ⵊⵉⵔⵓⵍⴰⵎⵓ ⴽⴰⵔⴷⴰⵏⵓ

ⵊⵉⵔⵓⵍⴰⵎⵓ ⴽⴰⵔⴷⴰⵏⵓ (ⵙ ⵜⵟⴰⵍⵢⴰⵏⵉⵜ: Gerolamo Cardano (ⵏⵖ Gironamo/Geronimo Cardano); ⵙ ⵜⵍⴰⵜⵉⵏⵜ: Hieronymus Cardamus) (24 ⵛⵓⵜⴰⵏⴱⵉⵔ 1501 - 21 ⵛⵓⵜⴰⵏⴱⵉⵔ 1576) ⵉⴽⴽⴰ ⵜ ⵏⵏ ⵉⴳⴰ ⵢⴰⵏ ⵓⴳⵜⵓⵙⵏⴰ ⴰⵡⵟⴰⵍⵢⴰⵏ, ⵓⵔ ⴰⵙ ⵢⵓⴼⵉ ⴰⴷ ⵢⴰⴷⴼ ⵖⵔ ⵜⵙⴷⴰⵡⵉⵜ ⵏ ⵉⵎⵊⵊⴰⵢⵏ ⴰⵛⴽⵓ ⵉⵍⵓⵍ ⴷ ⴰⵛⵏⵜⵉ, ⵎⴰⵛⴰ ⵡⴰⵅⵅⴰ ⵎⴽⴰⵏⵏ ⵉⵎⵓⵔⵙ ⵙⵓⵍ ⴳ ⵓⴱⵔⵉⴷ ⵏⵏⵙ ⴰⵎ ⵓⵎⵊⵊⴰⵢ, ⵢⵓⵔⴰ ⵖⴼ ⵜⵓⵙⵙⵏⴰ ⵓⴳⴳⴰⵔ ⵏ 200 ⵏ ⵜⵡⵓⵔⵉⵡⵉⵏ.

ⵉⵊⴳⵓⴳⵍ ⵙ ⵜⵙⵓⴳⴰⵔ ⵏⵏⵙ ⴷ ⵓⵢⵏⵏⴰ ⵙ ⵉⴽⴽⴰ ⴰⵔ ⵉⵜⵜⵔⴰⵔⴰ ⵜⴰⵢⵏⵉⵜ ⵖⴼ ⵎⵏⵏⴰⵡ ⵢⵉⴳⵔⴰⵏ; ⵣⵓⵏ ⴷ ⵜⵓⵙⵏⴰⴽⵜ, ⵜⴰⵙⵏⵉⵊⵊⵉⵜ, ⵜⴰⵙⵏⵓⴷⵔⵜ, ⵜⴰⵙⵏⴳⴰⵎⴰ, ⵜⴰⴽⵔⵓⵔⴰ, ⵜⴰⵙⵏⵉⵜⵔⵉⵜ, ⵜⴰⴼⵍⵙⴰⴼⵜ... ⵉⵜⵜⵢⴰⵡⵙⵙⴰⵏ ⵙ ⵓⵎⴰⵜⴰ ⵎⴰⵙ ⵜⵜ ⵏⵏ ⵉⴽⴽⴰ ⵉⴳⴰ ⵢⴰⵏ ⵙⴳ ⵉⵎⵓⵙⵏⴰⴽⵏ ⴰⴽⴽⵯ ⵏⵏⴰ ⵎⵉ ⵜⵅⴰⵜⵔ ⵜⵣⵔⵉⵔⵜ ⴳ ⵜⵍⵙⵍⴰⵍⵉⵜ, ⵢⴰⵏ ⵙⴳ ⵡⵓⴷⵎⴰⵡⵏ ⵉⵣⴰⵍⴰⵏⵏ ⴳ ⵓⵙⵙⵔⵙⵍ ⵏ "probability" ⴷ ⵓⵎⵙⵙⵉⴷⴼ ⴰⵎⵣⵡⴰⵔⵓ ⵏ "coefficients binomiaux" ⴷ "theorem binomial" ⵖⵔ ⵓⵎⴰⴹⴰⵍ ⴰⵡⵜⴰⵔⴰⵎ, ⴷ ⵙⴳ ⵖⵓⵔⵙ ⴰⴷ ⴷ ⵉⴽⴽⴰ ⵓⴳⵍⴰⵎ ⴰⵎⵣⵡⴰⵔⵓ ⵏ ⵜⵉⴼⵡⵉⴷ (typhoid). ⵉⵙⵏⵓⵍⴼⴰ ⴷ ⵎⵏⵏⴰⵡⵜ ⵜⵖⴰⵡⵙⵉⵡⵉⵏ, ⴰⴷ ⴳⵉⵙⵏⵜ ⵏⴰⴼ ⴽⴰⵔⴷⴰⵏ ⴳⵔⵉⵍⵍ (Cardan grill), ⵜⴰⵇⵛⵓⵛⵜ ⵏ "Pagenaudier" ⴷ ⵓⵙⵔⴳⵍ ⴱⵓ ⵜⵓⴷⴷⵙⴰ. ⵉⵙⴽⵔ ⴰⵡⴷ ⴽⵔⴰ ⵏ ⵜⵡⴰⴼⵓⵜⵉⵏ ⴳ ⵡⴰⵍⵊⵉⴱⵔ, ⵉⵙⵙⵓⵎⵔ ⴷ ⵉⵜⵙⵏⵜ ⵜⵖⴰⵔⴰⵙⵉⵏ ⵏⵏⴰ ⵙ ⴼⵔⵔⵓⵏⵜ ⵜⴰⴳⴷⵉⵡⵉⵏ "ⴽⵡⴰⵔⵜⵉⴽ" ⴷ "ⴽⵓⴱⵉⴽ".

