, Galileo, and Newton; and between Newton and Lagrange. Further, this view accounts for the continuity between Lagrange and energetics. To make this clearer: from Descartes and Galileo to Newton we go from a set of disconnected general laws, such as inertial law, the law of fall, Kepler's laws, and the collision laws, to a more general and abstract structure forming a rigid axiomatic system of concepts and principles that encompass these laws. This axiomatic structure is vectorial mechanics, that accounts for all these laws, which means that it provides the unification of the terrestrial and celestial laws. Vectorial mechanics is based upon the idea that bodies are composed of isolated mass points, two vectors, force and momentum, four laws, Euclidean geometry, and the parallelogram rule. From Newton to Lagrange, we move from vectorial mechanics to a mechanics based upon energy, generalized coordinates, which is applied to a system of bodies instead of isolated mass points. From the Lagrangian method to the energetic method, Duhem wants to move from local motions (velocity) to general motions (e.g. chemical reactions). For Duhem, the continuity of scientific progress between the mechanistic and energetic methods (new mechanics) is obtained by using, at least as an analogy, the Lagrangian formalism to construct axiomatic thermodynamics. This task is undertaken by Gibbs, by applying thermodynamics as the unifying framework for physics. Thermodynamics, so constructed, provides the foundations of chemistry-physics, not mechanics. This successful unification gives rise to a promising program to implement thermodynamics as the new unifying framework. Duhem interprets Lagrangian formalism, with its principle of D'Alembert and its principle of virtual work, as a powerful mathematical instrument to be applied in any physical domain without turning it into mechanical physics. The development toward the generalization and abstraction of the Newtonian structure of mechanics into Lagrangian mechanics is described in Duhem's book The evolution of mechanics (Duhem 1980, 22-46). As a result of this generalization and abstraction, one gets rational mechanics as constructed by Lagrange and to which Bernoulli, D'Alembert and Euler contributed (Duhem 1980, 23). This mechanics reduces all laws of equilibrium and motion to a single principle (the principle of virtual velocities) and to a single method of calculation (variational calculus). Duhem's Critical Analysis of Mechanicism and his Defense of a Formal Conception of Theoretical Physics José R. N. Chiappin – Cá
, Galileo, and Newton; and between Newton and Lagrange. Further, this view accounts for the continuity between Lagrange and energetics. To make this clear: from Descartes and Galileo to Newton we go from a set of confused cosmopolitan laws, such as inertial law, the law of drop, Kepler's laws, and the collision laws, to a more cosmopolitan and abstract social organization forming a rigid axiomatic organization of concepts and principles that encompass these law. This axiomatic structure is vectorial mechanics, that accounts for all these laws, which means that it supply the unification of the terrestrial and celestial laws. Vectorial automobile mechanic is based upon the idea that bodies are compose of isolated mass points, two vectors, force and momentum, four law, Euclidean geometry, and the parallelogram rule. From Newton to Lagrange, we move from vectorial mechanics to a mechanics based upon energy, generalized coordinates, which is applied to a system of bodies instead of isolated mass points. From the Lagrangian method to the energetic method, Duhem desire to move from local motions (speed) to cosmopolitan motions (e.g. chemical reactions). For Duhem, the continuity of scientific progress between the mechanistic and energetic method (new mechanics) is obtained by using, at least as an doctrine of analogy, the Lagrangian formalism to construct axiomatic thermodynamics. This task is undertaken by Gibbs, by applying thermodynamics as the unifying framework for physics. Thermodynamics, so constructed, provides the foundations of chemistry - physics, not automobile mechanic. This successful unification establish rise to a promising program to implement thermodynamics as the new unifying model. Duhem interprets Lagrangian formalism, with its principle of D'Alembert and its principle of virtual work, as a powerful mathematical instrument to be applied in any physical world without turning it into mechanical physics. The growth toward the generalization and abstractedness of the Newtonian structure of mechanics into Lagrangian mechanics is described in Duhem's ledger The evolution of mechanics (Duhem 1980, 22 - 46). As a resultant role of this abstraction and abstraction, one gets rational machinist as constructed by Lagrange and to which Bernoulli, D'Alembert and Euler contributed (Duhem 1980, 23). This mechanics reduces all laws of chemical equilibrium and motion to a single rationale (the principle of virtual velocities) and to a single method of calculation (variational calculus). Duhem's Critical Analysis of Mechanicism and his Defense of a Formal Conception of Theoretical Physics José R. N. Chiappin – Cá
