᱱᱤᱡ ᱜᱤᱫᱟᱨ ᱟᱜ ᱧᱩᱛᱩᱢ ᱛᱟᱦᱮᱸᱜ ᱠᱟᱱ ᱛᱟᱭᱟ᱾ ᱱᱚᱶᱟ ᱜᱨᱚᱸᱛᱷ ᱨᱮ ᱯᱟᱴᱤ ᱮᱞᱠᱷᱟ (ᱮᱞᱮᱞ), ᱟᱞᱡᱮᱵᱨᱟ ᱟᱨ ᱡᱤᱭᱚᱢᱮᱴᱨᱤ ᱨᱮᱱᱟᱜ ᱠᱩᱠᱞᱤ ᱟᱨ ᱚᱱᱟ ᱨᱮᱱᱟᱜ ᱛᱮᱞᱟ ᱠᱚ ᱢᱮᱱᱟᱜ ᱟ᱾ ᱠᱩᱠᱞᱤ ᱨᱮᱫᱚ ᱧᱮᱞ ᱟᱠᱟᱱ ᱞᱤᱞᱟᱣᱚᱛᱤ ᱜᱮ ᱠᱚ ᱞᱟᱹᱭ ᱠᱟᱛᱮᱜ ᱟᱨ ᱞᱟᱹᱭ ᱞᱮᱠᱟᱛᱮ ᱠᱩᱞᱤ ᱦᱩᱭ ᱟᱠᱟᱱᱟ᱾ ᱡᱟᱦᱟᱸᱭ ᱮᱞᱮᱞᱤᱭᱟ ᱥᱟᱛᱟᱢᱟᱱᱟ (ᱯᱨᱚᱠᱟᱨᱟᱱ), ᱨᱮᱱᱟᱜ ᱜᱟᱞᱚᱪ ᱦᱩᱭ ᱠᱟᱛᱮᱜ ᱞᱤᱞᱟᱣᱚᱛᱤ ᱠᱷᱚᱱ ᱢᱤᱫ ᱠᱩᱠᱞᱤ ᱠᱩᱞᱤ ᱦᱩᱭ ᱟᱠᱟᱱᱟ᱾ ᱡᱮᱞᱮᱠ ᱨᱮ ᱞᱟᱹᱜᱤᱫ ᱟᱭᱢᱟ ᱥᱞᱚᱠ ᱧᱮᱞ ᱢᱮ-

ᱱᱚᱶᱟ ᱫᱚ ᱥᱟᱸᱠᱨᱤᱛ ᱛᱮᱠᱚ ᱚᱞ ᱟᱠᱟᱫ

ᱟᱭᱮ ᱵᱟᱞᱮ ᱞᱤᱞᱟᱣᱚᱛᱤ ᱢᱚᱛᱤᱢᱚᱛᱤ ᱵᱨᱤᱦᱤ ᱥᱟᱦᱤᱛᱟᱢᱟᱱ ᱫᱣᱤᱯᱚᱸᱪ ᱫᱣᱚᱛᱨᱤᱸᱥᱷᱚᱛᱨᱤᱛᱱᱚ ᱣᱚᱛᱣᱤᱭᱩᱟᱷᱟᱛᱟᱴᱟᱫᱚᱥᱷ ᱫᱚᱥᱷ᱾ ᱟᱷᱚᱛᱚᱯᱮᱛᱟ ᱱᱮᱛᱟᱱᱭᱩᱛᱣᱤᱭᱩᱛ ᱛᱟᱸᱥᱷᱪᱟᱯᱤ ᱣᱚᱫ ᱢᱮ ᱡᱩᱫᱤ ᱣᱭᱟᱠᱛᱮᱣᱭᱚ ᱣᱚᱠᱞᱚᱱᱡᱟᱨᱜᱮ ᱥᱤ ᱥᱩᱠᱞᱟ ᱿ ᱞᱤᱞᱟᱣᱚᱛᱤ, ᱯᱚᱨᱤᱠᱟᱨᱢᱟᱥᱴᱠ, ᱑᱓) (ᱟᱭᱮ ᱵᱟᱞᱮ ᱞᱤᱞᱟᱣᱚᱛᱤ! ᱡᱩᱫᱤ ᱥᱮᱞᱮᱫ ᱟᱨ ᱵᱷᱮᱜᱮᱫ ᱨᱮᱱᱟᱜ ᱠᱟᱹᱢᱤ ᱨᱮ ᱫᱚᱪᱷ ᱦᱚᱸ ᱦᱩᱭ ᱮᱱᱟ ᱠᱟᱷᱱ ( ᱡᱩᱫᱤ ᱣᱭᱟᱠᱛᱮᱣᱭᱚ ᱣᱚᱠᱞᱚᱱᱡᱟᱨᱜᱮ ᱥᱤ ᱠᱩᱥᱞᱟ (ᱱᱚᱶᱟ) ᱡᱟᱲᱟᱣ ᱛᱮ (ᱥᱩᱦᱤᱛᱟᱱ) ᱞᱟᱹᱭ ᱢᱮ ᱫᱣᱤ ᱯᱟᱸᱪ ᱫᱣᱚᱛᱨᱤᱸᱥᱷᱚᱛᱨᱤᱛᱱᱚ(᱓᱒), ᱛᱨᱤᱱᱣᱚᱛᱤᱥᱟᱛ(᱑᱙᱓), ᱟᱥᱴᱟᱫᱚᱥᱷ(᱑᱘), ᱫᱟᱥᱷ(᱑᱐) --- ᱱᱚᱶᱟ ᱨᱮ ᱑᱐᱐ ᱥᱮᱞᱮᱫ ᱦᱩᱭ (ᱥᱷᱟᱛᱚᱯᱮᱛᱟᱱ), ᱑᱐ ᱜᱮᱥᱟᱭ ᱠᱷᱚᱱ(ᱟᱭᱩᱛᱟᱛ) ᱱᱚᱶᱟ ᱨᱮ ᱵᱷᱮᱜᱮᱫ ᱢᱮ(ᱣᱭᱩᱛᱚᱢ) ᱛᱚ)᱾