ⵉⴽⴽⴰ ⵜ ⵏⵏ ⴽⴰⵔⴷⴰⵏⵓ ⴳ ⵓⵎⴰⵜⴰ ⵏ ⵜⴽⴽⴰⵍ ⴰⵔ ⵉⵜⵜⵇⵎⵎⴰⵔ ⵙ ⵡⴰⵔ ⵜⵏⴱⴱⴰⴹⵜ, ⵢⴰⵏ ⴳ ⵉⴷⵍⵉⵙⵏ ⵏⵏⵙ, "Leber de lodu Aleae" (ⴰⴷⵍⵉⵙ ⵖⴼ ⵡⵓⵔⴰⵔⵏ ⵏ ⵡⴰⵏⵏⴰⵣ), ⴷⴰ ⴳⵉⵙ ⵉⵙⵙⵉⴷⵉⴼ ⵜⴰⵣⵔⴰⵡⵜ ⵜⴰⵏⴳⵔⴰⵡⴰⵏⵜ ⴰⴽⴽⵯ ⵉⵣⵡⴰⵔⵏ ⵏ "ⴱⵔⵓⴱⴰⴱⵉⵍⵉⵜⵉ" ⴷ ⵢⴰⵏ ⵓⴳⵣⵣⵓⵎ ⵉⵇⵇⵏⵏ ⵙ ⵓⵖⵏⴷⴼ ⵓⵍⴰ ⵏⵜⵜⴰ. ⵢⵓⵔⴰ ⵜ ⴳ ⵡⴰⵜⵜⴰⵢⵏ ⵏ 1564, ⵎⴰⵛ ⵉⵜⵜⵓⴼⵙⴰⵔ ⵜⵉⴽⴽⵍⵜ ⵉⵣⵡⴰⵔⵏ ⴹⴰⵕⴰⵜ ⵏ ⵜⵎⵜⵜⴰⵏⵜ ⵏⵏⵙ ⴳ 1663.

