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Metodos didacticos y sistemas de aprendizaje: Teneduria de Libros y Partida Doble en Inglaterra (siglos XVI-XIX).

I

La inmensa mayoria de autores de tratados sobre teneduria de libros, de los siglos XVI y XVII, ejercian la docencia de la materia. El metodo de exposicion que eligieron estuvo influido por la actitud contemporanea para ensenar las disciplinas academicas y la teoria contable que de forma consciente o inconsciente sostenian cada uno de ellos.

El Libro Diario era la piedra angular del sistema italiano de cuentas, compuesto por tres libros. El objetivo primordial de la ensenanza de teneduria de libros era la debida ordenacion del Debe y el Haber en ese libro. Una anotacion en el diario era algo que debia realizarse
   ... in a strict Form, and with all the Consideration and
   Discretion imaginable; and it will not be done hastily,
   unless it be a very plain Matter; but requires the solitude
   of a Compting-House, or Retirement from all manner of
   interruption (1).


La historia de la ensenanza de la teneduria de libros hasta, en la practica, finales del siglo XIX, es la evolucion de la metodologia utilizada para explicar como averiguar que cuentas son de cargo y de abono y como debe realizarse la anotacion en el Libro Diario.

El metodo habitual que siguieron los manuales hasta el siglo XVIII fue el de presentar gran cantidad de reglas aplicables a casos concretos de las mas variadas operaciones. Sorprendentemente, la excepcion mas destacable la encontramos en el primer tratado ingles sobre teneduria de libros, obra de Hugh Oldcastle, que ha llegado hasta nosotros por la reedicion de John Mellis, en 1588. La version original, de la que no se conservan ejemplares, se publico en 1543 (2). Segun Oldcastle/Mellis, cada anotacion en el Diario posee
   ... two denominations: to wit, by Debitor, and Creditor,
   whereof the first is the name of Debitor, reciuer or
   borrower: and the other of the Creditor, deliuerer,
   lender. To the furtherance whereof there is a Rule,
   which being well understood, will aide you greatly:
   which Rule is to bee learned as well by rote, as by
   reason, which is thus.

      All thinges receiued, or the receiuer must
         owe to all thinges deliuered, or to the
         deliuerer (3).


No se efectuo ninguna mejora de esta regla en los dos siglos siguientes. El Profesor P. Kats, en 1926, al percatarse de que esta norma no se encuentra en el tratado de Pacioli, del que el de Oldcastle es una traduccion, opina que corresponde al primer tratado de Peele, publicado en 1553 (4). La aportacion de Peele esta mas en consonancia con el resto de autores de los siglos XVII y XVIII. El metodo de Peele consiste en dar un ejemplo de transaccion (cuarenta y cuatro en total), al que sigue su correspondiente anotacion en el Diario, referenciandola en el resto de libros. Veamos tres ejemplos:
      [??] Money reciued of a debitour.
   You shall make the money reciued, debitour
   to the man that did pay it, as in the 37.
   parcell.

      [??] Money paied to the Creditour.
   You shall make contrariwise the man debitour
   to the money paied to hym, as in the. 38. parcell.

      [??] To deliuer a Debitours bill to a Creditour.
   You shall make the man that reciueth the bill,
   debitour to the other man, that ought your
   money by the bill, as in the. 39. parcell (5).


En su segunda obra de 1568, mucho mas extensa y detallada, el Maestro (Scholemaster), pronuncia las mismas palabras que mas tarde repetiria Mellis en su edicion de Oldcastle, aunque el discipulo (Scholler) dice que es capaz de responder de memoria, pero sin utilizar razonamiento alguno (I am alreadie able to aunswere (...) by rote, but the reason thereof I understande not) (6). La franqueza del discipulo esta compensada con un numero mayor de ejemplos, cada uno seguido de su cargo y abono. El numero de ejemplos en esta ocasion asciende a 187.

II

Ya en el siglo XVII, la norma general permanecia y el numero de ejemplos se acrecentaba. Richard Dafforne, en The Merchants Mirrour (1635) -el primer tratado en lengua inglesa que conocio numerosas ediciones-, presenta quince reglas de ayuda (Rules of aide) que nos ofrecen un retrato de la actitud y metodologia de presentacion del maestro. Las cuatro primeras son las siguientes:
Rules of aide, very requisite in Trades continuance, to be
learned without booke.

1. Whatsoever commeth unto       1. Whatsoever goeth from us
us (whether Mony, or             (whether Mony, or Wares) for
Wares) for Proper,               Proper, Factorage, or Company
Factorage, or Company            account, the same is
account, the same is             --Creditor.
--Debitor.

2. Whosoever Promiseth, the      2. Unto Whom wee Promise,
Promiser--Debitor.               the Promised man is
                                 --Creditor.

3. Unto whom wee pay             3. Of whom wee receive
(whether with Money, Wares,      (whether Mony, Wares,
Exchanges, Assignations)         Exchanges, Assignations)
being for his owne               being for his owne account:
account: that man is--Debitor.   that man is--Creditor.

4. Unto whom we pay (as          4. Of whom wee receive (as
above) for another mans          above) for another mans
account:                         account:
The man for whose account        The man for whose account
we pay is--Debitor.              wee receive is--Creditor. (7)


Las reglas pretendian cubrir todo tipo de operacion que un tenedor de libros pudiera encontrarse. Con tal fin las normas se fueron ampliando hasta finales del siglo XVIII. En su The Apprentices Time-Entertainer ... (1670), Richard Dafforne dobla el numero de sus normas de ayuda (rules of aide), si bien parece valorar el papel que puede desempenar la memoria. Asi, como elemento nemotecnico, traduce las reglas que Johannes Buingha recoge en su tratado holandes de 1627 (8):
Who the Debitor is, or oweth     Who the Creditor is, or must have

Is Debitor                       Is Creditor

1. What we have                   1. Whence it arriveth
2. Whoso receiveth                2. Whoso giveth out
3. What we buy                    3. Of whom we buy
4. Unto whom we sell              4. That which is sold
5. For whom we buy                5. They of whom we buy
6. Whoso must pay                 6. They that must have
7. For whom we pay                7. Wherewith we pay
8. What we cause to be insured    8. The Assuror
9. For whom we insure             9. Insurance reckoning
10. Whither-wards we send        10. What we send away
11. That which is gained upon    11. That which is lost
12. Profit and Loss              12. Profit and Loss (9)


La costumbre de incorporar casos o ejemplos numerosos prosiguio en el siglo XVIII. Edward Hatton en su obra The Merchant's Magazine (1701) presenta veintinueve casos para "Proper [sole traders] accounts in Domestick Trade"; dieciocho para "Accounts proper in Foreign Trade"; seis para "Factorage [agent's] Accompts in Domestick Trade"; cinco casos de "Factorage Accompts in Foreign Trade"; y dieciseis de "Company [partnership] Accompts" (10).

Charles Snell, despues de su tratado Rules for Book-keeping According to the Italian Manner ... (1701), publicado el mismo ano que el de Hatton, que consta de once paginas de normas, de un total de setenta (11), escribio el volumen The Merchants Counting-House (1718), que se compone de sesenta y nueve reglas (12). William Taylor en su libro A Complete System of Practical Arithmetic (1783) tan solo incorpora veintiuna normas, quizas porque se ocupa de la partida simple y doble en una breve extension de veintitres paginas (13).

J.H. Lewis, por su parte, en el tratado The Quick and Easy Method of Teaching Book-keeping ... (1860), senala en el Prefacio que los estudiantes
   ... have been discouraged in their first attempts to acquire a
   knowledge of the art, as they were confounded by the multiplicity
   of rules and examples; for, the various entries in the Waste-book,
   Journal, and Ledger, being both numerous and prolix, made it almost
   impossible they should have a just conception of their tendency.
   For the sake of such, the Author of this work has therefore made
   the examples few and the rules for posting and balancing plain and
   easy to be comprehended. In short, he has endeavoured to unite the
   elementary instructions of the schoolmaster with the practical
   improvements of the merchant; and persons who understand this
   treatise will soon be able to comprehend the business of any
   counting house (14).


Lewis nos presenta cuarenta y siete reglas.

A pesar de tantos y tantos ejemplos y normas, los autores eran conscientes de la dificultad de aprender la materia mediante reglas, lo que les llevo a intentar una mejora en la presentacion de las mismas. Y asi lo hicieron de tres maneras: primero procuraron explicarlas con mayor claridad; segundo, las pusieron en verso; y tercero, se realizo una clasificacion de normas.

John Collins, por ejemplo, en su Introduction to Merchants Accounts (1653) se entrego a un analisis minucioso de las normas que rigen el registro de diversas secciones de la teneduria de libros, aunque por razones tipograficas, o de otra indole, nadie continuo con su labor pionera. Mucho mas popular fue la utilizacion de ripios como ayuda nemotecnica (15).

III

La versificacion tiene una larga y acreditada historia en la teneduria de libros. Domenico Manzoni en su Qvaderno doppio col svo giornale (1540) ya expone sus normas en verso:
   Nota che la Regola del Giornale & Quaderno, in se contiene sei
      cose, cioe
   Dare, Hauere, Qualita, Quantita, Tempo & Ordine.
   Dare significa douer dar, cioe il debitore, o uno o piu che siano.
   Hauere, uuol dir douer hauere, cioe il creditore, o uno o piu che
      siano.
   Qualita, sono quelle cose che tu maneggi, & siano di che sorte si
      uogliono.
   Quantita, e il numero peso ouer misura, o piccioli, o grandi che si
      siano.
   Tempo, si e il giorno, il mese, & l'anno, sotto ilquale tu fai la
      partida.
   Ordine, quello, che nella presente opera con facilita insegnamo
      (16).


Por lo que se refiere a Gran Bretana, es indudable que el padre de la versificacion en la partida doble fue James Peele, padre de George Peele, dramaturgo isabelino. Al comienzo del Diario que recoge en su primera obra, The maner and fourme, leemos:
      Rules to be obserued

   Yf that in this accompt, these preceptes ye obserue,
      than I you wel assure, no part therof shall swerne.
   To make the thinges receiuyd, or the receiuer,
      Debter to the thinges deliuered, or to the deliuerer.
      And to reciue before you write, and write before you paye,
      So shall no parte of your accompt, in any wyse decaye.
   Obserue wel these rules, your Iournall boke throughout,
      So shall you make sure worke, of that you go about (17).


Los versos de Dafforne, que encontramos al inicio de su Libro Mayor, recogido en The Merchants Mirrour, son mas sencillos:
      In Briefe,
   The Ower, or the Owing Thing,
   Or what-so-ever comes to thee:
   Upon the Left-hand see thou bring;
   For there the same must placed be.
         But
      they unto whom thou doest owe,
   Upon the Right let them bee set;
   Or what-so-eve doth from thee goe,
   To place them there doe not forget (18).


Aunque los poemas se fueron haciendo mas breves y el vocabulario se volvio mas sencillo, la versificacion se convirtio en algo habitual en el siglo XIX. P. Kelly, en The Elements of Bookkeeping; Comprising A System of Merchants Accounts (1801), una obra clasica de la epoca, podemos leer:
   By Journal laws, what I receive
   Is debtor made to what I give;
   Stock for my Debts must debtor be,
   And Creditor my Property.
   Profit And Loss Accounts are plain
   I debit Loss and credit gain (19).


Geo H. Boulter en el Prefacio de su tratado A Course of Bookkeeping by Double and Single Entry ... (1857), despues de citar los versos de Kelly, refiriendose al alumno, dice:
   He then posts them into the Ledger, wondering all the
   time why the same transaction is entered on the Dr.
   side, and again on the Cr. side, (for we must remember
   that the principle of Double Entry has not been
   explained to him) and sorely puzzled to discover the
   meaning of those mysterious terms Dr. and Cr. when
   applied to any other than personal accounts (20).


IV

La tercera y mas importante mejora que los docentes procuraron en el uso de las normas, se refiere a la clasificacion. Esta tendencia marca el comienzo de una busqueda: hallar una regla general y sencilla que fuera aplicable a cualquier tipo de operacion.

John Carpenter en su obra A Most Excellent Instruction for the Exact and Perfect Keeping Merchants Bookes of Accovnts ... (1632) agrupa las normas en varias categorias. Veamos las tres primeras del apartado que se ocupa "Of receiving and buying money by bils of Exchange":

1 If any one deliver you a Bill of Exchange, which you send to another; you are to make him to whom you send it, Debtor to him that underwrit it.

2 Contrarily, if you deliver a Bill of Exchange to any one, which you have taken up upon another, you shall make him to whom you deliver it, Debtor to him upon whom you have charged it.

3 When one accepteth a Bill of Exchange which is sent to you, you are to make him who accepted the same, debtor to him who sent it you (21).

Otro pionero en el campo de la clasificacion fue Thomas Browne. En su libro The Accurate Accomptant (1670) realiza un "Analysis", que ocupa una pagina doble, del tamano de un pliego, en la que intenta reducir una multitud de normas en una clasificacion coherente. Asi agrupa todas las normas referentes a mercaderias (wares or goods) y pasa a analizar las que se refieren a compras de la siguiente manera:
Bought   For ready Mony. Debitor, the Wares
           bought.
         Creditor, cash ...
         For Time. Debitor, the Wares bought.
         Creditor, the party of whom
           bought ...

         For part Mony, part time Debitor,      Creditor, Cash for so
           those Wares bought.                  much ready Mony paid
         In Barter for Wares. Debitor the       Creditor, the part of
         Wares received. Creditor, the Wares    whom bought the
           delivered.                           remainder.
         If both of equal value (22).


Mathew Quin, a su vez, hizo un recorrido similar en sus Quin's Rudiments of Bookkeeping (1776). Simplifico la clasificacion en seis casos. Cada uno de ellos es un ejemplo de un apartado de la teoria de teneduria de libros:

THE SIX PLAIN CASES proposed in the title of my present plan are these

1st. To form a List or Inventory of my whole stock to begin trade with; and another, of what Debts I owe.

2d, is Buying;

3d, Selling;

4th, Receiving;

5th, Paying, and the

6th, Balancing. (23)

Con todo, no seria hasta bien entrado el siglo XIX, cuando las tres reglas de oro -una por cada una de las tres cuentas mas importantes-, fueron generalmente aceptadas como metodo habitual de exposicion.

La metodologia didactica del enfoque del Libro Diario a la teneduria de libros y la aplicacion de normas se produjo como vamos a ver a continuacion. En primer lugar, hay que encontrar la norma en el libro de texto que mejor se ajuste a la operacion que hay que anotar; hay que cotejar el folio del Borrador y localizar la mencionada operacion en el Diario y en el Mayor. Esto es, en esencia, lo que Thomas King nos dice en las instrucciones de su manual An Exact Guide to Book-keeping (1717) (24).

Las instrucciones para profesores (Directions to Teachers) que Robert Hamilton recoge en A Short System of Arithmetic and Book-keeping (1788) son tipicas:
   In teaching book-keeping by double-entry, the chief point is to
   convey to the learner a distinct notion of the nature of Dr. and
   Cr. and the contents of the accompts in the ledger. After he has
   been thoroughly instructed in the eight principal rules for
   journalizing (...) and has carefully perused the detail of the
   ledger accompts (...) he is to proceed to transcribe a portion of
   the waste-book, and try the computations; then he is to write in a
   scroll-book that part of the journal which is printed in italics,
   which expresses the Drs. and Crs. of the several articles. When
   this is done, it is to be compared with the printed journal, or
   examined by the teacher; then the narrations are to be filled up,
   and a fair copy of the whole transcribed into the journal (25).


La ensenanza, a base de repeticion de memoria, parece que fue uno de los pilares mas fuertes de instruccion. John Matheson, en The Theory and Practice of Book-keeping (1818) propone un modelo de ejercicio para el alumno, que despues revisara su profesor:

Q. Sold A. B. ten puncheons of rum, per bill at six months, required the Journal Entry?

A. Bills receivable Dr. to Rum, because a bill is received in payment of goods delivered, per rule 4th (26).

Los rasgos pedagogicos mas significativos de los primeros 250 anos de docencia en teneduria de libros quedan aqui expuestos de forma admirable. En primer lugar, se destaca el Diario como libro importante de registro y, en segundo lugar, el uso de reglas para determinar la anotacion que sea menester.

Y, al mismo tiempo, autores y docentes se empenaban en una mejora de los metodos de ensenanza que redujeran las grandes limitaciones que aquellos metodos podian tener. En concreto, es de destacar el desarrollo de los ejercicios para los alumnos. En los textos mas tempranos, la teoria de la materia, por lo general, estaba ilustrada con un juego de libros (Borrador, Diario y Mayor), si bien, habrian de pasar mas de 150 anos para que se reconociera el valor del Borrador como ejercicio para el alumno.

Al comienzo de The Merchants Mirrour (1636), Dafforne escribe una epistola "To the Book-keeping Teachers" en la que, entre otras cosas, dice:
   Daily experience approveth, that we which submit our selves to
   teach several Mothers children, are subject to the censure of many.
   Neverthelesse, I have imboldened my selfe to divulge this part of
   my labour, it being the first since I pitched my abode in London;
   but particularly (as very requisite) I dedicate the First and
   Second Waste-bookes unto you, not as teaching, but necessary
   assisting bookes: especially for such as have no opportunity to
   compile a Waste-booke for their Schooles proper use.

   Here you have matter to exercice your Scholars in diversities of
   accompts, and after severall manners of entrances, for the
   effecting of the same: the like (though spoken by mee) I have
   not seened presented to my nation (27).


Con estas palabras nacia el primer libro de ejercicios de teneduria de libros. Anos mas tarde, Dafforne, en The Apprentices Time-Entertainer (1640) alude a dos Borradores para ejercicios y anade:
   Here in these two Waste-books (which, by the scarcity of
   them in General, seem to be very difficult in their
   Composition; else they would be more common in our
   Schools ...) (28).


Ya en el siglo XVIII, Alexander Malcolm, en A Treatise of Bookkeeping, or, Merchants Accounts (1731) senala que los estudiantes deberian utilizar los ejemplos del Borrador:
   ... as there is a great Variety of Examples of Business in
   the two Waste-Books, they may considerer those as so
   many Questions proposed, in order to find the Debtors
   and Creditors; (which is the Purpose of all the tedious
   Instructions given in the Way of Question and Answer)
   and in the Journal they have the solutions (29).


Medio siglo despues Robert Hamilton continuo con esta linea en los "Sets for Practice" de su tratado An Introduction to Merchandize (1777). Y como prueba de perfeccionamiento en la presentacion, dispuso dos ejemplos de Borrador y Diario en paginas opuestas para que el lector los pudiera comparar (30).