ᱞᱤᱞᱟᱣᱚᱛᱤ ᱮᱞᱠᱷᱟ

ᱜᱮᱞ ᱫᱟᱥᱟᱠ ᱨᱮᱱᱟᱜ ᱠᱟᱛᱷᱟ ᱠᱟᱱᱟ, ᱫᱟᱪᱷᱤᱤ ᱛᱟᱦᱮᱸᱜ ᱠᱟᱱ ᱛᱟᱭᱟ᱾ ᱩᱱᱤ ᱜᱮ ᱥᱩᱢᱩᱝ ᱢᱤᱱ ᱥᱤᱧᱚᱛ ᱨᱮ ᱵᱷᱟᱥᱠᱟᱪᱟᱨᱭᱚ ᱱᱟᱢᱟᱠ ᱮᱞᱠᱷᱟ ᱟᱨ ᱡᱭᱚᱛᱤᱥ ᱥᱮᱪᱮᱫ ᱟᱱᱤᱡ ᱢᱤᱫ ᱟᱹᱰᱤ ᱢᱟᱨᱟᱝ ᱯᱚᱸᱰᱮᱛ ᱮ ᱛᱟᱦᱮᱸᱜ ᱠᱟᱱᱟ᱾ ᱩᱱᱤ‌ ᱨᱤᱱ ᱜᱤᱫᱨᱣᱟᱜ ᱧᱩᱛᱩᱢ ᱫᱚ ᱞᱤᱞᱟᱣᱚᱛᱤ ᱜᱤᱫᱟᱨ ᱮ ᱛᱟᱦᱮ ᱞᱮᱱ ᱛᱟᱭᱟᱭ᱾ ᱩᱱᱤ ᱫᱚ ᱡᱭᱚᱛᱤᱥ ᱨᱮᱱᱟᱜ ᱞᱮᱠᱷᱟ ᱠᱷᱚᱱ ᱵᱟᱰᱟᱭ ᱧᱟᱢ ᱠᱮᱫᱟᱭ ᱡᱮ ᱩᱱᱤ ᱫᱚ ᱵᱟᱯᱞᱟ ᱠᱷᱚᱱ ᱠᱤᱪᱷᱩ ᱫᱤᱱ ᱛᱟᱭᱱᱚᱢ ᱜᱮ ᱩᱱᱤ ᱫᱚᱭ ᱨᱟᱸᱰᱤ ᱦᱩᱭ ᱫᱟᱲᱮᱭᱟᱜ ᱟ᱾ ᱩᱱᱤ ᱟᱭᱢᱟ ᱜᱟᱱ ᱥᱚᱸᱪᱟᱣ ᱠᱟᱛᱮᱜ ᱚᱱᱟ ᱛᱟᱭᱚᱢ ᱚᱱᱠᱟᱱ ᱡᱤᱱᱤᱥ ᱮ ᱠᱷᱚᱡᱟᱣ ᱚᱰᱚᱜᱽ ᱠᱮᱫᱟ, ᱡᱟᱦᱟᱸ ᱡᱟᱦᱟᱸᱭ ᱵᱟᱯᱞᱟ ᱟᱠᱟᱱ ᱨᱮ ᱠᱩᱲᱤ ᱨᱟᱸᱰᱤ ᱵᱟᱭ ᱦᱩᱭ ᱫᱟᱲᱮᱭᱟᱜ ᱟ᱾ ᱵᱟᱯᱞᱟ ᱨᱮᱱᱟᱜ ᱥᱟᱹᱜᱩᱱ ᱫᱤᱱ ᱥᱮᱴᱮᱨ ᱦᱮᱡ ᱮᱱᱟ᱾ ᱫᱟᱜ ᱛᱷᱟᱨᱤ ᱠᱷᱚᱱ ᱜᱮ ᱚᱠᱛᱚ ᱫᱚ ᱧᱮᱞ ᱦᱩᱭᱩᱜ ᱠᱟᱱ ᱛᱟᱦᱮᱱᱟ᱾ ᱢᱤᱫ ᱢᱟᱨᱟᱝ ᱠᱷᱟᱸᱰᱟ ᱨᱮ ᱠᱟᱹᱴᱤᱡ ᱧᱚᱜ ᱵᱷᱩᱜ ᱠᱟᱛᱮᱜ ᱫᱟᱜ ᱨᱮᱱᱟᱜ ᱠᱟᱸᱰᱟᱣ ᱨᱮ ᱤᱠᱟ ᱦᱩᱭᱩᱜ ᱠᱟᱱ ᱛᱟᱦᱮᱱᱟ᱾