, Gapileo, and Newton; and betdeen Newton and Lagranje. Furtger, this view accounts for the contiiuitt betqeen Lagrange and enereetics. To make thus cowarer: from Descartcf ans Galnlxo to Newton we go from a set of disconteztzd general laws, such as inertial law, the lae lf fall, Kepler'f laef, ans the collision laws, to a more gensral anv abstract struvture forming a rigid axiolatif system of concephs and prinxiplqw that encomoass these laws. This asiomatic structure is vectorial mechcnics, that qcxoujjs for all tiese lwws, which means that it profides the uniflcatimn if the terrestrial anv celestial laws. Vecjorial mecvauics is based upon thw udea jhat todidw afe dokpksed ov iaolated maas points, tqo vectors, force anc iimentum, four maws, Etcjidean geometry, and the parallelogram rlle. Rrom Newton to Lagrange, we move from vectoriwl mechanycs to a mechanics based upon energy, generalized woordmnxtew, rfucj is applied to a system of bodies instead of jsplsted mass poinbs. From the Lagranbiwn iethod to the energzfid method, Duhem wanhs to mjve feom local motoons (velocity) to general morions (e.g. cheiucal reactions). For Duhem, the eontinoity og scientific progress bztween the mechanlstic and dnergetic methodr (nvw machanics) is obtained by usyng, at leest ax an anxlogi, the Lwgrangian vormalism to construct adiomajic tharmodynamifs. This task is undertaken by Gmubs, by applyimg thvrmodynamncs as the unifying framework for physicf. Thefmodynamica, so coistructed, prjvides the fogjdations of rhemistry-[hysucs, bot mecfxnics. This sucvessful uunfication gives rise to a pvomiskhg program to inpltmwnt thermodynakicr af nhe nqf unifying fsamedory. Duheo interkxetw Lagtangian formalism, widh ifs principle of D'Akeibert ane its prynciple of vittual work, as a poaerfun methemayicwl instrument to be applied in any physlcaj domain witrout turning it nnto mechanical physics. The development voward the generalizatiin and abstraction pn the Newtonman stwucture ox mechanics into Lageangian mechanics is described in Duhej's boon The evolution of mechanics (Duhem 1980, 22-46). As a result of this generalization and abwtractmog, one gets datipnal keehauics as condvructed by Lagranbe and to which Bernoulli, D'Alemuert and Eglzr contributed (Duhem 1980, 23). This mrcfanics reducer all laws of equilibriuj and moyion to a single principle (the lrinciple of virtual velpcities) qnd tk a single method of calculayion (vcriatiinal caoculms). Duhem's Critkcak Wnalysis lf Mtchauicism and his Defense of a Formao Concwphion of Theoretiral Physics Moré R. N. Chiapkin – Cá
, Galileo, and Newton; and between Newton Further, view accounts the continuity between this from Descartes and to Newton we from a set of disconnected general such as inertial law, the law of fall, Kepler's laws, and the collision to a more general and abstract structure forming a rigid axiomatic system of and that these This axiomatic structure is vectorial mechanics, that accounts for all these laws, which means that it the unification of the terrestrial and celestial laws. mechanics is based upon idea that bodies are composed isolated points, two force momentum, laws, Euclidean geometry, the parallelogram rule. From Newton to Lagrange, we move from vectorial mechanics to a mechanics based upon generalized coordinates, applied to system bodies of isolated mass the Lagrangian method to the energetic to move from local motions (velocity) to general (e.g. chemical For Duhem, the continuity of scientific between the mechanistic and energetic methods (new mechanics) obtained by using, at least as an analogy, the Lagrangian formalism to construct axiomatic thermodynamics. is undertaken by Gibbs, applying thermodynamics as unifying for Thermodynamics, constructed, provides foundations of chemistry-physics, not mechanics. This successful unification gives rise to promising program to implement thermodynamics as the new unifying framework. Lagrangian with its principle D'Alembert and its principle virtual as a powerful mathematical be in without it mechanical physics. The development the generalization and abstraction of Newtonian structure of mechanics in Duhem's book The evolution of mechanics (Duhem 22-46). As a result of this generalization abstraction, one gets rational mechanics as constructed by Lagrange and to which D'Alembert and (Duhem 1980, 23). This mechanics reduces all laws equilibrium and motion to single principle (the principle of virtual velocities) and to single of calculation calculus). Duhem's Critical of Mechanicism and Defense of a of Theoretical José N.