ⵜⵉⵣⵡⵉⵔⵉ ⵏ ⵜⵓⴷⵔⵜ ⴷ ⵓⵙⴳⵎⵉ
ⵉⵍⵓⵍ ⴷ ⴼ ⴱⴰⴼⵢⴰ, ⵍⵓⵎⴱⴰⵔⴷⵢⴰ, ⴷ ⵉⵛⵏⵜⵉ ⵏ ⴼⴰⵣⵢⵓ ⴽⴰⵔⴷⴰⵏⵓ. ⵉⴳⴰ ⴰⵏⵎⴼⴽⵉ ⴳ ⵜⵓⵙⵏⴰⴽⵜ, ⴰⵏⵣⵣⴰⵔⴼⵓ, ⵎⵙⵜⴰⵏ, ⴷ ⵓⵎⴷⴷⴰⴽⵯⵍ ⴰⵎⵢⴰⵥ ⵏ ⵍⵢⵓⵏⴰⵔⴷⵓ ⴷⴰ ⴼⵉⵏⵜⵛⵉ. ⵢⵓⵔⴰ ⴽⴰⵔⴷⴰⵏⵓ ⴳ ⵜⵙⴽⵏⵓⴷⵔⵜ ⵏⵏⵙ ⵜⴰⵏⵉⵎⴰⵏⵜ ⵖⴼ ⵢⵉⵎⵎⴰⵙ "ⵛⵢⴰⵔⴰ ⵎⵉⵛⵔⵉ", ⵎⴰⵙ ⵜⵙⵙⵎⵔⵙ ⵎⵏⵏⴰⵡ ⵉⵙⴰⴼⴰⵔⵏ ⵏ ⵓⵖⵔⴰⵢ ⴱⴰⵛ ⴰⴷ ⵜ ⵜⵙⴹⵕ; «ⵅⴼ ⵓⵢⵏⵏⴰ ⵙ ⵉⵢⵉ ⵜⵓⵍⵙ ⵉⵎⵎⴰ, ⵍⴷⵉⵏ ⵉⵢⵉ ⴷ ⴳ ⵓⴷⵉⵙ ⵏⵏⵙ ⵙ ⴱⵣⵣⵉⵣⵣ, ⵄⵍⴰⵢⵏ ⴰⴷ ⵎⵎⵜⵖ», ⴷⴰⵜ ⵏ ⵜⵍⴰⵍⵉⵜ ⵏⵏⵙ ⵙ ⵢⴰⵜ ⵜⵉⵣⵉ ⵉⴷⵔⵓⵙⵏ, ⵉⵍⵍⴰ ⵖⴼ ⵉⵎⵎⴰⵙ ⴰⴷ ⵜⵎⵎⵓⵜⵉ ⵙⴳ ⵎⵉⵍⴰⵏ ⵖⵔ ⴱⴰⴼⵢⴰ ⴰⴼⴰⴷ ⴰⴷ ⵜⵔⵡⵍ ⵉ ⵓⴱⴰⵢⵢⵓⵕ "ⵟⵟⴰⵄⵓⵏ", ⴰⵛⴽⵓ ⵏⵜⵜⴰ ⴰ ⵙ ⵎⵎⵓⵜⵏ ⴽⵕⴰⴹ ⵜⴰⵔⵡⴰ ⵏⵏⵙ ⵢⴰⴹⵏⵉⵏ.ⵊⵉⵔⵓⵍⴰⵎⵓ ⴽⴰⵔⴷⴰⵏⵓ ⴳ ⵡⵉⴽⵉⴱⵉⴷⵢⴰ ⵙ ⵜⵏⴳⵍⵉⵣⵜ, 13 ⵖⵓⵛⵜ 2021.

ⵢⵓⴷⴳⴼ ⴽⴰⵔⴷⴰⵏⵓ ⴳ ⵓⵙⴳⴳⵯⴰⵙ 1520 ⵖⵔ ⵜⵙⴷⴰⵡⵉⵜ ⵏ ⴱⴰⴼⵢⴰ ⵎⴳⴰⵍ ⵜⵉⵔⴰⵜ ⵏ ⴱⴰⴱⴰⵙ ⵏⵏⴰ ⴰⵙ ⵉⵔⴰⵏ ⵜⵉⵖⵓⵔⵉⵡⵉⵏ ⵏ ⵓⵣⵔⴼ. ⴷⴼⴼⵉⵔ ⵢⴰⵜ ⵜⵎⵥⵉ ⵏⵏⴰ ⵎⵉ ⵉⵅⵓⴱ ⵡⴰⴹⵓ, ⵉⴽⵜⵓⵔⵏ ⵙ ⵜⵎⵓⴹⴰⵏ ⵓⵔ ⵎⵉⴷⵏⵉⵏ, ⴷ ⵓⵙⴳⵎⵉ ⵉⵎⵔⴰⵏ ⵏ ⴱⵓ ⵜⵖⵏⵏⴰⵏⵜ ⵉⴳⴰⵏ ⴱⴰⴱⴰⵙ, ⵢⵓⴼⴰ ⵏⵏ ⵊⵉⵔⵓⵍⴰⵏⵓ ⵉⵅⴼ ⵏⵏⵙ ⴳ ⵜⴰⵢⵔⵉ ⵏ ⵜⴼⵍⵙⴰⴼⵜ ⴷ ⵜⵓⵙⵙⵏⴰ. ⴰⵎⵎⴰⵙ ⵏ ⵓⵎⴳⴰⵔⵓ ⴰⵡⵟⴰⵍⵢⴰⵏ ⵏ 1521-1526, ⵙⴱⵣⵣⵉⵣⵏ ⵉⴷⵓⴱⴰ ⵏ ⴱⴰⴼⵢⴰ ⵖⴼ ⵜⵙⴷⴰⵡⵉⵜ ⴰⴷ ⵜⵔⴳⵍ ⵜⵉⴼⵍⵉⵡⵉⵏ ⵏⵏⵙ ⴳ ⵓⵙⴳⴳⵯⴰⵙ 1524. ⵉⵙⵎⴷ ⴽⴰⵔⴷⴰⵏⵓ ⵜⵉⵖⵔⵉ ⵏⵏⵙ ⵉⵍⵎⵎⴰ ⴳ ⵜⵙⴷⴰⵡⵉⵜ ⵏ ⴱⴰⴷⵡⴰ, ⵢⵓⵎⵥ ⵜⴰⴷⵓⴽⵜⵓⵔⴰⵜ ⵏⵏⵙ ⴳ ⵜⵙⵏⵉⵊⵊⵉⵜ ⴰⵙⴳⴳⵯⴰⵙ ⵏ 1525. ⵓⵔ ⵜ ⵜⵓⵊⵊⵉ ⵜⵎⴰⵎⴽⵜ ⵏⵏⵙ ⵜⴰⵎⵏⴰⵍⴰⵏⵜ ⴰⴷ ⴱⴰⵀⵔⴰ ⵉⵙⴽⵔ ⵉⵎⴷⴷⵓⴽⴽⴰⵍ, ⴷ ⴰⵡⴷ ⴰⵙⵉⴳⴳⵍ ⵏ ⵜⵡⵓⵔⵉ; ⵉⵎⵔⵔⵜ ⴷⵉⴳⵙ ⴷⴼⴼⵉⵔ ⵎⴰⵢⴷ ⵉⵙⵎⴷ ⵜⵉⵖⵓⵔⵉⵡⵉⵏ ⵏⵏⵙ. ⴳ ⵓⵙⴳⴳⵯⴰⵙ 1525, ⵢⵓⵣⵏ ⴽⴰⵔⴷⴰⵏⵓ ⵜⵓⵜⵜⵔⵉⵡⵉⵏ ⵏⵏⵙ ⵏ ⵡⴰⴷⴰⴼ ⵉ ⵜⵖⵉⵡⴰⵏⵜ ⵏ ⵉⵎⵊⵊⴰⵢⵏ ⴳ ⵎⵉⵍⴰⵏ ⵎⵏⵏⴰⵡⵜ ⵜⵉⴽⴽⴰⵍ, ⵎⴰⴽⴰ ⵓⵔ ⵜ ⴷⴳⴳⵉⵏ ⵙ ⵓⵙⵔⴰⴳ ⵏ ⵡⴰⴷⴷⵓⵔ ⵏⵏⵙ ⵉⵅⵛⵏⵏ, ⴷ ⵜⵍⴰⵍⵉⵜ ⵏⵏⵙ ⵜⴰⵔⵓⵣⵔⵉⴼⵜ. ⵎⵇⵇⴰⵔ ⵎⴽⴰⵏⵏ, ⴰⵔ ⴷⵉⴷⵙ ⵜⵜⵏⵢⵉⵍⴽⵉⵎⵏ ⵉⵙⵍⵎⴰⴷⵏ ⴷ ⵉⵎⵣⵔⴰⵡⵏ ⵙⴳ ⵜⵖⵉⵡⴰⵏⵜ ⵏ ⵉⵎⵊⵊⴰⵢⵏ ⴰⵛⴽⵓ ⵉⴳⴰ ⵉⵎⵉⵢⵄⵉⵙ.
