Aggur:ⵜⵓⵙⵏⴰⴽⵜ

ⴰⵍⵓⴳⴰⵔⵉⵜⵎ ⴰⴳⴰⵎⴰⵏ ⵏⵖ ⴰⵍⵓⴳⴰⵔⵉⵜⵎ ⴰⵏⵉⴱⵉⵔⵉ (ⵙ ⵜⴰⵏⴳⵍⵉⵣⵜ : ⵏⴰⵜⵓⵔⴰⵍ ⵍⵓⴳⴰⵔⵉⵜⵀⵎ) ⵜⴳⴰ ⵢⴰⵜ ⵜⴰⵙⵖⵏⵜ ⵏⵖ ⵜⵡⵡⵓⵔⵉ ⵜⴻⵜⵜⵓⵢⵙⴰⵏ ⴱⴰⵀⵔⴰ ⵖ ⵜⵓⵙⵏⴰⴽⵜ, ⴰⵔ ⵜⵙⵏⴼⴰⵍ ⴰⴼⴰⵔⵉⵙ ⵙ ⵜⵉⵎⵔⵏⵉⵜ ⵣⵓⵏⴷ ⴰⴽⴽⵯ ⵜⵉⵙⵖⵏⵉⵏ ⵉⵍⵓⴳⴰⵔⵉⵜⵎ. ⴰⵔ ⵜⵜ ⵏⵜⴰⵔⴰ ⵙ ⵖⵎⴽ-ⴰⴷ : ${\displaystyle \ln()}$. ⴰⵔ ⵏⵜⵜⵉⵏⵉ ⵎⴰⵙ-ⴷ ⴰⵍⵓⴳⴰⵔⵉⵜⵎ ⴰⴳⴰⵎⴰⵏ ⵏⵖ ⴰⵏⵉⴱⵉⵔⵉ ⵉⴳⴰ ⵙ ⵓⵣⴰⴷⵓⵔ ⵏ ${\displaystyle e}$ ⴰⵛⴽⵓ ${\displaystyle ln(e)=1}$, ⵉⴳⴰ ⴰⵍⵓⴳⴰⵔⵉⵜⵎ ⴰⴳⴰⵎⴰⵏ ⵓⵍⴰ ⵜⴰⵎⵏⵣⵓⵜ ⵏ ⵜⴰⵙⵖⵏⵜ : ${\displaystyle x\longmapsto 1/x}$ ⵖ ⵓⵣⵉⵍⴰⵍ ${\displaystyle ]0;+\infty [}$ .

ⴰⵍⵓⴳⴰⵔⵉⵜⵎ ⴰⴷ ⴷⴰⵔⵙ ⵢⴰⵏ ⵢⵉⵙⵎ ⵢⴰⴹⵏⵉ ⴰⴱⵍⴰ "ⴰⴳⴰⵎⴰⵏ", ⵉⴳⴰ-ⵜⵜ "ⴰⵏⵉⴱⵉⵔⵉ". ⵉⵙⵎ ⴰⴷ ⵢⵓⵛⴽⴰⴷ ⵣⵖ ⵊⵓⵀⵏ ⵏⴰⴱⵉⵔ ⵏⵏⴰ ⵉⴳⴰⵏ ⵢⴰⵏ ⵓⵎⵓⵙⵏⴰⴽ ⴰⵙⴽⴰⵜⵍⴰⵏⴷⵉ, ⵏⵜⵜⴰⵜ ⴰⴷ ⴰⴽⴽⵯ ⵉⵣⵡⴰⵔⵏ ⴰⵢ-ⵙⴽⵔ ⵜⴰⴼⵍⵡⵉⵜ ⵜⴰⵍⵓⴳⴰⵔⵉⵜⵎ ( ⵓⵔ ⵜⵔⵡⴰⵙ ⵅⵜⴰⴷ ⵍⵍⵉ ⵏⵙⵙⵏ ⵖⵉⵍⴰ ⵏⴽⴽⵏⵉ ).

