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A Historical Outline of the Theorem of Implicit Nctions

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A Historical Outline of the Theorem of Implicit Nctions Divulgaciones Matem acute-a t icas Vol period 10 No period 2 open parenthesis 2002 closing parenthesis commannoindent pp periodDivulgaciones 171 endash 180 Matem $ nacutefag $ t icas Vol . 10No . 2 ( 2002 ) , pp . 171 −− 180 A .... Historical .... Outline .... of the .... Theorem .... of nnoindentImplicit ..A F-un h nctions f i l l H i s t o r i c a l n h f i l l Outline n h f i l l o f the n h f i l l Theorem n h f i l l o f Un Bosquejo Hist acute-o rico del Teorema de las Funciones Impl dotlessi-acute citas n centerlineGiovanni Mingarif I m pScarpello l i c i t nquad open parenthesis$ F−u $ giovannimingari n c t i o n s g at l ibero period it closing parenthesis Daniele Ritelli dr itelli at e c onomia period unibo period it n centerlineDipartimentofUn di Matematica BosquejoDivulgaciones per Hist Matem le Scienzea´ $ tn icasacute Economiche Vol .f 10og No$ .e 2 Sociali( rico 2002 )delcomma , pp . Teorema 171 { 180 de las Funciones Impl $ nBolognaacutefn ItalyimathgA$ c Historical i t a s g Outline of the Theorem Abstract n centerline f Giovanniof Mingari Scarpello ( giovannimingari $ @ $ l ibero . it ) g In this article a historical outline ofImplicit the implicit functionsF theory− u nctions is presented startingUn from Bosquejo the wiewpoint Hist ofo´ Descartesrico del Teorema algebraic geometry de las Funciones Impl ´{ citas n centerline f Daniele Ritelli dr itelli $@$ e c onomia . unibo . it g open parenthesisGiovanni 1 637 closing Mingari parenthesis Scarpello and Leibniz ( giovannimingari open parenthesis 1 676@ l or ibero 1 677 closing . it paren-) thesis comma Johann BernoulliDaniele open Ritelli parenthesisdr itelli 1 695 closing@ e parenthesis c onomia and . Euler unibo . it n centerline f Dipartimento di Matematica per le Scienze Economiche e Sociali , g open parenthesis 1 748 closingDipartimento parenthesis di Matematica infinitesimal per calculus le Scienze period Economiche .. The critical e Sociali contribution , is highlighted Bologna Italy n centerline f Bologna Italy g due to the italian mathematician Ulisse Dini who settledAbstract the matter in modern form inside the realIn functions this article theory a historical period outline .. The of paper the implicit supplies functions the theory is n centerline f Abstract g documented proof of Dinipresented quoteright starting s priority from thein the wiewpoint so called of implicitDescartes functions algebraic geometry theorem period In the( 1meanwhile 637 ) and Leibnizthe historical ( 1 676 lack or 1 in 677 attributing ) , Johann theBernoulli theorem ( 1 695 ) and Euler n centerline f In this article a historical outline of the implicit functions theory is g to Dini can be ascribed( to 1 748 the ) fact infinitesimal that he published calculus . his The proof critical only contribution in is highlighted his Lezioni open square bracketdue to the 3 italianclosing mathematician square bracket Ulisse comma Dini written who settled for thesupporting matter in his teaching n centerline f presented starting from the wiewpoint of Descartes algebraic geometry g period modern form inside the real functions theory . The paper supplies the Key words and phrases :documented implicit functions proof of comma Dini ' s contemporary priority in the so history called implicit functions n centerline f( 1 637 ) and Leibniz ( 1 676 or 1 677 ) , Johann Bernoulli ( 1 695 ) and Euler g Resumen theorem . In the meanwhile the historical lack in attributing the theorem En este art acute-dotlessito culo Dini se can presenta be ascribed un excursus to the fact hist that o-acute he published rico de his la proof teor acute-dotlessi only in a de n centerline f( 1 748 ) infinitesimal calculus . nquad The critical contribution is highlighted g las his Lezioni [ 3 ] , written for supporting his teaching . funciones impl acute-dotlessiKey citas words comma and phrases empezando : implicit con el punto functions de vista , contemporary de la geometr history dotlessi-acute n centerline fdue to the italian mathematician Ulisse Dini who settled the matter in g a Resumen algebraica de DescartesEn open este parenthesis art ´{ culo se 1 presenta 637 closing un excursus parenthesis hist yo´ elrico an de acute-a la teor lisis´{ a infinitesimal de las de n centerline fmodern form inside the real functions theory . nquad The paper supplies the g Leibniz open parenthesis 1funciones 676 impl ´{ citas , empezando con el punto de vista de la geometr ´{ a o 1 677 closing parenthesisalgebraica comma de Descartes Johan Bernoulli ( 1 637 ) openy el an parenthesisa´ lisis infinitesimal 1 695 closing de Leibniz parenthesis ( 1 676 y Euler n centerline fdocumented proof of Dini ' s priority in the so called implicit functions g open parenthesis 1 748 closingo 1 677 parenthesis ) , Johan Bernoulli period (Se 1 pone695 ) yen Euler evidencia ( 1 