ⵜⴰⵡⵓⵔⵉ ⵏⵏⵙ ⴳ ⵜⵙⵏⵉⵊⵊⵉⵜ
ⵉⵔⴰ ⴰⴷⵍⵍⵉ ⴽⴰⵔⴷⴰⵏⵓ ⴰⴷ ⵉⴳ ⴰⵎⵊⵊⴰⵢ ⴳ ⴽⵔⴰ ⵏ ⵜⵎⴷⵉⵏⵜ ⵉⵎⵇⵇⵓⵔⵏ ⵉⴳⴰⵏ ⵜⴰⵏⵙⴱⴰⵖⵓⵔⵜ ⵣⵓⵏ ⴷ ⵎⵉⵍⴰⵏ, ⵎⴰⵛⵛ ⵓⵔ ⴰⵙ ⵜⴻⵜⵜⵓⴼⴽⴰ ⵜⵓⵔⴰⴳⵜ ⵏ ⵜⵡⵓⵔⵉ, ⴰⵢⴰⵏⵏ ⴰ ⵅⴼ ⵉⵖⵜⵙ ⴰⴷ ⵉⵣⴷⵖ ⴳ ⵙⴰⴽⵓⵍⵓⴳⵓ, ⵉⴳ ⴷⵉⴳⵙ ⴰⵎⵊⵊⴰⵢ ⵎⵉⵏ ⵜⵓⵔⴰⴳⵜ, ⵢⴰⵡⵍ ⴷⵉⴳⵙ "ⵍⵓⵙⵢⴰ ⴱⴰⵏⴷⵉⵔⵉⵏⵉ" ⴳ ⵓⵙⴳⴳⵯⴰⵙ 1531, ⵢⴰⵔⵓ ⴰⴽⵉⴷⵙ ⴽⵕⴰⴹ ⵜⴰⵔⵡⴰ ⴷⴰⵜ ⴰⴷ ⵜⵎⵎⵜ ⴳ ⵓⵙⴳⴳⵯⴰⵙ 1546, ⵊⵢⵓⴼⴰⵏⵉ ⴱⴰⵜⵉⵙⵜⴰ (1543), ⵛⵢⴰⵔⴰ (1537) ⴷ ⴰⵍⴷⵓ ⵓⵔⴱⴰⵏⵉ (1543). ⵉⵏⵏⴰ ⴽⴰⵔⴷⴰⵏⵓ ⵎⴰⵙ ⵉⴷⴷⵔ ⵜⵓⵎⵔⵜ ⵉⴳⴳⵓⵜⵏ ⴳ ⵡⵓⵙⵙⴰⵏ ⵏⵏⴰ ⵉⵣⵣⵔⵉ ⴳ ⵙⴰⴽⵓⵍⵓⴳⵓ.

ⵢⵓⵎⵥ ⴽⴰⵔⴷⴰⵏⵓ ⵙ ⵜⵡⵉⵙⵉ ⵏ ⵉⵜⵙⵏ ⵉⵔⵉⵙⵜⵓⵇⵔⴰⵟⵉⵢⵏ ⵢⴰⵜ ⵜⵙⵖⵏⵜ ⴳ ⵓⵙⵍⵎⴷ ⵏ ⵜⵓⵙⵏⴰⴽⵜ ⴰⵎⵎⴰⵙ ⵏ ⵎⵉⵍⴰⵏ. ⴷⴼⴼⵉⵔ ⵎⴰⴷ ⵢⵓⵎⵥ ⵜⵓⵔⴰⴳⵜ ⵏⵏⵙ, ⵉⵙⵡⵓⵔⵉ ⴳ ⵜⵓⵙⵏⴰⴽⵜ ⴷ ⵜⵙⵏⵉⵊⵊⵉⵜ ⵙ ⵢⴰⵜ ⵜⵉⴽⴽⵍⵜ, ⵊⵊⵉⵏ ⵣⴼ ⵓⴼⵓⵙ ⵏⵏⵙ ⵜⵓⴳⵜⵜ ⵏ ⵉⵏⵎⵖⵓⵔⵏ ⵓⴹⵏⵏⵉⵏ, ⵉⴳ ⵉⵍⵎⵎⴰ, ⵙ ⵓⵙⵔⴰⴳ ⴰⴷ, ⵢⴰⵏ ⵙⴳ ⵉⴷⵓⴽⵜⵓⵔⵏ ⵏⵏⴰ ⵙ ⴷⴰ ⵜⵜⵍⵍⵉⵏ ⵎⵉⴷⴷⵏ ⵏ ⵎⵉⵍⴰⵏ, ⵉⵙ ⴰⴽⴽⵯ ⵢⵓⴼⴰ ⴳ ⵓⵙⴳⴳⵯⴰⵙ 1536 ⴰⴷ ⵉⴼⵍ ⵜⴰⵡⵓⵔⵉ ⵏⵏⵙ ⵏ ⵓⵙⵙⵍⵎⴷ, ⵎⵇⵇⴰⵔ ⵊⵊⵓⵏ ⵓⵔ ⵉⵙⴱⵉⴷⴷ ⴰⵏⵏⵣⴳⵎ ⵏⵏⵙ ⵙ ⵜⵓⵙⵏⴰⴽⵜ, ⵉⵜⵜⵓⵙⵙⴰⵏ ⴽⵉⴳⴰⵏ ⴳ ⵢⵉⴳⵔ ⵏ ⵜⵙⵏⵉⵊⵊⵉⵜ, ⵓⵔⵎⵏ ⴰⴽⴽⵯ ⴽⵔⴰ ⵏ ⵉⵔⵉⵙⵜⵓⵇⵔⴰⵟⵉⵢⵏ ⴰⴷ ⵜ ⵙⵙⴼⵓⵖⵏ ⴳ ⵎⵉⵍⴰⵏ. ⵉⵏⵏⴰ ⴽⴰⵔⴷⴰⵏⵓ ⴹⴰⵕⴰⵜ ⵏ ⵢⴰⵜ ⵜⵉⵣⵉ ⵎⴰⵙ ⵢⵓⴳⵉ ⴳ ⵓⵣⵎⵣ ⴰⵏⵏ ⵜⵓⵜⵜⵔⵉⵡⵉⵏ ⵏ ⵉⴳⵍⵍⵉⴷⵏ ⵏ ⴷⴰⵏⵎⴰⵔⴽ ⴷ ⴼⵕⴰⵏⵚⴰ, ⴷ ⵓⵍⴰ ⵜⴰⴳⵍⵍⵉⴷⵜ ⵏ ⵙⴽⵓⵜⵍⴰⵏⴷⴰ.

