Page:Joseph Louis de Lagrange - Œuvres, Tome 6.djvu/613

Or on a (n^o 42)

${\begin{alignedat}{2}\mathrm {A} =&451,\qquad &\log \mathrm {A} =&2{,}6541766,\\\mathrm {B} =&591,&\log \mathrm {B} =&2{,}7715875.\end{alignedat}}$

Donc

${\begin{aligned}\log -\mathrm {\frac {A}{F}} =&9{,}9702421=\log -\sin a',\\\log -\mathrm {\frac {G}{B}} =&9{,}9375701=\log -\sin b'.\end{aligned}}$

Donc

${\begin{array}{lcl}a'=180^{\circ }+69^{\circ }2'=249^{\circ }2',&{\text{ou}}&360^{\circ }-69^{\circ }2'=290^{\circ }58',\\b'=180^{\circ }+60^{\circ }\quad =240^{\circ },&{\text{ou}}&360^{\circ }-60^{\circ }\quad =300^{\circ }.\end{array}}$

À quoi on pourra encore ajouter ou en retrancher tel multiple de $360$ degrés qu’on voudra.

${\begin{alignedat}{3}2^{\mathrm {o} }\quad q+q'\quad =&0{,}83827,\\q-q'\quad =&0{,}41887,\qquad &\log =&9{,}6220793,\qquad &2\log =&9{,}2441586.\\(q-q')^{2}=&0{,}17546,\\-4p'=&{\underline {4{,}77972}}.\\&4{,}95518&\log =&0{,}6950594,&{\frac {1}{2}}\log =&0{,}3475297.\end{alignedat}}$

${\begin{aligned}{\sqrt {(q-q')^{2}-4p'}}=&2{,}22603,\\q+q'=&{\underline {0{,}83827}}.\\\mathrm {Somme} \ldots \ldots \ldots \ \ &{\underline {3{,}06430}}.\\\mathrm {Diff{\acute {e}}rence} \ldots \ldots \ \ &1{,}38776.\\\end{aligned}}$

Donc

$\varpi =0{,}69388,\quad \rho =-1{,}53215.$

Ensuite

${\begin{alignedat}{2}\log(q-q')=&9{,}6220793,\\\log {\sqrt {(q-q')^{2}-4p'}}=&{\underline {0{,}3475297}}.\\\mathrm {Diff{\acute {e}}rence} \ldots \ldots \ \ &9{,}2745496.\qquad &\mathrm {Nombre\ corr} .=0{,}18816.\end{alignedat}}$