A finales del siglo XVIII el Borrador se habia convertido en un buen utensilio para la practica. J.H. Wicks, "Master of the Boarding School, Englefield-House, Egham, Surry", incorporo como materia de curso de su texto Book-keeping Reformed ... (1797) un segundo Borrador para aquellos que deseasen realizar mas practica (31). Prometio publicar un Libro Diario y un Mayor para uso de los docentes, aunque si lo hizo, nosotros no hemos dado con su rastro.

No obstante, los ejercicios del Borrador eran extraordinariamente largos. La practica de acompanar la teoria de la materia con un juego completo de libros y uno o mas Borradores fue habitual hasta bien avanzado el siglo XIX. Asi, el libro de Hamilton y Ball, Book-Keeping (1869), texto que fue muy popular entre 1870 y 1890, recoge que ambos fueran examinadores de la Society of Arts. Dispone de un unico y extenso ejercicio, que contiene gran variedad de operaciones, todas ellas desarrolladas en su totalidad (32). J. Thornton en su texto First Lessons in Book-keeping (1879) considera digno de destacar que, en lugar de una serie de ochenta o cien transacciones, lo que significaria un trabajo de seis meses, el tan solo ofrezca una serie breve de tres con la que comenzar (33). G. F. C. Vernon publico, en 1893, Sets for Practice in Book-keeping. Se trata de un libro de ejercicios. El autor senala en el Prefacio:
   Long experience has taught the Author the necessity of
   providing his Pupils with such sets for practice as may be
   properly worked within the limits of one or two lessons.
   The sets in the present collection have actually been
   worked out with classes, under these conditions (34).


A comienzos del siglo XX, el Borrador, primer libro del sistema italiano, se habia transformado. Habia pasado de un registro de innumerables y miscelaneas operaciones a una serie de ejercicios breves directamente relacionados con el capitulo correspondiente del libro de texto. Es interesante especular hasta que punto la evolucion del Borrador en un libro de ejercicios ha fraguado en la practica de ensenar teneduria de libros con operaciones recogidas en un manual en lugar de hacerlo con documentos reales. Esta tecnica, sin duda, separo todavia mas el aula de los negocios.

V

La exposicion mediante la repeticion de un conjunto de normas oculto el hecho de que los autores de libros de texto sostenian, de forma consciente o inconsciente, una de las dos teorias de cuentas existentes. Esto es palmario por las contadas ocasiones en las que los autores intentan explicar o razonar sus normas. Por una parte existia un grupo que pretendia personificar las cuentas, mientras que, por otra, nos encontramos con un grupo reducido, con cierto peso en Estados Unidos, que sostenia lo que podemos denominar como teoria de cuentas de propiedad (ownership).

La atribucion de una personalidad viva e independiente tiene sus raices en las primeras formas de la teneduria de libros. Cuando menos tuvo dos fuentes. En primer lugar, no cabe duda de que los primeros Libros Mayores mostraban las relaciones de deuda entre comerciantes (35). Con el desarrollo del sistema de la partida doble, los terminos deudor y acreedor se hicieron extensivos, en primer lugar a cuentas de objetos (cuentas de existencias) y, posteriormente a clasificaciones abstractas (cuentas nominales). Por consiguiente, se hizo habitual ampliar el significado de los terminos debito y credito mas alla de la connotacion personal original y aplicarlos a objetos inanimados y conceptos abstractos. El proceso en si mismo forjo un instrumento pedagogico.

Otra fuente que impulso el concepto de la personificacion es la practica de registrar las relaciones financieras entre el propietario de una hacienda y su administrador o contable en la forma de una cuenta de cargo y abono. El administrador se cargaba con la parte de la propiedad que se le habia confiado, incluidos todos los recibos aceptados en representacion del senor y se abonaba con los gastos realizados en nombre de su patron y el dinero pagado al propietario de la hacienda. El uso del termino cargo se amplio desde su aplicacion personal a la de cuentas de cargo. Cualquiera que fuera su origen, la practica de explicar como deben anotarse las partidas en el Libro Mayor, mediante la personificacion de cuentas, la encontramos en los primeros tratados britanicos y guarda una estrecha relacion con el origen del sistema de teneduria de libros.

Podemos identificar tres formas principales de personificacion. En la primera se considera a la cuenta como una entidad independiente y viva. En la segunda, la cuenta representa al propietario del negocio. Finalmente, existe una combinacion de estas dos formas en la que imaginamos que la cuenta es un individuo distinto del propietario, aunque el sea el ultimo responsable. Estas tres formas, con frecuencia, estan entrelazadas de modo inextricable en cualquier texto y, desde el punto de vista historico, se fueron desarrollando al unisono.

La forma original veneciana de una partida del Diario era prologar la cuenta en la que se cargaba con un PER y la cuenta de abono con una A. Estas palabras eran meros terminos tecnicos que habian perdido su significado gramatical. A la hora de traducir, los autores no encontraron terminos ingleses que correspondieran directamente y se manifestaron reacios a acunar unos nuevos. Asi, para los terminos italianos debito y credito, entendieron que correspondian a oweth y trusts, terminos de relacion que solo son aplicables a personas. Partidas que en el tratado de Pacioli tenian la forma "PER caja, A capital", despues de la traduccion de Oldcastle adoptaron la forma "Money oweth to Thomas Lee". El dinero (money) adquiria una existencia personal independiente. James Peele utilizo una secuencia de palabras similar. A su vez, el enigmatico W. P., en su tratado The Pathway to Knowledge (1596), anota las partidas del Mayor con la frase Peter Garetson ought to give to money ..., cuando se trata de cargar en la cuenta personal. Y utiliza las palabras ought to have of cuando son cuentas acreedoras. Estas frases indican la imagen mental que los autores tenian del dinero y de otras cuentas de existencias: les atribuian cualidades humanas (36).

A comienzos del siglo XVII las partidas del Diario ya eran muy similares a las modernas en su forma: X Debtor to Y. De esta expresion de la partida es de donde se deriva la explicacion. En la obra de Richard Dafforne, The Merchants Mirrour, se produce un dialogo entre el maestro "Philo-Mathy" y el discipulo "School-Partner" en los siguientes terminos:
   Phil. How booke you the Ready mony after the way of
   Debitor and Creditor?

   Sch. Cash Debitor to Stocke.

   Phil. Why make you Cash Debitor?

   Sch. Because Cash (having received my mony into it) is
   obliged to store it againe at my pleasure: for Cash
   representeth (to mee) a man, to whom I (only upon
   confidence) have put my mony into his keeping; the
   which by reason is obliged to render it backe, or, to give
   mee an account what is become of it: even so, if cash be
   broken open, it giveth mee notice what's become of my
   mony, else it would redound it wholly backe to mee (37).


La cuenta de caja, que Pacioli denomina "cassa", y que Oldcastle traduce de forma erronea por chest, es la cuenta mas facil de personificar, pues el receptaculo para el almacenamiento de monedas lo podemos imaginar y verlo como receptor (receiving) y pagador (paying).

El concepto de personificacion, por extension, se aplico a objetos inanimados (cuentas de existencias), en lo que Alexander Malcolm denomina "... artificial and improper Sense, which is borrowed from Persons". Asi lo afirma en 1731 en el tratado que ya hemos considerado, A Treatise of Book-keeping. Y anade:
   ... when any Thing becomes mine, I consider it as a
   Subject which owes, or is accountable to me for such a
   Sum of Money as it has cost me, either in Specie, or
   other Effects, or I owe for it, or which I expect to make
   out of it (cost what it will) ... (38).


En The Pathe waye to perfectness (1569), James Peele, por boca del maestro, es mas explicito y advierte al discipulo:
   Then marke me well, and I declare the same to you in
   few wordes. where as I saide before, that the thinges
   receaued must owe, I meane therby that the goodes
   bought, or monie receaued of anye man, must in all
   percelles be made debetour, (that is to saye) to owe
   unto the parties of whom it is receaued or bought. As for
   example, Imagine that you haue bought clothes of
   William Jones, then obserue the rule you must enter the
   percell in your Journall sayinge, Clothes oweth to William
   Jones. & c. Yf you receaue monie of anye man, accordinge
   to the same rule you must saye, Monie oweth to Frauncis
   Taillor. & c. and hereby it apperes in that parte, howe
   the same rule is obserued, contrarie wise if you sell
   goodes, or paye monie to anye, then to the obseruinge
   of the same rule, you shall saye, William Thomsome & c.
   oweth to clothes, or Jhon Ball & c oweth to money (39).


Una explicacion, o razonamiento, de este metodo de exposicion lo encontramos en The Accountant and Geometrician de Benjamin Donn (1765):
   As I may expect to make of [sell] my Goods as much as
   they cost me, they are in Effect the same to me as if
   their Value was due to me from some person: and as, in
   such Case, that Person would be Debtor, so I may make
   the Goods in my Possession Debtor for their first Cost (40).


Otro desarrollo del principio de la personificacion fue la evolucion de la idea de que las cuentas que no sean personales tambien representan al propietario. Edmond Degrange, en su tratado La Tenue des livres rendue facile (1795), es uno de los pioneros en senalarlo:
   ... pour se faire une idee exacte de ces comptes, il ne
   faut voir en eux que ceux du negociant dont on tient les
   livres, et il faut concevoir que debiter l'un de ces
   comptes, c'est debiter le negociant lui-meme, sou le
   nom de ce compte en particulier.

   C'est sur cette inv41ention qu'est fonde l'art de tenir livres
   en partite double (41).


No obstante, la idea basica puede derivar de los primeros ejemplos de teneduria de libros por partida doble (42). Se entendia que el propietario debia registrarse dos veces para cada una de las transacciones.