ᱠᱟᱸᱰᱟ ᱨᱮᱱᱟᱜ ᱫᱟᱜ ᱠᱷᱚᱱ ᱡᱚᱠᱷᱚᱱ ᱠᱟᱴᱚᱨᱟ ᱮᱢᱟᱱ ᱠᱚᱨᱮ ᱯᱮᱨᱮᱡᱽ ᱦᱩᱭᱩᱜ ᱠᱟᱱ ᱛᱟᱦᱮᱱ ᱟᱨ ᱫᱟᱜ ᱨᱮ ᱰᱩᱵᱩᱡ ᱦᱩᱭᱩᱜ ᱠᱟᱱ ᱛᱟᱦᱮᱱᱟ, ᱛᱚᱠᱷᱚᱱ ᱢᱤᱫ ᱜᱟᱹᱲᱤ ᱛᱟᱦᱮᱱ ᱠᱟᱱ ᱛᱟᱦᱮᱱᱟ᱾ ᱵᱩᱫᱷᱟᱛᱟ ᱨᱮᱱᱟᱜ ᱜᱮ ᱥᱚᱪᱟ ᱛᱟᱦᱮᱱ ᱠᱟᱱ ᱛᱟᱦᱮᱱᱟ᱾ ᱞᱤᱞᱟᱣᱚᱛᱤ ᱥᱟᱡ ᱥᱤᱸᱜᱟᱨ ᱞᱟᱹᱜᱤᱫ ᱥᱟᱡᱟᱣ ᱠᱟᱛᱮᱜ ᱫᱩᱲᱩᱵ ᱟᱠᱟᱱ ᱛᱟᱦᱮᱸᱜ᱾ ᱥᱟᱱᱟᱢ ᱦᱚᱲ ᱜᱮ ᱩᱱ ᱚᱠᱛᱮ ᱥᱚᱨᱮᱥ ᱠᱟᱨᱚᱱ ᱨᱮᱱᱟᱜ ᱠᱟᱹᱢᱤ ᱛᱟᱸᱜᱤ ᱨᱚᱠᱚ ᱛᱟᱦᱮᱱ ᱠᱟᱱ ᱛᱟᱦᱮᱸᱜ ᱡᱮ ᱢᱤᱫ ᱢᱚᱛᱤ ᱞᱤᱞᱟᱣᱚᱛᱤ ᱭᱟᱜ ᱦᱚᱨᱚᱜ ᱠᱷᱚᱱ ᱨᱟᱹᱯᱩᱫ ᱧᱩᱨ ᱛᱷᱟᱹᱨᱤ ᱨᱮ ᱧᱩᱨ ᱮᱱᱟ ᱟᱨ ᱚᱠᱚᱭ ᱦᱚᱸ ᱵᱟᱝ ᱜᱮ ᱠᱚ ᱵᱟᱰᱟᱭ ᱫᱟᱲᱮ ᱟᱫᱟ ᱟᱨ ᱥᱩᱨᱟᱸᱠᱷ ᱵᱚᱸᱫᱚ ᱮᱱᱟ᱾ ᱥᱟᱹᱜᱩᱱ ᱠᱟᱹᱢᱤ ᱨᱮᱱᱟᱜ ᱞᱟᱜᱚᱱ ᱵᱤᱛᱟᱣ ᱤᱫᱤ ᱮᱱᱟ ᱟᱨ ᱚᱠᱚᱭ ᱦᱚᱸ ᱵᱟᱝ ᱠᱚ ᱵᱟᱰᱟᱭ ᱫᱟᱲᱮ ᱟᱫᱟ᱾ ᱵᱟᱯᱞᱟ ᱫᱚᱥᱟᱨ ᱞᱟᱜᱚᱱ ᱨᱮ ᱜᱮ ᱦᱩᱭ ᱮᱱᱟ, ᱞᱤᱞᱟᱣᱚᱛᱤ ᱮ ᱨᱟᱸᱰᱤ ᱮᱱᱟ, ᱟᱡ ᱵᱟᱵᱟ ᱟᱨ ᱜᱤᱫᱟᱨᱟᱜ ᱫᱷᱚᱨᱭᱚ ᱨᱮᱱᱟᱜ ᱥᱟᱹᱜᱟᱹᱭ ᱨᱟᱹᱯᱩᱫ ᱮᱱᱟ᱾ ᱢᱟᱹᱭᱟᱹᱜ ᱥᱚᱠᱛᱚ ᱫᱩᱠᱷ ᱥᱟᱦᱟᱭ ᱠᱷᱟᱹᱛᱤᱨ ᱛᱮ ᱵᱷᱟᱥᱠᱟᱪᱟᱨᱭᱚ ᱫᱚ ᱩᱱᱤ ᱮᱞᱠᱷᱟ ᱯᱟᱲᱷᱟᱣ ᱮ ᱮᱦᱚᱵ ᱮᱱᱟ᱾ ᱩᱱᱤ ᱦᱚᱸ ᱮᱞᱠᱷᱟ ᱨᱮᱱᱟᱜ ᱯᱟᱲᱷᱟᱣ ᱨᱮ ᱜᱮ ᱥᱟᱨᱮᱡ ᱡᱤᱵᱚᱱ ᱨᱮᱱᱟᱜ ᱟᱹᱰᱤ ᱮ ᱫᱚᱨᱠᱟᱨ ᱟᱱᱟᱜ ᱮ ᱟᱹᱭᱠᱟᱹᱣ ᱠᱮᱫᱟ᱾ ᱠᱤᱪᱷᱩ ᱫᱤᱱ ᱛᱟᱭᱱᱚᱢ ᱜᱮ ᱩᱱᱤ ᱫᱚ ᱟᱭᱢᱟ ᱜᱟᱱ ᱥᱟᱠᱡᱮᱠᱴ‌ ᱨᱮ ᱢᱟᱨᱟᱝ ᱯᱚᱸᱰᱮᱛ ᱮ ᱦᱩᱭ ᱮᱱᱟ, ᱟᱞᱡᱮᱵᱨᱟ, ᱯᱟᱴᱤ ᱮᱞᱠᱷᱟ ᱟᱨ ᱡᱭᱚᱛᱤᱥ ᱥᱟᱵᱡᱮᱠᱴ ᱨᱮᱱᱟᱜ ᱢᱤᱫ ᱜᱨᱚᱸᱛᱷ 'ᱥᱤᱫᱷᱸᱛᱥᱷᱤᱨᱚᱢᱚᱬᱤ' ᱵᱷᱟᱥᱠᱟᱪᱟᱨᱭᱚ ᱫᱚᱭ ᱵᱟᱱᱟᱣ ᱟᱠᱟᱫᱟ᱾

ᱵᱟᱦᱨᱮ ᱡᱚᱱᱚᱲ

• Bhaskaracharya's Lilavathi - Book Review
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• Khagol Mandal