ⵜⵓⵙⵏⴰⴽⵜ
ⵉⵜⵜⵢⴰⵡⵙⵙⴰⵏ ⴽⴰⵔⴷⴰⵏⵓ ⵙ ⵎⴰⵙ ⵉⴳⴰ ⴰⵎⵓⵙⵏⴰⴽ ⵉⵣⵡⴰⵔⵏ ⵙ ⵓⵙⵙⵎⵔⵙ ⴰⵏⴳⵔⴰⵡⴰⵏ ⵏ ⵡⵓⵟⵟⵓⵏⵏ ⵓⵣⴷⵉⵔⵏ, ⵉⴼⵙⵔ ⴷ ⵙ ⵓⵣⴷⴰⵢ ⴳ ⵓⴷⵍⵉⵙ ⵏⵏⵙ ⵏ 1545 ⴰⵔⵙ ⵎⴰⴳⵏⴰ, ⴰⴼⵙⵙⴰⵢ ⵏ ⵙⵉⴱⵢⵓⵏⵉ ⴷⵉⵍ ⴼⵉⵔⵔⵓ ⵉ ⵜⴳⴷⴰ "ⴽⵓⴱⵉⴽ" ⴷ ⵓⴼⵙⵙⴰⵢ ⵏ ⵓⵏⵍⵎⴰⴷ ⵏⵏⵙ ⵍⵓⴷⵓⴼⵉⴽⵓ ⴼⵉⵔⵔⴰⵔⵉ ⵉ ⵜⴳⴷⴰ "ⴽⵡⴰⵔⵜⵉⴽ". ⵉⵍⴽⵎ ⵜ ⵉⴷ ⵓⴼⵙⵙⴰⵢ ⵏ ⵢⴰⵜ ⵜⵎⴰⵛⴽⵓⵜ ⵉⵥⵍⵉⵏ ⵏ ⵜⴳⴷⴰ "ⴽⵓⴱⵉⴽ" {x^{3}+ax+=0} ⵙⴳ ⵖⵓⵔⵔ ⵏⵉⴽⵓⵍⵓ ⴼⵓⵏⵜⴰⵏⴰ ⵜⴰⵔⵜⴰⴳⵍⵢⴰ ⴳ ⵓⵙⴳⴳⵯⴰⵙ 1539, (ⵉⵏⵏⴰ ⵉⴳⴳⵓⵍⵍ ⴰⵙ ⴽⴰⵔⴷⴰⵏⵓ ⵓⵔ ⵉⵎⵎⴰⵍⴰ ⴰⴼⵙⵙⴰⵢ ⵉ ⴰⵡⴷ ⵢⴰⵏ, ⵉⵙⵏⴽⵔ ⴷⵉⵙ ⵙ ⵜⵎⵏⵜⵉⵍⵜ ⴰⴷ ⵢⴰⵏ ⵓⵎⵙⴳⴷⴰⵍ ⵉⵖⵣⵣⵉⴼⵏ ⵙ ⵜⵎⴷⵢⴰⵣⵜ) ⵎⴰⵛⴰ ⵉⵣⵡⴰⵔ ⵓⴼⵙⵙⴰⵢ ⵏ ⴼⵉⵔⵔⵓ ⵡⵉⵏ ⴼⵓⵏⵜⴰⵏⴰ. ⵉⴷⴳⴳⴰ ⴳ ⵓⴼⴰⵙⵔ ⵏⵏⵙ ⵙ ⵓⵢⵏⵏⴰ ⵎⵉ ⵇⵇⴰⵔⵏ ⵖⵉⵍⴰⴷ ⵓⵟⵟⵓⵏⵏ ⵉⵙⵓⴳⵏⴰⵏⵏ, ⵡⴰⵅⵅⴰ ⴰⴷⵍⵍⵉ ⵓⵔ ⵉⴳⵣⵉ ⵉⵎⵏⵣⴰⵢⵏ ⵏⵏⵙⵏ ⵏⵏⴰ ⴷ ⵉⴳⵍⵎ ⴳ ⵓⵣⵎⵣ ⵏⵏⵙ ⴰⵡⵟⴰⵍⵢⴰⵏ ⵔⴰⴼⴰⵢⵉⵍ ⴱⵓⵎⴱⵉⵎⵉⵍⵍⵉ ⵜⵉⴽⴽⵍⵜ ⵜⴰⵎⵣⵡⴰⵔⵓⵜ. ⵉⵙⵙⵉⴷⴼ "Binomial coefficients" ⴷ "Binomial theorem" ⴳ ⵓⴷⵍⵉⵙ ⵏⵏⵙ "Opum Novum de Ptoportionibus".