Por ejemplo: si se compraban mercaderias a credito a Z, el analisis que se derivaria es, siguiendo al Profesor Littleton: "Goods shall give to propietor (who now places the responsibility upon that account), Z shall have or receive from propietor (what Z now places in his hands)" (43). Una ampliacion de este concepto la encontramos en Degrange: el propietario queda registrado en todas y cada una de las operaciones y con el fin de no entorpecer su cuenta personal con una partida por transaccion, propone sus comptes generaux, representando todas ellas al comerciante (44).

El concepto de que las cuentas representan al propietario pronto gano terreno en Gran Bretana. Asi, a mediados del siglo XIX James Henry Lewis, en su ya mencionado tratado The Quick and Easy Method of Teaching Book-keeping ... (1860), explica:
   ... by an ingenious and useful fiction, which has long
   been employed in book-keeping, the article received is
   always made Dr. to the person from whom it was
   received; and the person who receives an article is
   always made Dr. to the article which he has received. So
   that, instead of the merchant's name standing as Debtor
   or Creditor in his own books, he is personated by the
   goods: this is uniformly the practice in keeping books,
   whether the article received be goods, cash, or bills (45).


La direccion que tomo el desarrollo de esta idea la podemos observar en un extracto de la obra de Philip Crellin, Bookkeeping for Teachers and Pupils (1892):
   It is, indeed, the trader himself who is the owner of this
   property, it is he who receives and parts with it, and it is
   he who, it may be thought, should be debited and
   credited rather than "Goods". But the trader, it must be
   remembered, has several kinds of goods, has cash, and
   bills, and fixtures, and leases, & c. and if all transactions
   occurring in these various forms of property were
   brought together into one account and entered under his
   name, it is evident that it would be very voluminous,
   and that it would be impossible without great waste of
   time to ascertain particulars regarding any one of them.
   Hence the advantage of sorting these several items,
   bringing together all that relate to the same thing,
   naming the accounts correspondingly, and treating them
   in the way of debiting and crediting as if they were
   living persons having charge of, and responsible for, the
   property to which they refer (46).


No obstante, con el fin de indagar mas en esta forma de personificacion debemos volver sobre nuestros pasos.

VI

La teoria de la personificacion mas completa surge cuando se otorga una identidad personal a las cuentas de las que es responsable el propietario, aunque desde una perspectiva material sean completamente independientes.

A la quinta edicion del tratado Elements of Arithmetic (1846), de Augustus de Morgan, se incorporo un anejo titulado "On the main principle of Book-keeping". Es, con toda probabilidad, la pieza mas influyente en la docencia de la teneduria de libros que se publico en el siglo XIX. Por lo que a la personificacion respecta, hizo explicito y amplio, hasta su conclusion logica, lo que con anterioridad estaba implicito en los metodos de ensenanza. Con este texto se inicia el movimiento que finalmente desemboco en el rechazo del Diario, principal escollo en el aprendizaje de la materia.

Indicios de la idea de de Morgan sobre la responsabilidad que los escribanos adquieren al asentar partidas en los libros de cuentas ya se aprecian en la obra de Richard Hayes, Modern Book-keeping (1731):
   Now observe that each of those Particulars your Inventory
   does consist of, are therefore made Debtor to Stock
   [Capital] in your Leger, because they are in Effect so
   many Stewards to whom you intrust your Estate, and
   each of them are accountable to you for their several
   Parts of it (47).


Al ano siguiente, en un libro del que no se conservan ejemplares, Lectures on Accompts (1732), de J. Clark, la teoria de la personificacion se expresa en unas palabras que anos mas tarde, B.F. Foster recogio en su obra The Origin and Progress of Book-keeping (1852):
   Lectures on Accompts; or Book-keeping after the Italian
   manner, in which the fundamental principles of the art
   are laid down, and some of the most material accompts
   exemplified and explained. By JOHN CLARK, Writing
   Master, & c. London, 1732.

   "Let it be supposed," says Clark, "that the account of
   Stock is a real person employed to take care of my state
   and to render an account of the improvement he has made
   of it. In a like manner, Cash, and all other accounts
   which I may have occasion to keep, may be considered
   as persons employed by Stock to take care of that part
   of my state with which they are entrusted, and to
   render an account thereof to Stock. Then Cash, or the
   person entrusted with the care of my money, owes to
   Stock so much as he is entrusted with. Upon this hypothesis
   every transaction must be considered as though it had
   been transacted between persons who managed affairs
   for me. For there can be no business transacted but
   between two or more persons; and as there is no such
   thing as a person being debtor, but that he must owe
   some other person, and for that reason whom he oweth
   is called creditor. Hence, if the ledger is to contain an
   exact register of all my transactions, they must be
   doubly or twice entered; that is, the sum that any person
   oweth must be entered in his account that oweth, and
   also in the person's account he oweth it to ..." (48).


El breve apendice de de Morgan sobre teneduria de libros, que propone la personificacion absoluta de todas las cuentas en la persona de un escribano u oficial no fue, segun acabamos de ver, una propuesta novedosa por completo. Lo que si hizo fue aparecer en un momento oportuno para adoptar una nueva metodologia docente. La relevancia de de Morgan contribuyo a la aceptacion y desarrollo de la nueva idea (49):
   The accounts are kept as if every different sort of account
   belonged to a separate person, and had an interest of its
   own, which every transaction either promotes or injures.
   If the student find that it helps him, he may imagine a
   clerk to every account: one to take charge of, and
   regulate, the actual cash; another for the bills which the
   house is to receive when due; another for those which it
   is to pay when due; another for the cloth (if the concern
   deal in cloth); another for the sugar (if it deal in sugar);
   one for every person who has an account with the house;
   one for the profits and losses; and so on.

   All these clerks (or accounts) belonging to one merchant,
   must account to him in the end -must either produce all
   they have taken in charge, or relieve themselves by
   shewing to whom it went. For all that they have received,
   for every responsibility they have undertaken to the
   concern itself, they are bound, or are debtors; for
   everything which has passed out of charge or about which
   they are relieved from answering to the concern, they are
   unbound, or are creditors. These words must be taken in
   a very wide sense by any one to whom book-keeping is
   not a mystery. Thus, whenever any account assumes
   responsibility to any parties out of the concern it must be
   creditor in the books, and debtor whenever it discharges
   any other parties of their responsibility. But whenever
   an account removes responsibility from any other account
   in the same books it is debtor, and creditor whenever it
   imposes the same.

   To whom are all these parties, or accounts, bound, and
   from whom are they released? Undoubtedly the merchant
   himself, or, more properly, the balance clerk, presently
   mentioned (50).


James Collier en Bookkeeping by Double Entry (1884) y S. Dyer en A Common-Sense Method of Double-Entry Bookkeeping (1897) adoptaron por completo las ideas expuestas por de Morgan. Dice James Collier en su Prefacio:
   It is becoming an axiom in education that every subject
   taken up by the pupil should be made the means of
   exercising as many powers of the mind as possible, and
   not be merely an exercise of the memory. Hence we have
   appealed strongly to the imagination to create an array
   of clerks who must be anything but dummies, and we have
   reasoned out everything from the principles enounced.

   Some critics may object to the idea of clerks especially
   to Profit and Loss. We have, however, the authority of
   the late Professor A. de Morgan for this view. Will anyone
   assert it was not in the minds of the inventors of the art?
   Certainly in the course of some twenty five years'
   experience in teaching, we have constantly found it to be
   the "enlightening fact" to the learner, and the progress
   has commonly been in proportion to the learner's grasp
   of this notion (51).


Collier explica las nociones fundamentals de la teneduria de libros de la siguiente manera:

In Bookkeeping the whole business is supposed to be carried on by clerks. There is supposed to be a clerk called Capital or Stock who represents the owner of the business (or the Firm). There is supposed to be a clerk called Goods who takes charge of the merchandise. There is supposed to be a clerk called Bills Receivable who takes charge of all "Bills" payable by the Firm. There is supposed to be a clerk called Bills Payable who takes charge of all "Bills" payable by the Firm. There is supposed to be a separate clerk for each and every person or firm with whom the Firm has credit transactions, i.e. transactions in which a debt is incurred. There is supposed to be a clerk called Profit and Loss who--
RECEIVES:--                                     GIVES:--

All sums lost by the Firm,              All sums gained by the Firm
All money expended in Trade expenses,   All discounts allowed to the
All discounts allowed by the Firm,        Firm.
All money withdrawn by members
of the Firm.
These are all of the nature of          These are all of the nature
  Losses.                                 of Gains.


There is supposed to be a clerk called Balance of whom we shall speak hereafter. We shall often use the word Sundries, but Sundries is not a clerk. The word means "two or more clerks named below."

N.B.- These clerks mind their own business and do not interfere in another's department. Thus, if perchance "Goods" receives some money he instantly hands it over to "Cash" because he himself has no business with money (52).

Todas las operaciones se analizan en terminos de movimientos de valor entre los escribanos u oficiales (clerks). Por ejemplo, la primera regla es:
   RULE I.- In every transaction there is a clerk (A) who
   gets something of a certain value from another clerk
   (B). Then A is Debtor to B and B is Creditor by A for that
   amount (53).


S. Dyer utiliza exactamente el mismo metodo, que denomina e incorpora al titulo de su obra como A Common Sense Method of Double-Entry Bookkeeping (1897). La aceptacion de una personificacion absoluta estaba en consonancia con la oposicion al prendizaje de memoria, que se produjo en Gran Bretana en la segunda mitad del siglo XIX (54).

