## Sentence Examples

**Fermat**,**Roberval****and****Desargues****took****exception****in****their****various****ways****to****the****methods****employed****in****the****geometry**,**and****to****the****demonstrations****of****the****laws****of****refraction****given****in****the****Dioptrics****and****Meteors**.**In****another****question****connected****with****this**,**the****problem****of****drawing****tangents****to****any****curve**,**Descartes****was****drawn****into****a****controversy****with****Pierre**(**de**)**Fermat**(1601**-**1663),**Gilles****Persone****de****Roberval**(1602**-**1675),**and****Girard****Desargues**(1593**-**1661).**Fermat****and****Descartes****agreed****in****regarding****the****tangent****to****a****curve****as****a****secant****of****that****curve****with****the****two****points****of****intersection****coinciding**,**while****Roberval****regarded****it****as****the****direction****of****the****composite****movement****by****which****the****curve****can****be****described**.**GILLES****PERSONNE****ROBERVAL**(**or**[[**Personier**)**De**]] (1602**-**1675),**French****mathematician**,**was****born****at****Roberval**,**near****Beauvais**,**on****the**8th**of****August**1602.**His****name****was****originally****Gilles****Personne**,**that****of****Roberval**,**by****which****he****is****known**,**being****taken****from****the****place****of****his****birth**.**A****condition****of****tenure****attached****to****this****chair****was****that****the****holder****should****propose****mathematical****questions****for****solution**,**and****should****resign****in****favour****of****any****person****who****solved****them****better****than****himself**;**but**,**notwithstanding****this**,**Roberval****was****able****to****keep****the****chair****till****his****death**,**which****occurred****at****Paris****on****the**27th**of****October**1675.**Roberval****was****one****of****those****mathematicians****who**,**just****before****the****invention****of****the****infinitesimal****calculus**,**occupied****their****attention****with****problems****which****are****only****soluble**,**or****can****be****most****easily****solved**,**by****some****method****involving****limits****or****infinitesimals**,**and****in****the****solution****of****which****accordingly****the****calculus****is****always****now****employed**.**Between****Roberval****and****Descartes****there****existed****a****feeling****of****ill**-**will**,**owing****to****the****jealousy****aroused****in****the****mind****of****the****former****by****the****criticism****which****Descartes****offered****to****some****of****the****methods****employed****by****him****and****by****Pierre****de****Fermat**;**and****this****led****him****to****criticize****and****oppose****the****analytical****methods****which****Descartes****introduced****into****geometry****about****this****time**.**De****C**.**Condorcet**,**Eloge****de****Roberval**(**Paris**, 1773):**J**.**The****cycloid****was****a****famous****curve****in****those****days**;**it****had****been****discussed****by****Galileo**,**Descartes**,**Fermat**,**Roberval****and****Torricelli**,**who****had****in****turn****exhausted****their****skill****upon****it**.**P**.**de****Roberval**,**but****his****investigation****was****unknown****in****Italy**.**The****evaluation****of****the****area****of****the****curve****had****made****Roberval****famous****in****France**,**but****Descartes****considered****that****the****value****of****his****investigation****had****been****grossly****exaggerated**;**he****declared****the****problem****to****be****of****an****elementary****nature****and****submitted****a****short****and****simple****solution**.**At****the****same****time****he****challenged****Roberval****and****Fermat****to****construct****the****tangent**;**Roberval****failed****but****Fermat****succeeded**.