ⵉⵙⴳⴳⵯⴰⵙⵏ ⵉⵏⴳⴳⵓⵔⴰ ⴷ ⵜⵎⵜⵜⴰⵏⵜ
ⵙⵉⵏ ⴳ ⵜⴰⵔⵡⴰ ⵏ ⴽⴰⵔⴷⴰⵏⵓ -ⴳⵉⵓⴼⴰⵏⵏⵉ ⴱⴰⵜⵜⵉⵙⵜⴰ ⴷ ⴰⵍⴷⵓ ⵓⵔⴱⴰⵏⵓ- ⴳⵓⵍⴰⵏ ⵏⵏ ⴳⴰⵔ ⵜⴳⵉⵔⵉⵡⵉⵏ. ⵊⵢⵓⵓⴼⴰⵏⵏⵉ ⴱⴰⵜⵉⵙⵜⴰ, ⴰⵎⵏⵣⵓ ⵏⵏⵙ, ⵉⵜⵜⵡⴰⵣⵔⴼ ⵙ ⵜⵓⴱⴱⵢⴰ ⵏ ⵢⵉⵅⴼ ⴳ 1560, ⴰⵛⴽⵓ ⵉⵏⵖⴰ ⵜⴰⵎⵖⴰⵔⵜ ⵏⵏⵙ ⵙ ⵉⵔⵉⵏ ⴹⴰⵔⵜ ⵎⴰⴷ ⵢⵓⴼⴰ ⵜⴰⵔⵡⴰ ⵏⵏⵙ ⵙ ⴽⵕⴰⴹ ⵓⵔ ⴰⴽⴽⵯ ⴳⵉⵏ ⵡⵉⵏⵏⵙ. ⴰⵍⴷⵓ ⵓⵔⴱⴰⵏⵓ ⵉⵜⵜⵓⴱⵍⴰⵏ ⵙ ⵜⵇⵎⵎⴰⵕⵜ, ⵉⴳⴷⵍ ⴼⵍⵍⴰⵙ ⴱⴰⴱⴰⵙ ⵜⴰⴽⵓⵙⵉ ⴳ ⵓⵙⴳⴳⵯⴰⵙ 1569 ⴰⵛⴽⵓ ⵉⴽⴽⴰ ⵜⵜ ⵏⵏ ⴷⴰ ⴰⵙ ⵉⵜⵜⴰⴽⵯⵔ ⵉⵇⴰⵔⵉⴹⵏ ⵏⵏⵙ.