Al explicar la estructura de las cuentas mediante la forma de una relacion de deuda, los docentes reconocian, de modo explicito, la dificultad de presentar la teneduria de libros en terminos personales. Y, aunque un tanto inadecuados para explicar las partidas que se deben anotar en las cuentas personales, el significado de los terminos deudor y acreedor tuvo que llevarse hasta el absurdo a la hora de abordar las cuentas nominales y de existencias.

Edward Thomas Jones fue el primer contable que formulo un ataque frontal contra el sistema establecido de teneduria de libros por partida doble y, consecuentemente se burla de sus metodos de exposicion en Jones English System of Book-keeping by Single or Double Entry (1796):
   ... Why should a Merchant's, or tradesman's Book be stuffed with
   such ridiculous and mysterious nonsense, as appears on every leaf
   of those kept by Double Entry. - Such as "Sundry Accounts debtor to
   Sundry Accounts; -A. B. Dr to Wine; - Wine Dr to Profit and Loss:
   C.D. Dr to Deals, & c. & c. Now if A. B. owes Wine money, why not
   let Wine call for payment? But if A. B. do not owe Wine money, why
   make the entry in such way as only tends to confuse the mind of a
   person who is not a good accomptant? It will be replied, that this
   is necessary to form the plan of Double Entry. But as I am
   confident that no Man in WHOLE COMMERCIAL WORLD can take a set of
   Books, kept after the Italian Method, and prove in those Books that
   they are right, I shall insist upon it, that no persons in trade
   ought to keep their Books by that method, as they are continually
   liable to be injured by fraud or mistakes, and that therefore the
   Italian method of Book-keeping ought to be totally ABOLISHED (55).


B.F. Foster, siempre dispuesto a anunciar las ventajas de sus libros de texto y de su metodo, enseno, en exclusiva, en su "establecimiento" de Londres, situado en 161a Strand, no tuvo inconveniente en reproducir algunos ejemplos confusos como uno, que vemos a continuacion, tomado de The Whole Science of Double-Entry Book-keeping (1850) de Daniel Sheriff (56):

"Robert Henderson Dr. to Bills Payable.... 337.10s [libras esterlinas]."

"Elucidation.- Henderson is debtor because he owes us, we having paid him the amount that we owed him. Bills payable are creditor, because the note to which that title is given has paid Henderson for us; therefore we owe it" (57).

Podria ser interminable citar ejemplos similares de los textos contemporaneos. Collier, utilizando la personificacion completa de de Morgan, se ve obligado a explicar:
   When we write "Cash debtor to Goods 50 [libras esterlinas]," it
   does not necessarily mean that the cash-clerk owes the goods-clerk
   (the creditor) has discharged a debt of 50 [libras esterlinas]
   owing by him to the cash-clerk. It means that the cash-clerk has
   got (or received) 50 [libras esterlinas] from the goods-clerk and
   of course that the latter has parted with 50 [libras esterlinas]
   (or its value) to the former (58).


En pocas palabras: el significado aceptado de deudor y acreedor ni siquiera es satisfactorio en este contexto. Ridiculizar la exposicion del metodo de personificacion es muy sencillo. Asi, Charles Sprague, en Estados Unidos, llego a escribir una satira referente a como saldar el Libro Mayor, incluyendo el reparto. Se trata de The Bookkeeper (1882):
Stock, a merchant                  Profit-and-Loss, the economical
Balance, his accountant            business-manager.
Cash, keeper of the money chest    Expense, his subordinate,
Merchandise, a salesman            a spend-thrift, but good-hearted
Wm. Receivable, protector of the   Smith, Jones, Brown,
  portfolio                        Sundries, Wm. Payable, and
                                   others, friends and
                                   customers (59)


Esta obra literaria no estaba mas lejos de la realidad que algunos libros de texto.

La explicacion de las cuentas nominales es la bestia negra del enfoque de personificacion, pues estas cuentas son meras abstracciones. El problema de su explicacion no se hizo acuciante hasta mediados del siglo XIX, pues hasta esa fecha comerciar, en cualquier libro de texto, se consideraba una operacion con sus gastos correspondientes que se le debian imputar. De forma implicita, se recurria a la tecnica de cargo y abono que habia surgido de la relacion financiera entre el principal y el agente. Sin embargo, resulta imposible explicar beneficios y gastos en terminos de relaciones personales de deuda. Finalmente, se explicaron como partes de la cuenta de capital.

La exposicion mediante la personificacion de las cuentas solo fue un aspecto a considerar en el ataque contra el metodo del Diario en la ensenanza de teneduria de libros con un aprendizaje memoristico apoyado en normas y versificacion. Algunos autores de los primeros tratados ya criticaron el sistema de aprendizaje memoristico. Asi, Roger North, en The Gentleman Accomptant (1714), dice:
   I shall not in this my Understanding, labour very hard, or
   penetrate deep, by exaggerating Multitudes of Rules and
   perplexed Examples, as most Writers of this Subject
   have done; but in a familiar discursive Way, copy, as it
   were, my own Sentiments and Reflections, with all the
   Ease and Freedom, as I suppose one of my own Rank,
   accountable, as I am, only to himself and his Family, will
   be content to peruse. And for the Method, I shall here
   only pre-advertise, that I propose first to give a general
   Scheme or Description of the Art of keeping Accompts by
   Dr. and Cr. and then apply it to Practice, as well in the
   true Writing, as correcting Errors; and subjoin a fictitious
   Specimen, to render what is discours'd intelligible (60).


Malachy Postlethwayt, a mediados del siglo XVIII, en su tratado The Merchant's Public Counting-House (1750), especifica su programa para una institucion ideal que formase mercaderes. Al referirse a los maestros de teneduria de libros, dice:
   ... we shall, in a natural progression, proceed to explain
   systematically the axioms, and rational maxims and
   principles, whereupon the whole art of accountantship,
   as practised by the most skilful merchants, according to
   the method of double-entry, is grounded (...).

   This inimitable method of accounts being founded on the
   principles of reason, will prove a kind of practical logick
   to young people, when it is rationally and methodically
   communicated, not mechanically, and by rules depending
   on the memory only; wh61ich latter does not merit the
   name of instruction at all (61).


El metodo memoristico en la docencia de la teneduria de libros era tan frecuente que algunos autores eran reacios a incorporar la materia a su obras. Benjamin Donn, en su ya citado The Accountant and Geometrician (1765) afirma de forma incorrecta:
   As book-keeping is a Subject which has not hitherto been inserted
   in any Course of the Mathematicks, some perhaps may not considerer
   it as Part thereof (...). But if they would but consider, that,
   though Book-keeping has commonly been treated of and taught by Way
   of Rote, or arbitrary Rules without shewing the Reason of them; yet
   as the Subject is of great Utility, is now introduced and taught in
   all our Acedemies which qualify Youth for Business, requires no
   inconsiderable Knowledge of Numbers, and in capable of being
   treated of in a rational Manner (62).


Y, consecuentemente, incluye la teneduria de libros en su tratado de aritmetica.

De igual modo se expresa Alexander Malcolm en A New Treatise of Arithmetick and Book-keeping (1718):
   Tho' I do not pretend to a New Art, yet I have delivered the Rules
   of Book-keeping in a new Way. I proposed chiefly to explain and
   clear the Foundation, and give such Rules and Directions as might
   make the Practice a Work of Judgement rather than of Memory; every
   Thing in this excellent Art has a Reason which may, and ought to be
   shown: I have endeavoured this in laying down the first general
   Principles, and therefore in the rest I have nothing to do but make
   every Thing agree to these fundamental Notions, and answer the End;
   which is either manifest at sight, or I demonstrate it as any
   Difficulty occurs (63).


A pesar de todo, aunque los docentes eran contrarios al aprendizaje memoristico, se limitaron a que se razonara la aplicacion de las normas; las premisas y la justificacion de las mismas no las contemplaron. James Bryce, a modo de ejemplo, en su libro A Treatise of Book-keeping by Double and Single Entry (1860), afirma:
   ... the learner must exercise his judgement to determine, by the
   rules, in what book each transaction is to be entered, and how the
   entry of it is to be expressed. The judicious teacher will perceive
   the necessity of exercising his pupils in this way, instead of
   allowing them merely to copy the books (64).


Con toda probabilidad, la denuncia mas nitida de este enfoque la encontramos en Double Entry Elucidated (1852) de B.F. Foster que, a su vez, propone:
   The study of book-keeping affords an excellent means of
   intellectual discipline; that is, when its principles are
   exhibited, as well as their application -when the reasoning powers
   are called into exercise, as well as the memory. The student who
   has carefully attended to the instructions, and who is the master
   and not the slave of rules, will experience no difficulty in
   unravelling or adjusting any set of accounts, however complicated
   or diversified (65).


VII

La disputa entre los que eran partidarios del Diario y aquellos que preferian el Mayor como libro de ensenanza, no era otra cosa mas que la traduccion del conflicto entre el enfoque memoristico y el racional de la teneduria de libros. Los maestros que utilizaban el Diario para presentar la materia estaban condenados a usar las reglas. Los que manejaban el Mayor tambien podian servirse de las normas, aunque podian desarrollar ciertos principios racionales, si lo estimaban oportuno.

La lucha entre estos dos metodos opuestos suscito aspectos fundamentales para la docencia de la teneduria de libros. Se resolvio en una batalla entre "antiguos", partidarios del Diario, y "modernos", que preferian el Mayor. El resultado fue la derrota del Diario como Libro principal para la presentacion de los principios de la teneduria de libros y quedo relegado a una posicion insignificante en la metodologia docente. No obstante, esta exclusion no fue solo el resultado de presiones pedagogicas. Su apartamiento lo acelero el hecho de que el Diario estaba desapareciendo del ambito de los negocios. Los seguidores del enfoque del Mayor salieron doblemente reforzados: significaba una ensenanza mas racional y un cambio en las exigencias de los negocios.