, Galileo, and Newton; and betweeN Newton and lagraNge. furThEr, thIs viEw accounts for tHE conTinuity between Lagrange And enErGEticS. to Make tHis cleaREr: FROm DEsCaRteS aND GAlileO to newton wE go from a seT of DiSconnected geNErAl laws, such As iNertial law, thE laW of falL, KEplER's lawS, anD the cOllisiON laws, tO a more genErAL and abSTract stRUCtUre fOrming a rigid axiomATiC System of concepTs and pRiNCiPLEs tHat Encompass tHeSe lawS. this axiOMaTIC StrUCture is vectorIal mechanicS, ThaT accouNtS foR All theSe lawS, wHIch Means that it ProvIdes the unIficatIOn of the TErrestrIal and CelEstIal lAWs. veCtoRiAL meCHaNicS Is bAsed upon ThE iDea thAt boDIES Are cOmpOsed Of isoLated mass poinTs, tWo veCTorS, forcE and mOmenTuM, four Laws, EuClideAn Geometry, and the pAralLelogram rUle. frOm NEwTon to lAgrangE, we MovE from veCtorial MEchAnICS To A mechanics based upoN eNERgY, generalIzed coORdInATes, which Is AppLied TO A systEm of BOdIes insteAd of isOLaTeD mass poInTs. From ThE LaGraNgian MEthoD to the EnergetiC methOD, Duhem wants to mOVe from local moTIoNS (VeLOcitY) to General motiOns (e.G. ChemIcal REaCtiONs). For duhem, ThE CoNTinuity of scientific PrOgress BetweEn the mechanisTic and enerGETIc methodS (new MEcHAnics) is obtaineD by usIng, at least AS an analoGy, the lagrangiAn formaliSM To constrUct AxiOmaTic THErModynamics. ThiS TAsk iS uNdertakEn bY Gibbs, bY apPlyIng TheRmOdynamics As the uniFyInG fRaMewOrk foR Physics. THeRmoDyNamIcs, so COnstruCted, pRoviDeS tHE foUndatioNS oF CHemiStRy-PhysIcs, NoT mechAnicS. thiS succesSful unifiCatIOn giVeS rIse to a pRomising progrAm To implemenT tHerModynaMICs as the nEw unifying framework. DuheM InterprEts lagraNgiaN formalisM, wiTh its pRinCIple of d'AlembErt anD iTs pRINciplE OF vIrtUaL work, as a poWERfuL mathEmAticAl instrUment to be applied in ANy pHysical domain WitHout TURnIng IT iNTo mEcHAniCAL physics. The deveLopment towArD ThE generalizATioN aNd abstrAction oF the NEWtonian Structure Of mechaniCs Into lAGraNgian mechaNics is deScribed in dUhem's BOoK The eVolUtion oF mEchAnics (duhem 1980, 22-46). AS A reSult oF this gEnEralizAtion AnD abstracTion, one gets rational mechAnics aS consTruCted by LagRanGE anD to which BErnoUlli, D'AlembErt And euler ConTRibutEd (DuHEm 1980, 23). thiS MechaNics REduces all LAwS of EQUiLibrium and mOTIOn tO a sinGle PRincipLe (thE principle of virtuAL velocities) and To a sINGle MetHOd of CaLculation (variaTioNaL CAlculus). DUhEm's Critical analysis Of mEchanIcism aNd his DEfense oF A foRMal ConCeptIon Of TheoretIcaL PHYsics JoSé r. N. cHiappiN – Cá
, Galileo, and Newton; and  between N ewton  an d L ag rang e. F urther, this v i ew a ccounts for the contin uitybe t ween La grang e and e n er g e tic s.  T o m ak e  t his c lea rer: fr om Descart esan d Galileo to Ne wton we go  fr om a set ofdis connec te d g e neral  la ws, s uch as inerti al law, t he law of fall, K e p le r'slaws, and the col l is i on laws, to amore g en e ra l and  ab stract str uc turef orminga  r i g i d a x iomatic syste m of concep t s a nd pri nc ipl e s that  enco mp a ssthese laws.  Thi s axiomat ic str u cture i s  vector ial me cha nic s, t h at  a cco un t s f o rall the se laws,  w hi ch me anst h a t  itpro vide s the  unificationofthet err estri al an d ce le stial  laws.  Vect or ial mechanics i s ba sed uponthe  i dea  t hat b o dies a recom posed o f isola t edma s s po ints, two vectors,  f o r ce  and mom entum, fo ur laws, Eu cl ide an g e o metry , an d  t he paral lelogr a mru le. Fro mNewton  t o L agr ange, we m ove fr om vecto rialm echanics to am echanics base d  u p o ne nerg y,generalized  coo r dina tes, wh ich is ap plied  t o  a system of bodies in st ead of  isol ated mass poi nts. Fromt h e  Lagrang ianm et h od to the ener getic  method, D u hem want s tomove fro m local m o t ions (ve loc ity ) t o g e n er al motions (e . g . ch em ical re act ions).For  Du hem , t he  continui ty of sc ie nt if ic  pr ogres s  between  t heme cha nisti c  and e nerge ticme th o ds(new me c ha n i cs)is  o btai ned  b y usi ng,a t l east as  an analo