ⵜⴻⵜⵜⵢⴰⵡⵙⴽⴰⵔ ⵜⴰⵣⵎⵉⵍⵜ ⵏ ⵓⵍⵓⴳⴰⵔⵉⵜⵎ ⵏⵏⴰ ⴼ ⵏⵙⴰⵡⴰⵍ ⵏⴽⴽⵏⵉ ⵖⵉⵍⴰ ⵙ ⵉⴼⴰⵙⵙⵏ ⵏ ⴳⵔéⴳⵓⵉⵔⴻ ⴷⴻ ⵙⴰⵉⵏⵜ-ⴼⵉⵏⵛⴻⵏⵜ ⴷ ⴰⵍⴱⵀⵓⵏⵙⴻ ⴰⵏⵜⵓⵏⵉⵓ ⴷⴻ ⵙⴰⵔⴰⵙⴰ ⵖ ⵓⵙⴳⴳⵯⴰⵙ ⵏ 1649

ⴰⴷ ⵜⴳ ${\displaystyle a\in ]0;+\infty [}$, ⵏⵣⴹⴰⵔ ⴰⴷ ⵏⵉⵏⵉ ⵎⴰⵙ-ⴷ ⴰⵙⵏⵎⵍ ⵏ ⵜⴰⵙⵖⵏⵜ ⵜⴰⵍⵓⴳⴰⵔⵉⵜⵎ ⵜⴳⴰ-ⵜⵜ ⵓⵏⵔⴰⵔ ⵍⵍⵉ ⵉⵍⵍⴰⵏ ⵖ ⵉⵣⴷⴷⴰⵔ ⵏ ⵜⴰⵙⵖⵏⵜ ${\displaystyle x\mapsto 1/x}$ ⴳⵔ ${\displaystyle a}$ ⴷ 1.

ⵖⵉⴽⴰⴷ ⴰⵙⵜ ⵏⵜⵜⴰⵔⴰ :

${\displaystyle \ln a=\int _{1}^{a}{\frac {1}{x}}\,dx.}$ ... (ⵖⵔ ⵓⴳⴳⴰⵔ...)

ⴰⵙⴽⵜⵉⵖⵎⵔ ⵜⴳⴰ ⵢⴰⵏ ⵓⴳⵎⵉⵡ ⵖ ⵜⵓⵙⵏⴰⴽⵜ ⵏⵏⴰ ⵉⵜⵅⴷⴰⵎⵏ ⵙ ⵉⵣⴷⴰⵢⵏ ⴳⵔ ⵉⵣⴰⵔⵓⵜⵏ ⴷ ⵜⵉⵖⵎⵔⵉⵡⵉⵏ ⵖ ⴰⵎⵎⴰⵙ ⵏ ⵉⵎⴽⵕⴰⴹⵏ ⴷ ⵜⵉⵙⵖⴰⵏ ⵜⵉⵙⴽⵜⵓⵖⵎⵉⵔⵉⵏ ⵣⵓⵏⴷ ⵓⴽⴰⵏ ⵙⵉⵏⵓⵙ, ⴽⵓⵙⵉⵏⵓⵙ ⴷ ⵜⴰⵏⵊⵓⵏⵜ.