El Diario habia dominado la situacion durante casi 350 anos hasta que, a mediados del siglo XIX, perdio su posicion dominante. No obstante, antes de esa fecha ya se habian formulado criticas a la repeticion memoristica de reglas y a su sistema encorsetado de anotar las partidas.

En la teneduria de libros era corriente que el sistema de aprendizaje, el Plan of Tuition, como dice Philip Comins en The Science of Commerce (1814), consistiera en "to read over and over again, very attentively, the entire of my General Instructions" (66). Las instrucciones referidas consisten, nada menos, que en doce paginas de letra pequena. Otra alternativa era que el alumno se condenara a la pesadez de "copying a multitude of similar examples, which gives him employment for some months, before he learns the manner of balancing a single account", segun dice R.B. Roe en An Introduction to Book-keeping (1825) (67).

Theodore Jones, por su parte, en Jone's English System of Book-keeping for Schools (1840), nos dice:
   If the learner is not quite master of the subject, after
   writing up the first Set of Exercises once, he is
   recommended to write it again and if necessary, repeat
   it till he has acquired such proficiency as to be able to
   write up and balance the first set complete (68).


Siendo justos con los docentes de la epoca, hemos de recordar que tanto Comins como Jones era hombres de negocios, lo que, por otra parte, era habitual en los ensenantes .

El Reverendo Ebenezer Cobham Brewer, autor prolifico de libros de todas las materias, en An Entire New System of Book-keeping by Single Entry (1850) dice que pretende que sus alumnos copien su libro rellenando los huecos de supuestos practicos de aritmetica. Afortunadamente para los maestros, existia una clave para la resolucion de aquellos (69).

El objetivo de que los estudiantes copiasen ejemplos era mejorar su escritura. Practical Book-keeping Made Easy (1876), de James Dimelow, es el mejor ejemplo de este tipo de enfoque. Sus paginas son pliegos con una bonita letra inglesa en la parte izquierda que tiene que copiarse en la derecha (70).

La clase de teneduria de libros que se ensenaba y la metodologia no satisfacia a nadie mas que a los maestros. En una recension de Double Entry Elucidated, de B.F. Foster, que The Times publico el 17 de octubre de 1845, leemos:

"There needs little observation to know that the manner in which merchants' accounts are taught in the generality of schools is tedious, defective, and unsatisfactory. The pupil is disgusted, because the systems adopted are incomprehensible, or so perplexed with difficulties that the reason is fettered, and all attempts at deductions from the premises are futile, and so much labour lost. Now Mr. Foster teaches book-keeping -not by drilling the learner into a calculating machine, but by enabling him to reason upon and comprehend what he is doing, or about to do. The science is laid down with clearness and perspicuity; the rules are plain, comprehensible and unerring; and the whole is illustrated by examples, so that any person of common capacity may understand the system, and be able to unravel any set of accounts, however complicated, or to keep his own or his employer's books in a satisfactory manner" -The Times; Oct. 17, 1845 (71).

El factor decisivo en la sustitucion del Diario por el Mayor como libro principal para la presentacion del sistema esta en que, a principios del siglo XX, el Diario como libro unico de registro cronologico, en la practica, habia dejado de existir. Con independencia de su valor educativo, no debemos olvidar que la teneduria de libros tiene un fundamento profesional y si este cambia de forma, entonces la estructura general tambien debe hacerlo.

Ademas de las razones profesionales, cabria preguntarnos por la base pedagogica que se utilizo para preferir el Mayor al Diario. Digamos, brevemente, que las partidas del Diario eran registros con los que no se podia tomar ningun tipo de decision hasta comprender el efecto que ejercian en el Mayor. Las partidas del Diario, en realidad, eran las partidas del Mayor en estilo tecnico. Y el intento de dejar los tecnicismos de la materia a un lado fue lo que condujo al declive del uso del Diario como medio pedagogico. B.F. Foster en su tratado de didactica -probablemente el primero-, de la teneduria de libros, Counting-House Instruction. Remarks on the Ordinary Modes of Teaching Writing and Book-keeping (1846), dice:
   The ordinary mode of teaching book-keeping is to
   commence by copying from some popular treatise a series
   of transactions, such as receipts, payments, purchases,
   sales, consignments and the like. After being wearied,
   secundum artem, with this work, the student is made to
   construct a journal; that is, to narrate under what heads
   in the ledger the respective items are to be placed, the
   substance of his instruction being, that "the thing received
   is debtor to the thing delivered"; but as to the object of
   making one thing debtor to another, he must be totally
   ignorant; for every journal entry has reference to the
   ledger, and the ledger is a sealed book to him. His whole
   progress through the journal is, therefore, a blind process
   of guessing; and when, ultimately; he transfers these
   items to the ledger, and balances his books, he does so
   more like an automaton than a rational being (72).


Y, de forma mas directa, lo vuelve a repetir en su Double Entry Elucidated (1852) cuando advierte de que es imposible entender los tecnicismos del Diario, salvo que se conozca la estructura y uso de cada cuenta del Mayor; de ahi que -prosigue-, el Mayor deba ser el primero y no el ultimo libro que se debe revisar.

Con anterioridad ya se habia producido un ataque similar al enfoque del Diario en Estados Unidos con Thomas Jones a la cabeza. El Profesor Littleton en su libro Accounting Evolution to 1900 cita una carta que B.F. Foster dirigio a Thomas Jones en la que le concede el honor de haber generado el metodo que comienza la explicacion teorica con el Libro Mayor (73).

Pero la apreciacion de la supremacia del Mayor en la ensenanza no fue un descubrimiento casual de mediados del siglo XIX. Asi, Alexander Malcolm, en su ya mencionado A Treatise of Bookkeeping, or, Merchants Accounts (1731), considera que el Libro Mayor es el mas importante de todos los libros de cuentas. Sin embargo, en la didactica, el Mayor no adquirio esa carta de naturaleza hasta el siglo XIX.

James Morrison fue uno de los primeros en advertir de su importancia en The Elements of Book-keeping (1813):
   ... we shall next consider the Ledger, because, though the
   Journal comes before it in the order of writing yet the
   Journal cannot be well understood until the nature of
   the Ledger be explained (74).


Sin embargo, hasta que el Profesor de Morgan se adhirio a la "escuela del Mayor", no se produjo una verdadera proliferacion de libros que utilizan este enfoque. La importancia que de Morgan concede a la naturaleza de la teneduria de libros por partida doble con la personificacion de las cuentas, le llevo a adquirir una autoridad academica que le permitio decir que
   The only book that need be explained is the ledger. All
   the other books, and the manner in which they are kept,
   important as they may be, have nothing to do with the
   main principle of the method (75).


No debemos olvidar que el anejo de de Morgan sobre teneduria de libros no se publico hasta 1846 y no fue ampliamente conocido hasta su siguiente edicion, treinta anos mas tarde. Durante este interregno de tres decadas solo hemos logrado localizar un tratado que utilice el enfoque del Mayor. Se trata de la obra de Henry Manly, "Principal Writing-Master and Teacher of Book-keeping in the City of London School", The Principles of Book-keeping by Double Entry (1864) (76). Pero despues de 1876 el ritmo de aparicion de tratados se hizo mas rapido. First Lessons in Book-keeping de J. Thornton, que ya hemos mencionado, se publico en 1879 y Elementary Book-keeping, de George Lisle, en 1894 (77). Ambos muestran todas las operaciones a traves del Mayor antes de ocuparse del Diario.

En la decada de 1890 la cuestion fue cobrando interes y el nombre de de Morgan se cita frecuentemente. En efecto; E.E. Whitfield lo menciona en su obra Introduction to the Commercial Sciences (1900):
   The disrepute into which Book-keeping as a school
   subject had fallen down to a recent period is traceable to
   the mistaken postponent of work upon the ledger to the
   detail consideration of other books of account. Professor
   De Morgan showed that it is in ledger work that the main
   principle is learnt (78).


Andrew Sarll, por su parte, en Double Entry Book-keeping in Theory and Practice (1881) tambien utiliza el enfoque del Mayor, con lo que, a principios del siglo XX, este metodo de presentacion era suficientemente conocido en los circulos docentes (79).

VIII

Hasta el siglo XIX, como hemos visto, la racionalizacion mas importante de las partidas de teneduria de libros fue la personificacion de cuentas. No obstante, tan solo es una de las teorias que influyo en el metodo de exposicion. Una teoria alternativa es la que podemos denominar teoria de la propiedad de las cuentas y que se ocupa del significado de estas desde el punto de vista del propietario.

