Page:Annales de mathématiques pures et appliquées, 1810-1811, Tome 1.djvu/98

94

FORMULES.

${\begin{array}{ll}2\mathrm {MT} \ldots \ldots \ldots &=0,00000\,00000\,00001\,26621\,87057\,73076\,12429\,70490\,38067\,46583\,69037\\\mathrm {L_{1302}} \ldots \ldots \ldots &=3,11461\,09842\,32173\,14288\,76871\,56690\,66025\,17555\,92700\,28095\,44686\\\mathrm {L_{1308}} \ldots \ldots \ldots &=3,11660\,77439\,88248\,46292\,30190\,00317\,97664\,93787\,13149\,94289\,66296\\\mathrm {L_{1310}} \ldots \ldots \ldots &=3,11727\,12956\,55764\,26081\,00542\,70697\,73859\,47801\,63117\,12162\,69690\\\mathrm {L_{1300}} \ldots \ldots \ldots &=3,11394\,33523\,06836\,76920\,65051\,57942\,32843\,08297\,29188\,38706\,82718\\\mathrm {L_{1313}} \ldots \ldots \ldots &=3,11826\,47260\,89479\,34348\,16933\,36165\,26634\,40490\,18543\,59352\,08632\\\hline {\text{Somme}}\ldots \ldots \ldots &=15,58069\,81022\,72503\,24552\,76646\,94890\,09456\,78422\,54766\,79190\,41059\\\hline {\text{C. arith. de la somme}}&=84,41930\,18977\,27496\,75447\,23353\,05109\,90543\,21577\,45233\,20809\,58941\\\mathrm {2L_{1305}} \ldots \ldots \ldots &=6,23122\,10233\,48599\,5334\,83273\,49609\,98516\,57727\,24529\,61287\,40588\\\mathrm {2L_{1298}} \ldots \ldots \ldots &=6,22654\,93849\,28700\,85244\,91905\,0100\,32301\,48032\,73093\,71865\,37029\\\mathrm {2L_{1312}} \ldots \ldots \ldots &=6,23586\,76700\,79282\,94n5\,62126\,47181\,29186\,67429\,26082\,28845\,95911\\\hline \mathrm {L_{1297}} \ldots &=3,11293\,99760\,84080\,08149\,60658\,02806\,50547\,94766\,68938\,82808\,32469\\\hline \end{array}}$

Résultat exact jusques au 45.^me chiffre inclusivement, et qui surpasse la vraie valeur du logarithme cherché de $0,00000\,00000\,00000\,00000\,00000\,00000\,00000\,00000\,00000\,89696\,66717$

ainsi qu’il est facile de le vérifier en observant que

$\mathrm {L_{1297}=L_{999987}-L_{3}-L_{257}}$, et que ces trois derniers logarithmes sont au nombre de ceux qui ont été calculés par Sharp.