ⵖ ⵜⵓⵙⵏⴰⴽⵜ, ⵜⴰⵔⴳⴰⴷⴷⴰ ⵏⵖ ⵜⴰⵎⵢⴰⴳⴰⵔⵜ ⵏ ⵛⴰⵓⵛⵀⵢ–ⵙⵛⵀⵡⴰⵔⵣ, ⵜⴻⵜⵜⴰⵡⵙⴰⵏ ⵓⵍⴰ ⵙ ⵢⵉⵙⵎ ⵏ ⵜⴰⵔⴳⴰⴷⴷⴰ ⵏ ⵛⴰⵓⵛⵀⵢ–ⴱⵓⵏⵢⴰⴽⵓⴼⵙⴽⵢ–ⵙⵛⵀⵡⴰⵔⵣ, ⵜⴳⴰ ⵢⴰⵜ ⵜⴰⵔⴳⴰⴷⴷⴰ ⴱⴰⵀⵔⴰ ⵉⵙⵜⴰⵡⵀⵎⴰⵏ ⵖ ⵜⵓⵙⵏⴰⴽⵜ ⴽⵓⵍⵍⵓⵜ, ⴰⵔ ⵙⵉⵙ ⵏⵙⵡⵓⵔⵔⵉ ⵖ ⴰⵍⵊⵉⴱⵔ ⵉⵎⵣⵉⵔⴳ, ⵜⴰⵙⵍⵟ, ⵜⵉⵥⵔⵉ ⵏ ⵜⵙⵇⵇⴰⵔⵜ ⴷ ⴽⵉⴳⴰⵏ ⵏ ⵜⵖⴰⵡⵙⵉⵡⵉⵏ ⵢⴰⴹⵏⵉ. ⵜⴰⵔⴳⴰⴷⴷⴰ ⴰⴷ ⵉⵙⵙⵓⴼⵖⵜ-ⵉⴷ ⵢⴰⵏ ⵓⵎⵓⵙⵏⴰⴽ ⴰⴼⵔⴰⵏⵙⵉⵙ ⵉⴳⴰ ⵙ ⵢⵉⵙⵎ ⴰⵓⴳⵓⵙⵜⵉⵏ-ⵍⵓⵓⵉⵙ ⵛⴰⵓⵛⵀⵢ ⵖ ⵓⵙⴳⴳⵡⴰⵙ ⵏ 1821, ⵙⵍⵉⵖ ⵢⵓⴼⴰ ⴼⵉⴽⵜⵓⵔ ⴱⵓⵏⵢⴰⴽⵓⴼⵙⴽⵢ ⵢⴰⵜ ⵜⴰⵔⴳⴰⴷⴷⴰ ⵜⵔⵡⴰⵙⵜ ⴰⴽⴽ ⵖ ⵎⴰⴷ ⵉⵣⴷⵉⵏ ⴷ ⴰⵖⵔⴷ ⵖ ⵓⵙⴳⴳⵡⴰⵙ ⵏ 1859, ⵎⵏ ⴱⵄⴷ ⵢⵓⴼⴰⵜⵜ ⴷⴰⵖ ⵢⴰⵏ ⵓⵎⵓⵙⵏⴰⴽ ⴰⵍⵎⴰⵏⵉ ⵀⴻⵔⵎⴰⵏⵏ ⴰⵎⴰⵏⴷⵓⵙ ⵙⵛⵀⵡⴰⵔⵣ ⵖ ⵓⵙⴳⴳⵡⴰⵙ ⵏ 1888.

ⴰⵔ ⵜⵜⵉⵏⵉ ⵜⴰⵔⴳⴰⴷⴷⴰ ⵏ ⵛⴰⵓⵛⵀⵢ–ⵙⵛⵀⵡⴰⵔⵣ ⵎⴰⵙ ⵉ ⴰⴽⴽ ⵙⵉⵏ ⵉⵎⴰⵡⴰⵢⵏ ${\textstyle u}$ ⴷ ${\textstyle v}$ ⵏ ⵢⴰⵜ ⵜⴰⵍⵍⵓⵏⵜ ⴳⵉⵙ ⴰⴼⴰⵔⵉⵙ ⴰⴳⵏⵙⴰⵏ ⵀⴰⵏⵏ ⵔⴰⴷ ⴷⴰⵔⵏⵖ ⵜⵉⵍⵉ

${\displaystyle |\langle \mathbf {u} ,\mathbf {v} \rangle |^{2}\leq \langle \mathbf {u} ,\mathbf {u} \rangle \cdot \langle \mathbf {v} ,\mathbf {v} \rangle }$

ⵎⴰⵖ ${\displaystyle \langle \cdot ,\cdot \rangle }$ ⵉⴳⴰ ⵢⴰⵏ ⵓⴼⴰⵔⵉⵙ ⴰⴳⵏⵙⴰⵏ. ⵙ ⵓⵎⴷⵢⴰ ⴰⴼⴰⵔⵉⵙ ⴰⴳⵏⵙⴰⵏ ⴳⵉⵙ ⴰⴼⴰⵔⵉⵙ ⴰⴼⵙⵏⴰⵏ ⵏ ⵉⵍⴰⵡⵏ ⴷ ⵉⵙⵎⵍⴰⵍⵏ. ⵙ ⵖⵎⴽⴰⴷ, ⵉⵖ ⵏⵓⵙⵉ ⴰⵥⵓⵔ ⵓⵣⵎⵉⵔ-ⵙⵉⵏ ⵖ ⵜⵙⴳⵉⵡⵉⵏ ⵙ ⵙⵏⴰⵜ, ⴷ ⵉⵖ ⴰⵙⵏ ⵏⴳⴰ ⴰⵍⵓⴳⵏ. ⴰⵔ ⵏⵜⵜⴰⴼⴰ ⵜⴰⵔⴳⴰⴷⴷⴰ ⴰⴷ :

${\displaystyle |\langle \mathbf {u} ,\mathbf {v} \rangle |\leq \|\mathbf {u} \|\|\mathbf {v} \|.}$

ⴷ ⵢⴰⵜ ⵜⵖⴰⵡⵙⴰ ⵢⴰⴹⵏ, ⵜⴰⵙⴳⵉⵡⵉⵏ ⵙ ⵙⵏⴰⵜ ⴳⴰⴷⴷⴰⵏ ⵉⵖ ${\textstyle \mathbf {u} }$ ⴷ ${\textstyle \mathbf {v} }$ ⴳⴰⵏ ⵉⵍⴻⵍⵍⵉⵢⵏ ⵉⵎⵣⵉⵔⴳⵏ (ⵢⴰⵄⵏⵉ ⴳⴰⵏ ⵉⵎⵙⴰⴷⴰⵖⵏ). ⵉⵖ ${\textstyle u_{1},\ldots ,u_{n}\in \mathbb {C} }$ ⴷ ${\textstyle v_{1},\ldots ,v_{n}\in \mathbb {C} }$ ⴷ ⵓⴼⴰⵔⵉⵙ ⴰⴳⵏⵙⴰⵏ ⵉⴳⴰ ⴰⴼⴰⵔⵉⵙ ⴰⴳⵏⵙⴰⵏ ⴰⵙⵎⵍⴰⵍ ⴰⵏⴰⵡⴰⵢ, ⵀⴰⵏⵏ ⵜⴰⵔⴳⴰⴷⴷⴰ ⵜⵣⴹⴰⵔ ⴰⴷ ⵜⵜⵢⵓⵔⴰ ⵣⵓⵏⴷ ⵖⵉⴽⴰⴷ (ⵎⴰⵖ ⵜⵉⵔⵔⴰ ⵏ ⵜⴰⵄⵕⵕⴰⴹⵜ ⴰⵔ ⵙⵉⵙ ⵏⵎⵎⴰⵍ ⵓⵏⴰⴼⵜⴰⵢ ⵏ ⵉⵙⵎⵍⴰⵍⵏ): ⵉ ${\displaystyle \mathbf {u} ,\mathbf {v} \in \mathbb {C} ^{n}}$, ⴷⴰⵔⵏⵖ

${\displaystyle \left|\langle \mathbf {u} ,\mathbf {v} \rangle \right|^{2}=\left|\sum _{k=1}^{n}u_{k}{\bar {v}}_{k}\right|^{2}\leq \langle \mathbf {u} ,\mathbf {u} \rangle \langle \mathbf {v} ,\mathbf {v} \rangle }$

${\displaystyle =\left(\sum _{k=1}^{n}u_{k}{\bar {u}}_{k}\right)\left(\sum _{k=1}^{n}v_{k}{\bar {v}}_{k}\right)}$

${\displaystyle =\sum _{j=1}^{n}|u_{j}|^{2}\sum _{k=1}^{n}|v_{k}|^{2}}$

ⴰⴷ ⵜ ⵉⴳⴰⵏ,

${\displaystyle |u_{1}{\bar {v}}_{1}+\cdots +u_{n}{\bar {v}}_{n}|^{2}\leq (|u_{1}|^{2}+\cdots +|u_{n}|^{2})(|v_{1}|^{2}+\cdots +|v_{n}|^{2})}$

(ⵖⵔ ⵓⴳⴳⴰⵔ...)