748 la ) . Se pone en evidencia la contribuci o-acute n decisivacontribuci delo´ matemn decisiva a-acute del matem tico it alianoa´ tico it Ulisse aliano Dini Ulisse comma Dini , quien quien plan - hyphen n centerline f theorem . In the meanwhile the historical lack in attributing the theorem g te acute-o la cuestite o-acuteo´ la cuesti n eno´ tn acute-e en t e´ rminosrminos modernos modernos , encomma el a´ mbito en el de a-acute la teor mbito´{ a de de las la teor acute-dotlessi a de las funciones de variables reales , produciendo la prueba documentada de su n centerline f to Dini can be ascribed to the fact that he published his proof only in g funciones de variablespaternidad reales comma en lo produciendoque , hoy en d la´{ pruebaa , es el documentada teorema de las de funciones su impl ´{ ci - paternidad en lo quetas comma . Tambi hoye´ n en se d evidencia acute-dotlessi que el vac a comma´{ o historiogr es el teoremaa´ fico en de la atribucilas funcioneso´ n impl n centerline f his Lezioni [ 3 ] , written for supporting his teaching . g dotlessi-acute ci hyphen del teorema a Dini puede depender del hecho de que e´ l public o´ una tas period Tambi acute-eRecibido n 2002 se evidencia / 3 / 1 3 . queRevisado el vac 2002 dotlessi-acute / 10 / 0 1 . Aceptado o historiogr 2002 /acute-a 10 / 7 . fico en la atribuci n centerline fKey words and phrases : implicit functions , contemporary history g o-acute n MSC ( 2000 ) : Primary 1 A 95 ; Secondary 26 B 10 . del teorema a DiniResearch puede dependersupported by del MURST hecho grant de queMetodi acute-e matematici l public in o-acute economia una n centerlineRecibido 2002fResumen slash 3 slashg 1 3 period Revisado 2002 slash 10 slash 0 1 period Aceptado 2002 slash 10 slash 7 period n centerlineMSC open parenthesisfEn e s t e 2000 ar t closing $ nacute parenthesisfnimath : Primaryg $ 1culo A 95 se semicolon presenta Secondary un excursus 26 B 10 period hist $ nResearchacutefo supportedg $ rico by MURST de la teorgrant Metodi $ nacute matematicifnimath ing economia$ a de l a s g n centerline f funciones impl $ nacutefnimathg $ citas , empezando con el punto de vista de la geometr $ nacutefnimathg $ a g n centerline f algebraica de Descartes ( 1 637 ) y el an $ nacutefag $ lisis infinitesimal de Leibniz ( 1 676 g n centerline fo 1 677 ) , Johan Bernoulli ( 1 695 ) y Euler ( 1 748 ) . Se pone en evidencia la g n centerline f contribuci $ nacutefog $ n d e c i s i v a d e l matem $ nacutefag $ tico it aliano Ulisse Dini , quien plan − g n centerline f te $ nacutefog $ l a c u e s t i $ nacutefog $ n en t $ nacutefeg $ rminos modernos , en el $ nacutefag $ mbito de la teor $ nacutefnimathg $ a de l a s g n centerline f funciones de variables reales , produciendo la prueba documentada de su g n centerline f paternidad en lo que , hoy en d $ nacutefnimathg $ a , es el teorema de las funciones impl $ nacutefnimathg $ c i − g n centerline f tas . Tambi $ nacutefeg $ n se evidencia que el vac $ nacutefnimathg $ o historiogr $ nacutefag $ fico en la atribuci $ nacutefog $ n g n centerline f del teorema a Dini puede depender del hecho de que $ nacutefeg $ l p u b l i c $ nacutefog $ una g nnoindent Recibido 2002 / 3 / 1 3 . Revisado 2002 / 10 / 0 1 . Aceptado 2002 / 10 / 7 . nnoindent MSC ( 2000 ) : Primary 1 A 95 ; Secondary 26 B 10 . nnoindent Research supported by MURST grant Metodi matematici in economia 1 72 .... Giovanni Mingari comma Daniele Ritelli nnoindentdemostraci1 acute-o 72 n h n f rigurosai l l Giovanni solamente Mingari en sus Lezioni , Daniele open square Ritelli bracket 3 closing square bracket comma como soporte de su n centerlineactividad docentef demostraci period $ nacutefog $ n rigurosa solamente en sus Lezioni [ 3 ] , como soporte de su g Palabras y frases c lave : funciones impl acute-dotlessi citas comma historia contempor a-acute nea periodn centerline f actividad docente . g 1 .. Introduction n centerlineThis paper goesf Palabras back1 72 to the y frases implicit functions c lave theory : funciones and to the impl Giovanni relevant $ Mingarinacute ,fn Danieleimathg Ritelli$ citas , historia contempor $ nanalyticalacutefag questions$ nea perioddemostraci . g .... Allo´ thisn rigurosa was matter solamente of research en sus Lezioni for Descartes[ 3 ] , como and othersoporte de su mathematicians since the first half of the 1 7 to theactividad power docente of t h century . for almost two hundred nnoindentyears comma1 n butquad onlyPalabrasIntroduction at the end y frases of the c 1 lave 800 : quoterightfunciones s impl the theory´{ citas received , historia a contempor satisfactorya´ nea set hyphen . t lement by the Italian1 mathematicianIntroduction Ulisse Dini open parenthesis 1 845 hyphen 1 9 1 8 closing parenthesisnnoindent periodThis .. paper FurthermoreThis paper goes goes back back to to the the implicit implicit functions functions theory and theory to the relevant and to the relevant bibliographical supportanalytical is given questions by us about.
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