ⵉⵎⵎⵓⵜⵉ ⴽⴰⵔⴷⴰⵏⵓ ⵙⴳ ⴱⴰⴼⵢⴰ ⵖⵔ ⴱⵓⵍⵓⵏⵢ, ⵙⴳ ⵢⴰⵜ ⵜⵙⴳⴰ; ⴰⵛⴽⵓ ⵉⴼⵍⵙ ⵙ ⵎⴰⵙ ⴷ ⵉⴽⴽⴰ ⵓⵖⵜⴰⵙ ⵏ "ⵉⵄⴷⴰⵎ" ⵏ ⵎⴻⵎⵎⵉⵙ ⵊⵢⵓⴼⴰⵏⵉ ⵜⴰⵣⵔⵉⵔⵜ ⵏ ⵜⴰⵥⵉⵜ ⵏⵏⵙ ⴷ ⵜⵎⵔⵙⵍⵜ ⵜⴰⴽⴰⴷⵉⵎⵉⴽⵜ ⵏ ⴱⴰⴼⵢⴰ, ⴷ ⵜⵓⵙⵎⵉⵏ ⵏⵏⴰ ⴰⵙ ⵓⵙⵉⵏ ⵉⵎⵉⴷⴰⵡⵏ ⵏⵏⵙ ⵖⴼ ⵉⵙⵎⴷⵓⵜⵏ ⵏⵏⵙ ⵓⵙⵙⵏⴰⵏⵏ, ⴷ ⴰⵛⴽⵓ ⵜⵔⵓⴱⵍⵏ ⴰⵍⵜⵓ ⵙ ⵜⵓⵎⵍⵉⵡⵉⵏ ⵏ ⵡⵓⵏⵓⴼⵏ ⵉⴳⵏⵓⵙⴰⵏⵏ ⴷ ⵉⵏⵍⵎⴰⴷⵏ ⵏⵏⵙ.

ⵉⵜⵜⵢⴰⵎⴰⵥ ⴽⴰⵔⴷⴰⵏⵓ ⴷⴰⵔ "ⵉⵏⵇⵓⵉⵙⵉⵜⵉⵓⵏ" ⴳ ⵓⵙⴳⴳⵯⴰⵙ 1570 ⵙ ⵉⵜⵙⵏⵜ ⵜⵎⵏⵜⴰⵍ ⵜⵉⵔⵓⵙⵙⵉⵏⵉⵏ, ⵉⵜⵜⵓⴱⵣⵣⴰⵣ ⴼⵍⵍⴰⵙ ⴰⴷ ⵉⵣⵣⵔⵉ ⵢⴰⵏ ⵎⵏⵏⴰⵡ ⵡⴰⵢⵢⵓⵔⵏ ⴳ ⵓⴱⵏⵉⵇ ⴷ ⴰⴷ ⴷ ⵉⵙⴹⵕ ⵜⴰⵙⵖⵏⵜ ⴰⵏⵏ ⵏⵏⵙ ⵏ ⵓⵙⵍⵎⴷ. ⵉⵎⵎⵓⵜⵉ ⵖⵔ ⵕⵓⵎⴰ, ⵢⴰⵎⵥ ⴳⵉⵙ ⵢⴰⵜ "ⴰⵏⵏⵓⵉⵜⵢ" ⴰⵔ ⵜⵉⵎⴹⵍⵜ ⵙⴳ ⵖⵓⵔ ⵓⴱⴰⴱⴰ ⴳⵔⴳⵓⵔⵉ ⵡⵉⵙⵙ 13 (ⴷⴼⴼⵉⵔ ⵎⴰⴷ ⵢⵓⴳⵉ ⵓⴱⴰⴱⴰ ⴱⵢⵓⵙ ⵡⵉⵙⵙ ⵙⵎⵎⵓⵙ ⵜⵓⵜⵜⵔⴰ ⵏⵏⵙ), ⵉⵙⵎⴷ ⵉⵍⵎⵎⴰ ⴷⵉⵏⵏ ⵜⴰⵙⴽⵏⴷⵓⵔⵜ ⵏⵏⵙ ⵜⴰⵏⵉⵎⴰⵏⵜ.

ⵉⵜⵜⵓⴷⴳⴳⴰ ⴳ ⵜⵖⵉⵡⴰⵏⵜ ⵜⴰⴳⵍⴷⴰⵏⵜ ⵏ ⵉⵎⵊⵊⴰⵢⵏ, ⵉⵙⵎⴷ ⵡⴰⵅⵅⴰ ⵎⴽⴰⵏⵏ ⵅⴼ ⵜⵣⵔⴰⵡⵉⵏ ⵏⵏⵙ ⵜⵉⴼⵍⵙⴼⵉⵏ ⵙ ⵓⵏⵎⵉⵍⴰ ⴷ ⵜⵡⵓⵔⵉ ⵏⵏⵙ ⴳ ⵜⵙⵏⵉⵊⵊⵉⵜ ⴰⵔ ⵜⴰⵎⵜⵜⴰⵏⵜ ⵏⵏⵙ ⴳ ⵓⵙⴳⴳⵯⴰⵙ 1576.

ⵉⵙⴰⵖⵓⵍⵏ

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