ⵙⵙⵏⴼⵍ

• ⵜⵓⵙⵏⴰⴽⵜ
• ⵙⵉⵏⵓⵙ (ⵜⵓⵙⵏⴰⴽⵜ)
• ⴻ (ⴰⵎⴹⴰⵏ ⵏ ⵜⵓⵙⵏⴰⴽⵜ)
• ⴰⵍⵊⵉⴱⵔ
• ⴰⵎⴹⴰⵏ
• ⴱⵉ
• ⴰⵙⴽⵜⵉⵖⵎⵔ
• ⴻⵓⵛⵍⵉⴷⴻ
• ⵜⴰⵔⴳⴰⴷⴷⴰ ⵏ ⵛⴰⵓⵛⵀⵢ ⵙⵛⵀⵡⴰⵔⵣ
• ⴰⵍⵓⴳⴰⵔⵉⵜⵎ ⴰⴳⴰⵎⴰⵏ
• ⴱⵏⵓ ⵔⵓⵛⴷ
• ⴳⴻⵔⵓⵍⴰⵏⵓ ⵛⴰⵔⴷⴰⵏⵓ
• ⵡⵉⴽⵉ:ⴰⵎⴰⵡⴰⵍ
• ⵍⵢⵓⵏⴰⵔⴷⵓ ⴷⴰ ⴼⵉⵏⵜⵛⵉ
• ⵓⴳⵓⵚⵜⵉⵏ-ⵍⵓⵡⵉⵙ ⴽⵓⵛⵢ
• ⴰⵎⴹⴰⵏ ⴰⵎⵏⵣⵓ
• ⴰⵣⵡⵉⵍ
• ⴰⵙⵏⴼⵓⵍ ⵏ ⵏⵢⵓⵟⵓⵏ
  ⵙⵙⵏⴼⵍ

ⴰⵎⴹⴰⵏ ⴰⵎⵏⵣⵓ ⵉⴳⴰ ⵢⴰⵏ ⵓⵎⴹⴰⵏ ⵓⵎⵎⵉⴷ ⴰⴳⴰⵎⴰⵏ ⵉⵍⴰⵏ ⵖⴰⵔ ⵙⵉⵏ ⵉⵏⴱⴹⴰⵢⵏ ⵉⵎⵢⴰⵍⵍⴰⵏ ⵉⴳⴰⵏ ⵓⵎⵎⵉⴷⵏ ⴳⵏ ⵉⵎⵓⴼⵔⴰⵔⵏ (ⴰⴷ ⵜⵏ ⵉⴳⴰⵏ 1 ⴷ ⵏⵜⵜⴰⵏ ⵏⵉⵜ). ⵙ ⵖⵎⴽⴰ, 1 ⵓⵔ ⵉⴳⵉ ⴰⵎⵏⵣⵓ ⴰⵛⴽⵓ ⵓⵔ ⴷⴰⵔⵙ ⴰⴱⵍⴰ ⵢⴰⵏ ⵓⵏⴱⴹⴰⵢ ⵓⵎⵎⵉⴷ ⴰⵎⵓⴼⵔⴰⵔ; ⵓⵍⴰ 0 ⵓⵔ ⵜ ⵉⴳⵉ ⴰⵛⴽⵓ ⵉⵙⵙⵏ ⴰⴷ ⵉⵜⵜⵓⴱⴹⴰ ⴼ ⵉⵎⴹⴰⵏⴻⵏ ⵓⵎⵎⵉⴷⵏ ⵉⵎⵓⴼⵔⴰⵔⵏ ⵙ ⵜⵉⵎⵎⴰⴷ ⵏⵏⵙⵏ.

ⵖ ⵓⵏⵎⴳⴰⵍ, ⴰⵎⴹⴰⵏ ⵓⵎⵎⵉⴷ ⴰⵔⵉⵍⵎ ⵉⴳⴰⵏ ⴰⴼⴰⵔⵉⵙ ⵏ ⵙⵉⵏ ⵉⵎⴹⴰⵏⴻⵏ ⵓⵎⵎⵉⴷⵏ ⵉⴳⴰⵎⴰⵏⴻⵏ ⵏⵜⵜⵉⵏⵉ ⴰⵙ ⵓⴷⴷⵉⵙ. ⵙ ⵓⵎⴷⵢⴰ 6 ⴷ 12 ⴷ ⵓⴷⴷⵉⵙⵏ ⴰⵛⴽⵓ 6 = 2 × 3 ⴷ 12 = 3 × 4 ⵏⵖ 2 × 6, ⵎⴰⵛ 11 ⵉⴳⴰ ⴰⵎⵏⵣⵓ ⴰⵛⴽⵓ 1 ⴷ 11 ⴽⴰ ⵉⴳⴰⵏ ⵉⵏⴱⴹⴰⵢⵏ ⵏⵏⵙ.