Desde una perspectiva tecnica, la teoria de la propiedad de las cuentas conlleva un balance de situacion o un enfoque de ecuacion de balance porque el objeto de atencion y el punto de partida y de llegada es el balance de situacion. Esto supone un cambio radical respecto al concepto de relacion de deuda de las cuentas en el que el balance de situacion es el resultado final de las anotaciones en cuenta. Por el contrario, en el caso de la teoria de la propiedad, el balance de situacion se concibe mas como un mecanismo activador que como objetivo ultimo. Se trata del desarrollo logico para configurar un ciclo de operaciones. Se considera el balance de situacion como la cristalizacion de la posicion financiera del negocio. En lugar de detallar todos los efectos de las operaciones en el balance de situacion, como en el metodo "ciclico", se analiza la transaccion con el fin de determinar los cambios que supondra en la estructura financiera. Lo que sera el nuevo balance de situacion y las anotaciones en cuenta se formula como resultado de este analisis. Es un enfoque completamente diferente. La atencion no se centra en el "intercambio" entre cuentas sino en las transformaciones de cada lado del balance de situacion. Se analizan las transacciones en terminos de mutacion de activos y pasivos de la empresa y sus efectos en el beneficio de la propiedad. La argumentacion discurre en terminos de conversion mas que de relacion de deuda; de relacion estadistica impersonal mas que de relacion personal; de analisis mas que de norma y memoria. Las cuentas son crecientes o decrecientes en vez de abonarse o cargarse. La atencion pasa de la ficcion a la realidad de la teneduria de libros.

El origen de la teoria de la propiedad, en esencia, se encuentra en el tratado de Hustcraft Stephens, Italian Book-keeping Reduced Into an Art (1735) (80).

Stephens consiguio salir del embrollo de la personificacion en un momento en el que no se conocia, ni se contemplaba, ninguna otra alternativa. Su enfoque era tan novedoso que se vio obligado a acunar nuevas palabras para expresar sus ideas. Desde una perspectiva docente, su metodo de exposicion se adelanto un siglo en emanciparse de las reglas. El plan de la obra lo recoge en el Prefacio:
   For as the treats of Italian Book-keeping after a Manner
   so intirely New, it were unreasonable to expect that He
   should confine Himself to any particular Terms or Forms
   dogmatically prescribed by others; when his Design is to
   offer no Rules, until he has shewn them to be the
   Consequences of Conclusions, plainly drawn from Self-evident
   Principles, or what are previously demonstrated
   from such; and to make Use of no Terms in a different
   Sense from the common Acceptation, until He has first
   sufficiently explaind them, and given His Reason for it (81).


En su Introduccion pone los cimientos de su teoria de la mutacion de activos y pasivos definiendo el capital como un ente independiente de la empresa:
   That Portion of Things which a Man possesses, or has
   otherways belonging to him, as a Security, taken all
   together, I call the Estate, and the Worth of a Man's
   Estate, consider'd abstractly from the Things which are
   valued, I call the computed Value or Extent of a Man's
   Estate (82).


Por lo general, utiliza el termino Condition para lo que hoy denominamos activos (assets) y Extent para los pasivos (liabilities). Ambas palabras poseen una carga semantica especial debido a la inexistencia de terminos apropiados. Y, con sencillez, expresa la finalidad de la teneduria de libros:
   ... it is indispensably required of every prudent Man to
   know exactly the computed Value and Condition of his
   Estate, in order to the well governing himself in the
   Management of his worldly Affairs: for without that
   Knowledge, he cannot make any one Step in them with
   Certainty; but must grope blindly in the Dark, and by
   Chance sink or swim; which is a Hazard no wise Man
   would willingly trust his Fortune to (83).


El paso siguiente es la clasificacion de las transacciones en tres categorias, dependiendo de la forma en la que puedan afectar a activos, a pasivos, o a ambos al mismo tiempo. Igualmente introduce la idea, novedosa para su epoca, de que el propietario es un acreedor del negocio. En efecto; resulta interesante observar que la palabra propietario (proprietor) se utiliza con el sentido que hoy damos a acreedor (creditor), lo que indica que Stephens concebia el lado del pasivo del balance de situacion como componente natural de una lista de fuentes o recursos, con lo que se aparta del concepto de teneduria de libros de mero registro de relaciones de deuda.

La explicacion de Hustcraft Stephens de la funcion de las cuentas demuestra una perfecta comprension de su uso como herramienta aritmetica para mostrar las variaciones de activos y pasivos individuales:
   I say, the various Securities must be so divided, that
   when by any Transaction it becomes necessary to add to,
   or taken from the respectively any Quantity, Number, or
   Sum, we may do it so, that the remaining Quantity,
   Number, or sum, with the Alterations that produced them,
   may appear: for which Reason there must be a competent
   Space allow'd each Division (wherein the first Quantities,
   Numbers, or Sums are noted) for the Recital of the
   Alterations of adding to, or taking from, as Occasions
   offer (84).


Mas adelante muestra los efectos de compras, ventas, ingreso y pago en metalico en la posicion financiera del negocio. Por ejemplo: la venta de 500 libras de azucar a 50 libras y la compra de 3000 a 150 se sustancia del siguiente modo:
Second Account.

Sugar bears Part of the                  l.    s.   d.
Condition of my State.

I have                    1000 lb. for   100   0    0
Alter. I. Sold out        500 lb. for    50    0    0
First Remains             500 lb. for    50    0    0
Alter.2. Bought           3000 lb. for   150   0    0
Second Remains            3500 lb. for   200   0    0

Third Account.

Money bears Part of the
Condition of my Estate.

I have                                   200   0    0
Alter. I. Receiv'd for                   50    0    0
  Sugar
First Remains                            250   0    0
Alter.2. Bought Sugar;                   150   0    0
  for which I paid
Second Remains                           100   0    0 (85)

      Las sumas y restas constantes son tediosas,

   ... whereas, were all these Alterations which cause an
   Increase of the Condition, and those which likewise bear
   a Part of the Extent, respectively gather'd together, they
   might at Pleasure be compar'd by one Substraction after
   their Sums were severelly added up (86).


Y de este modo, llegamos a la forma habitual de la cuenta con dos lados.

El tratado de Stephens significa un distanciamiento total de la explicacion imperante: la personificacion. Los autores que le sucedieron no lo mencionan y sus conceptos no se desarrollaron durante setenta y cinco anos; pero ya se disponia de un marco para un enfoque impersonal y estadistico, con una exposicion completa de la funcion aritmetica de la cuenta. Ahi es donde reside el valor de la aportacion de Stephens al metodo docente.

Esta vision de la estructura de las cuentas no volvio a ser abordada hasta el inicio del siglo XIX. John Williamson Fulton, "Book-keeper in the Office of the Accountant to the Board of Revenue, Bengal", habia comprobado que era bastante dificil obtener una vision general rapida de la situacion financiera personal o del negocio con los metodos existentes de teneduria de libros. En consecuencia, el objetivo de su libro British-Indian Book-keeping era exponer un metodo de llevar las cuentas que reflejara "the progressive effect of all transactions on the General Stock daily or monthly, according as the entries and adjustments are made" (87). Teniendo presente su objetivo, habia captado un aspecto importante de la teoria de la propiedad en contabilidad: que las cuentas constituyen un metodo para registrar cambios en los activos y pasivos de la persona o de la compania y que todos estos cambios deben reflejarse en el balance de situacion.

Fulton destaca que, en esencia, unicamente es necesario distinguir entre la cuenta de capital y el resto, porque
   ... the stock account is that of the principal (...) of a
   concern: it is not composed of a particular independent
   property (d), like each of the other accounts, but arises
   from the state of all these collectively taken, which thus
   form merely the particulars of it: and the grand aim of
   double entry is, to ascertain the true state of the account
   (...) and to check the balance thereof, by the net
   balance collectively of all the other accounts (88).


Y prosigue senalando que la igualdad de cargos y abonos no se ve entorpecida:
   If a gain be made, Cr. side of the stock account is
   thereby increased, and of course the whole Cr. line; but
   at the same time the Dr. side of cash or some other, one
   or more, accounts must be equally increased. A loss will
   increase the Dr. side of stock, and increase in an equal
   degree the Cr. side of some other account or accounts.
   In buying and selling, receiving and paying, drawing and
   remitting, bartering & c. this equality, in the amount of
   the respective Drs. and Crs. affected by each of these
   various transactions, will still be found to hold good; so
   that the extension or diminution of the two lines in
   question must ever be equal in regard to each other (89).


Reconoce y destaca que el saldo de la cuenta de capital no es unicamente la diferencia entre activos y pasivos, sino tambien el saldo original junto con el efecto neto de los cambios que se derivan de perdidas y ganancias. Mediante columnas adicionales en su Diario, Fulton, al distinguir entre partidas de capital e ingresos, puede analizar el efecto neto sobre el capital de todas las transacciones para asi extraer el saldo neto de capital en cualquier momento y equipararlo con el efecto neto de cambios en otros saldos de cuentas. Con independencia del valor practico de su aportacion, la obra de Fulton supone un paso mas en la nueva forma de considerar el objetivo de la teneduria de libros y las interrelaciones entre las cuentas del Libro Mayor.

Dieciocho anos despues de la publicacion del tratado de Fulton, la exposicion de la teoria de la propiedad la completo F.W. Cronhelm con su libro Double Entry by Single (1818) (90).

La contribucion de Cronhelm se sustancia en su enunciado del capital como un "todo"; su diferenciacion de las partes que lo constituyen y el inevitable "equilibrio" del todo con las partes. Su enfoque es matematico, aunque tiene algunos lapsus de personificacion.

Cronhelm, lo mismo que Stephens y Fulton, considera la teneduria de libros como un metodo para registrar la propiedad y los cambios que en ella se producen, mas que relaciones de deuda:
   The purpose of Book-keeping, as a record of property, is to
   shew the owner at all times the value of his whole capital,
   and of every part of it. The component parts of property
   in trade, are in a state of continual transformation and
   change; but whatever variations they undergo, and
   whether the whole capital increase, diminish or remain
   stationary, it is evident that it must constantly be equal
   to the sum of all its parts. This EQUALITY is the great
   essential principle of Book-keeping (91).


