## Sentence Examples

**These****papers****are****chiefly****geometrical**,**many****of****them****being****developments****and****applications****of****the****methods****laid****down****in****his****great****work**,**Der****barycentrische****Calcul**(**Leipzig**, 1827),**which**,**as****the****name****implies**,**is****based****upon****the****properties****of****the****mean****point****or****centre****of****mass**(**see****Algebra**:**Universal**).**In**1741**he****received****his****first****public****distinction****in****being****admitted****a****member****of****the****Academy****of****Sciences**,**to****which****he****had****previously****presented****several****papers**,**including****a****Memoire****sur****le****calcul****integral**(1739).**In**1746**and**1748**he****published****in****the****Memoirs****of****the****Academy****of****Berlin**"**Recherches****sur****le****calcul****integral**,"**a****branch****of****mathematical****science****which****is****greatly****indebted****to****him**.**Besides****the****separate****works****already****named****are****Resolution****des****equations****numeriques**(1798, 2nd**ed**., 1808, 3rd**ed**., 1826),**and****Lecons****sur****le****calcul****des****fonctions**(1805, 2nd**ed**., 1806),**designed****as****a****commentary****and****supplement****to****the****first****part****of****the****Theorie****des****fonctions**.**The****analytical****tournament****closed****with****the****communication****to****the****Academy****by****Laplace**, 1 "**Recherches****sur****le****calcul****integral**,"**M**é**langes****de****la****Soc**.**Roy**.**Although****relegated****to****a****note**(**vii**.),**and****propounded**"**Avec****la****defiance****que****doit****inspirer****tout****ce****qui****n'est****point****un****resultat****de****l'observation****ou****du****calcul**,"**it****is****plain**,**from****the****complacency****with****which****he****recurred****to****it**3**at****a****later****date**,**that****he****regarded****the****speculation****with****considerable****interest**.**Lacroix'****s****Traite****elementaire****du****calcul****des****probabilites****and****De****Morgan'****s****Essay**,**published****in****Lardner'****s****Cabinet****Cyclopaedia**.**Mobius**,**Der****barycentrische****Calcul**(**Leipzig**, 1827) (**reprinted****in****his****collected****works**,**vol**.**Continued****fractions**,**one****of****the****earliest****examples****of****which****is****Lord****Brouncker'****s****expression****for****the****ratio****of****the****circumference****to****the****diameter****of****a****circle**(**see****Circle**),**were****elaborately****discussed****by****John****Wallis****and****Leonhard****Euler**;**the****convergency****of****series****treated****by****Newton**,**Euler****and****the****Bernoullis**;**the****binomial****theorem**,**due****originally****to****Newton****and****subsequently****expanded****by****Euler****and****others**,**was****used****by****Joseph****Louis****Lagrange****as****the****basis****of****his****Calcul****des****Fonctions**.**Other****works****of****Cournot'****s****were****Traite****elementaire****de****la****theorie****des****fonctions****et****du****calcul****infinitesimal**(1841);**Exposition****de****la****theorie****des****chances****et****des****probabilLites**(1843);**De****l'origine****et****des****limites****de****la****correspondance****entre****l'algebre****et****la****geometrie**(1847);**Traite****de****l'enchainement****des****idees****fondamentales****dans****les****sciences****et****dans****l'histoire**(1861);**and****Revue****somma**.**ire****des****doctrines****economiques**(1877).**Lagrange****realized****its****powers****and****termed****it**"**le****principal****fondement****du****calcul****erentiel**."**The****idea****may****be****compared****with****that****of****Joseph****Louis****Lagrange'****s****Calcul****des****Fonctions**.**Besides****papers****in****scientific****periodicals****he****published****Indagaciones****sobre****el****estanada****de****cobre**,**la****vajilla****de****estano****y****el****vidriado**(1803);**Memoire****sur****le****sucre****de****raisins**(1808);**Recueil****des****memoires****relatifs****d****la****poudre****a****canon**(1815);**and****Essai****sur****une****des****causes****qui****peuvent****amener****la****formation****du****calcul**(1824).**The****contents****of****these****memoirs****are****included****in****the****first****volume****of****his****Exercices****de****calcul****integral**(1811).**The****Exercices****de****calcul****integral****consist****of****three****volumes**,**a****great****portion****of****the****first****and****the****whole****of****the****third****being****devoted****to****elliptic****functions**.**Prony****was****charged****with****the****direction****of****the****work**,**and****was****expressly****required**"**non****seulement****a****composer****des****tables****qui****ne****laissassent****rien****a****desirer****quant****a****l'exactitude**,**mais****a****en****faire****le****monument****de****calcul****le****plus****vaste****et****le****plus****imposant****qui****eut****jamais****ete****execute****ou****meme****congu**."**Combebiac**,**Calcul****des****triquaternions**(**Paris**, 1902);**Don****Francisco****Perez****de****Munoz**,**Introduction****al****estudio****del****cdlculo****de****Cuaterniones****y****otras****Algebras****especiales**(**Madrid**, 1905);**A**.- 3
**Lecons****de****calcul****des****variations**(**Paris**, 1861).