ⵉⵎⴹⴰⵏⴻⵏ 0 ⴷ 1 ⵓⵔ ⴳⵉⵏ ⵉⵎⵏⵣⴰ ⵡⴰⵍⴰ ⴳⴰⵏ ⵓⴷⴷⵉⵙⵏ. ⴽⵔⴰ ⵏ ⵉⵎⵓⵙⵏⴰⴽⵜⵏ ⵙⵙⵉⴹⵉⵏⴻⵏ ⵣⵉⴽⴽ-ⵍⵍⵉ (ⴰⵔ ⵜⴰⵙⵓⵜ ⵜⵉⵙⵙ 19) 1 ⴷ ⴰⵎⴹⴰⵏ ⴰⵎⵏⵣⵓ, ⵎⴰⵛ ⵖ ⵜⵉⵣⵡⵓⵔⵉ ⵏ ⵜⴰⵙⵓⵜ ⵜⵉⵙⵙ 20, ⵉⵙⵙⵉⵏⴼ ⵢⴰⵏ ⵓⵎⵙⴰⵙⴰ 1 ⵣⵖ ⵉⵎⴹⴰⵏⴻⵏ ⵉⵎⵏⵣⴰ

25 ⵏ ⵉⵎⴹⴰⵏⴻⵏ ⵉⵎⵏⵣⴰ ⵉⵎⵥⵥⵉⵢⵏ ⴼ 100 :

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 ⴷ 91. (ⵖⵔ ⵓⴳⴳⴰⵔ...)

ⵖ ⵜⴰⵙⴽⵔⵉⵖⵎⵔⵜ, ⴰⵙⴰⴹⵓⴼ ⵏ ⵉⴷ ⴽⵓⵙⵉⵏⵓⵙ (ⵉⵜⵜⴰⵡⵙⴰⵏ ⵓⵍⴰ ⵙ ⵢⵉⵙⵎ ⵏ ⵜⴰⵏⴼⴰⵍⵉⵜ ⵏ ⴽⵓⵙⵉⵏⵓⵙ ⵏⵖ ⴰⵙⴽⴽⵓⴷ ⵏ ⴰⵍ ⴽⴰⵛⵉ) ⵜⴳⴰ ⵢⴰⵏ ⵓⵙⴰⴹⵓⴼ ⵏⵏⴰ ⵉⵙⵎⵓⵏⵏ ⵜⵉⵖⵣⵉⵡⵉⵏ ⵏ ⵜⴰⵙⴳⵉⵡⵉⵏ ⵏ ⴽⵔⴰ ⵏ ⵓⵎⴽⵕⴰⴹ ⴷ ⴽⵓⵙⵉⵏⵓⵙ ⵏ ⵢⴰⵏ ⵣⵖ ⵜⵉⵖⵎⵔⵉⵡⵉⵏ. ⵙ ⵓⵙⵡⵓⵔⵉ ⵏ ⵜⵉⵔⵔⴰ ⵣⵓⵏⴷ ⵜⵉⵏ ⴼⵉⴳ. 1, ⴰⵙⴰⴹⵓⴼ ⵏ ⵉⵡⴰⵏⴽⵏ ⵏ ⵉⴷ ⴽⵓⵙⵉⵏⵓⵙ