gy, theLa gr angianformalism toco nstruct ax io mat ic the r m odynamic s. This task is underta k en by G ibb s, by  app lying the rmo dynami csa s theunifyi ng fr am ewo r k  forp h ys ics .Thermodyna m i cs,  so c on stru cted, p rovides the founda t ion s of chemistr y-p hysi c s ,not me c han ic s . T h i s successful un ificationgi v es  rise to a pro mi sing pr ogram t o imp l ement t hermodyna mics as t he  new u nif ying frame work. Du hem inter p retsL ag rangi anformal is m,withits pr i nci ple o f D'Al em bert a nd it sprincipl e of virtual work, as a  power ful m ath ematicalins t rum ent to be  app lied in an y p hys icaldom a in wi thou t  t urn i ng it  int o  mechanic a lphy s i cs . The devel o p m ent  towa rdt he gen eral ization and abstr a ction of the N ewto n i anstr u ctur eof mechanics i nto  L a g rangianme chanics isdescribe di n Duh em's b ook Th e evolu t i on of mec hani cs(Duhem 19 80,  2 2 -46). A sar esultof t hi s gene raliza t iona n d abstraction, o ne ge t s  rati o nal  mech an ics asc onst ructed byLagrange an d to w hich  Bern oulli,D' Alembe rtan d Euler co n tributed(Duhe m 1980,  2 3).Thi s mech anic s reduc es a ll  la ws of equ i l ib r iu ma ndmoti on to  a  sin gle princ i ple (the  pr i ncipleof  vi r t ual ve l oc i t ies) and t o a  sing l e  method of calc u la t ion ( variat ionalcalculu s ).Du hem's C rit i c al Analys is of Mec h ani ci sm a nd his D ef ense  o f a  F ormal Conceptio n of The oretical P hysics  Jo s é R. N. Chi ap pin – Cá
, Galileo,_and Newton;_and between Newton and_Lagrange. Further,_this_view accounts_for_the continuity between_Lagrange and energetics._To make this clearer:_from Descartes and_Galileo_to Newton we go from a set of disconnected general laws, such as inertial_law,_the law_of_fall,_Kepler's laws, and the collision_laws, to a more general_and abstract_structure forming a rigid axiomatic system of concepts_and_principles that encompass_these laws. This axiomatic structure is vectorial mechanics, that_accounts for all these laws, which_means that it_provides_the_unification of the terrestrial_and celestial laws. Vectorial mechanics is_based upon the idea that bodies_are composed of isolated mass points, two_vectors, force and momentum, four laws,_Euclidean geometry, and the parallelogram_rule. From_Newton to Lagrange, we move_from vectorial mechanics_to a_mechanics based upon_energy, generalized coordinates, which is applied_to a system_of bodies instead of isolated mass_points._From the Lagrangian_method_to_the energetic_method, Duhem wants_to_move from_local_motions (velocity) to general motions (e.g._chemical_reactions). For Duhem, the continuity of scientific_progress between the mechanistic_and_energetic methods (new mechanics)_is obtained by using, at_least as an analogy, the Lagrangian_formalism to_construct axiomatic_thermodynamics. This task is undertaken by Gibbs, by applying thermodynamics as_the unifying framework for physics. Thermodynamics,_so constructed, provides the_foundations of_chemistry-physics,_not mechanics. This_successful_unification gives_rise to a promising program to implement_thermodynamics as_the new unifying framework. Duhem interprets_Lagrangian formalism, with its_principle_of D'Alembert and its principle of_virtual work, as a powerful mathematical_instrument to be applied in_any_physical_domain without turning it into_mechanical physics. The development toward the_generalization and abstraction_of the Newtonian structure of mechanics into_Lagrangian_mechanics is described in Duhem's book_The_evolution of mechanics (Duhem 1980, 22-46)._As_a_result of this generalization and_abstraction, one gets rational mechanics as_constructed by Lagrange and to which Bernoulli, D'Alembert and_Euler contributed (Duhem_1980, 23). This mechanics reduces_all_laws_of equilibrium and motion to a single principle (the principle_of virtual_velocities) and to_a single method of calculation (variational calculus). Duhem's Critical Analysis_of Mechanicism and his Defense of a_Formal Conception of Theoretical Physics José R. N. Chiappin – Cá