${\displaystyle c^{2}=a^{2}+b^{2}-2ab\cos \gamma ,}$

ⵎⴰⵖ ${\displaystyle \gamma }$ ⵜⴳⴰ ⵜⵉⵖⵎⵔⵜ ⵍⵍⵉ ⵉⵍⵍⴰⵏ ⴳⵔ ⵜⵉⵖⵣⵉⵡⵉⵏ ${\displaystyle a}$ ⴷ ${\displaystyle b}$ ⴷ ⵜⴰⵙⴳⴰ ⵜⴰⵎⵓⵣⵣⵍⵜ ⵏ ${\displaystyle c}$. ⵉ ⵜⴰⵡⵍⴰⴼⵜ ⴰⵏⵏ ⵏⵉⵜ ⵔⴰⴷ ⴷⴰⵔⵏⵖ ⵉⵍⵉⵏ ⵓⵍⴰ:

${\displaystyle a^{2}=b^{2}+c^{2}-2bc\cos \alpha ,}$

${\displaystyle b^{2}=a^{2}+c^{2}-2ac\cos \beta .}$

ⴰⵙⴰⴹⵓⴼ ⵏ ⵉⴷ ⴽⵓⵙⵉⵏⵓⵙ ⴰⵔ ⵜⵙⴽⴰⵔ ⴰⵙⵎⴰⵜⴰ ⵉ ⴰⵙⴽⴽⵓⴷ ⵏ ⴱⵢⵜⵀⴰⴳⵓⵔ, ⵏⵏⴰ ⵓⵔ ⵉⵍⵍⴰⵏ ⴷⴰⵔ ⵉⵎⴽⵕⴰⴹⵏ ⵓⵏⵣⵉⵖⵏ: ⵉⵖ ⵜⴳⴰ ${\displaystyle \gamma }$ ⵜⵉⵖⵎⵔⵜ ⵜⴰⵖⴰⴷⴰⵏⵜ (ⵏⵏⴰ ⴷⴰⵔ ⵉⵍⵍⴰ 90 ⴷⴰⵔⴰⵊⴰ, ⵏⵖ ${\textstyle {\pi \over 2}}$ ⵙ ⵔⴰⴹⵢⴰⵏ), ⵀⴰⵏⵏ ${\textstyle cos(\gamma )=0}$, ⵙ ⵖⵎⴽ ⴰⴷ ⴰⵙ ⵉⵙⴽⴰⵔ ⵓⵙⴰⴹⵓⴼ ⵏ ⵉⴷ ⴽⵓⵙⵉⵏⵓⵙ ⴰⵙⵎⴰⵜⴰ ⵉ ⴰⵙⴽⴽⵓⴷ ⵏ ⴱⵢⵜⵀⴰⴳⵓⵔ:

${\displaystyle c^{2}=a^{2}+b^{2}.}$

ⴰⵔ ⵏⵙⵡⵓⵔⵔⵉ ⵙ ⵓⵙⴰⴹⵓⴼ ⵏ ⵉⴷ ⴽⵓⵙⵉⵏⵓⵙ ⵏ ⵉⴷ ⴽⵓⵙⵉⵏⵓⵙ ⵉⵖ ⵏⵔⴰ ⴰⴷ ⵏⵃⴰⵙⴱ ⵜⵉⵖⵎⵔⵜ ⵜⵉⵙⵙ ⴽⵔⴰⴹⵜ ⵏ ⴽⵔⴰ ⵏ ⵓⵎⴽⵕⴰⴹ ⵉⵖ ⵢⴰⴷ ⵜⴰⵡⵙⵙⴰⵏ ⴷⴰⵔⵏⵖ ⵙⵏⴰⵜ ⵜⴰⵙⴳⵉⵡⵉⵏ ⴷ ⵜⵉⵖⵎⵔⵜ ⵏⵏⵙⵏ ⵉⵇⵇⵏⵏ, ⴷ ⵓⵍⴰ ⵖ ⵍⵃⵙⴰⴱ ⵏ ⵜⵉⵖⵎⵔⵉⵡⵉⵏ ⵏ ⴽⵔⴰ ⵏ ⵓⵎⴽⵕⴰⴹ ⵉⵖ ⵢⴰⴷ ⵜⵜⴰⵡⵙⵙⴰⵏ ⴷⴰⵔⵏⵖ ⵜⴰⵙⴳⵉⵡⵉⵏ ⵏⵏⵙ ⵙ ⴽⵔⴰⴹ-ⵉⵜⵙⵏⵜ. (ⵖⵔ ⵓⴳⴳⴰⵔ...)