Desde esta perspectiva, ninguna cuenta puede considerarse ficticia o imaginaria. Todas son reales; y buena parte de la confusion que se habia suscitado con la teoria de la personificacion, desaparece. Con el rechazo de la personificacion se abria el camino para un enfoque matematico abstracto:
   The introduction of Credit and Bills into commerce,
   produced two kinds of property directly contrary in their
   natures:

   1st, Positive Property, consisting of Goods, Cash, Bills
   Receivable, and Debts Receivable.

   2d, Negative Property, consisting of Bills Payable, and
   Debts Payable.

   And as these two kinds of property mutually destroy each
   other, it is evident that the Stock, or entire capital,
   must always be equal to the difference between them,
   and be of the same nature as that which preponderates.

   Hence arise three varieties of Stock or Property; the
   Positive, the Neutral, and the Negative; in the first two of
   which the proprietor is solvent, in the latter, insolvent (92).


Desde la idea de la cuenta de capital, como herramienta de equilibrio matematico, logicamente se infiere que debe ser una partida de abono:
   Should it be inquired why the Stock appears to be negative
   when the property is positive, and positive when the
   property is negative, this seeming contradiction will be
   removed by the following consideration. In these general
   relations of Debtors and Creditors, the estate or concern
   itself is abstracted from its proprietor, and becomes a
   whole, of which the Stock or proprietor's Account is now
   also of the component parts. if, therefore, his property be
   positive, the Concern is Debtor to him for that property,
   the same as to any other person; and he classes among
   its other Creditors. If, on the other hand, his property be
   negative, or himself insolvent, the Concern is Creditor,
   and he classes among the other Debtors (93).


Ademas de la cuenta de capital, todas las demas son factores de equilibrio:
   ... when we thus abstract a Concern from its Proprietor,
   and place the account of Stock or entire capital among
   the component parts, the Concern itself is constantly
   neutral, consisting of a mass of relations between Debtors
   and Creditors, in perpetual and necessary equilibrium.
   The Concern thus abstracted, is always a cypher; and all
   its component parts are equally and mutually dependent
   upon each other, and upon the whole. It is no longer
   merely the Stock which is the result of all the other
   Accounts collected together: every Account has the same
   property, and may be found or proved in the same
   manner (94).


Y expresa el mismo razonamiento en forma algebraica:
    Let a,b,c & c. represent the positive parts, or Debtors;
    l,m,n & c. the negative parts, or Creditors; and s the
    Stock, or proprietor's real worth. Then as the whole is
    equal to the sum of its parts,

      a + b + c, & c. - l - m - n, & c. = [+ o -] s.

   By transposition we obtain

      a + b + c, & c. - l - m - n, & c. [??] s = 0,

   or that general equation, in which the whole Estate is
   neutral or a cypher, and includes the Stock as one of its
   component parts. Hero too, it may be observed that the
   transposition of s changing its sign, explains the reason
   why the Stock, when positive in itself, becomes negative
   or creditor as a component part of the estate, and
   positive or debtor when negative.

   Again, by transposing any one of the terms in the general
   equation, it may be proved to be equal to all the rest.
   Thus,

        b + c, & c. - l - m - n, & c. m s = - a;

      a + b + c, & c. - m - n, & c. [??] s = l;

      a + b + c, & c. - l - m - n, & c. = [??] s.

    Hence the truth of that general proposition already laid
    down, that any debtor or creditor in the books is equal to
    the collective result of the other debtors and creditors, an
    affection which ha95s been commonly supposed peculiar to
    the stock account (95).


Esta ecuacion general, no obstante, es un concepto estatico y cuando se realizan las transacciones se requiere una exposicion de formas dinamicas. Las partes que las componen estan en constante fluctuacion. Para ello Cronhelm desarrolla una teoria de la propiedad que considera la transformacion de una clase de propiedad en otra:
   The component parts of property in trade are in a state
   of continual fluctuation and change. In purchases, cash
   is converted into goods; and in sales, goods are
   reconverted into cash. Or, if credit allowed, the changes
   are still more numerous. Purchases create personal
   creditors and goods; sales convert goods into personal
   debtors; receipts convert personal debtors into cash;
   whilst payments destroy cash and personal creditors.
   The introduction of bills would multiply the changes by
   an intermediate stage between personal debts and cash.
   But all these creations, metamorphoses, and destructions
   of the parts, resolve themselves into the single case,
   that in every transaction two accounts are affected, the
   one receiving what the other communicates. The imparting
   account is always creditor, and the recipient always
   debtor; so that in each occurrence debtor and creditor
   must perfectly equilibrate (96).


Y prosigue aplicando el sistema a las perdidas y ganancias, considerandolas aumento o disminucion del capital. La funcion de la cuenta de perdidas y ganancias es, pues, una especie de metodo para agrupar todos los aumentos o disminuciones individuales de capital, con lo que el resultado general se puede transferir, en una cantidad total, a la cuenta de capital.

Por todo lo dicho, los principios basicos de la teoria de la propiedad ya estaban expuestos, de modo sencillo y claro, en 1818. Esos principios suponian la separacion radical de propietario y negocio; la ecuacion fundamental de la propiedad; y el concepto de transaccion que afecta a esta ecuacion, segun aumenten o disminuyan los activos, pasivos o el capital. Este metodo de explicar y ensenar la teneduria de libros desaparecio de las aulas britanicas, aunque a lo largo del siglo XIX siguieron apareciendo tratados que se fundamentan en la teoria de la propiedad. Ese es el caso de A New System of Book Keeping (1828) de P.C.L. Vautro (97); The Perfect Book-keeper (1849), de J.H. Chauvier (98); A Treatise on Book-keeping (1867), de R.Y. Barnes (99); o Book-keeping and Accounts (1891), de Percy Child (100), ya al borde del siglo XX.

El rasgo sorprendente de este enfoque, despersonalizado y matematico, de la teneduria de libros es que, aunque fue el metodo habitual en Estados Unidos y en algunos paises europeos, tuvo que esperar hasta 1949 para ser incorporado a los libros de texto britanicos.

Aun es pronto para hacer una valoracion de lo sucedido en la docencia de la teneduria de libros en Gran Bretana, a lo largo del siglo XX.

Goethe, por boca de uno de sus personajes, declaro que la partida doble es una de las invenciones mas bellas de la mente humana. Seguro que no se imagino que iba a ser objeto de controversias de concepto, de desarrollo de metodo didactico, de sistemas de aprendizaje y de competencia. Despues de todo y como en todo, la invencion bella ha pasado por los filtros de las artes y de las ciencias, salvaguardando, claro esta, un principio siempre respetado por todos: business is business.

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DAFFORNE, Richard (1670) [1640] The Apprentices Time-Entertainer Accomptantly: Or A Methodical means to obtain the Exquisite Art of Accomptantship: Digested in Three Parts.... London: W. Godbid.

DE MORGAN, Augustus (1876) Elements of Arithmetic, Sixth Edition. London: Edward Stanford.

DEGRANGE, Edmond (1806) La tenue des livres rendue facile, ou nouvelle methode d'enseignement a l'usage des personnes destinees au commerce, avec une nouvelle methode pour tenir des livres en double partie, par le moyen d'un seul registre dont tous les comptes balancent journellement. Sixtieme edition, revue, cossignee et augmentee. Paris: Hocquart & Bordeaux, chez l'auteur et chez Filiatre [&] de l'imprimerie de J. Foulquier.

DIMELOW, James (1876) Practical Book-keeping Made Easy. A Series of Practical Book-keeping, Including An Entirely New Mode of Teaching It (...) for the Use of Commercial Schools and for Self-Tuition. London & Glasgow: William Collins, Sons & Co.

DONN, Benjamin (1765) The Accountant and Geometrician: Containing the Doctrine of Circulating Decimals, Loga rithms, Book-keeping and Plain Geometry.... London.

DYER, S. (1897) A Common Sense Method of Double-Entry Bookkeeping on First Principles. As Suggested by De Morgan, 2 vols.. London: George Philip & Son.

FOSTER, B.F. (1846) Counting-House Instruction. Remarks on the Ordinary Modes of Teaching Writing and Book-keeping. London.

--(1852) Double Entry Elucidated, Fifth Edition. London: John Souter.

--(1852) The Origin and Progress of Book-keeping: Comprising an Account of All the Works on This Subject, Published in the English Language, from 1543 to 1852, with Remarks, Critical and Historical. London: John Souter.

FULTON, John Williamson (1800) British-Indian Book-keeping. A New System of Double Entry and Progressive Adjustment; Exemplified in a Variety of Comprendious Methods, for the Practical Purposes as well of the Private Gentleman as of the Merchant. The whole Calculated to Supply a Desideratum in the Art, by a Perspicuous Process, never before adverted to.... London: G. Auld.

GRIFFIN, Charles H. and Thomas H. Williams (1963) "A Comparative Analysis of Accounting and Mathematics", Accounting Review, 37 (No. 3, Jul.), pp. 410-4.

HAMILTON, R. (1788) A Short System of Arithmetic and Bookkeeping. With A Supplement; Containing Answers to the Arithmetical Questions. London: C. Elliot & T. Kay and Edinburgh: C. Elliot.

HAMILTON, R.G.C. and John Ball (1869) Book-Keeping. Oxford: At the Clarendon Press.

HAMILTON, Robert (1777) An Introduction to Merchandize. Containing A Compleat System of Arithmetic. A system of Algebra. Book-keeping in various forms. An Account of the Trade of Great Britain, and the Laws and Practices which Merchants are Chiefly Interested In, 2 vols., Edinburgh: Printed for the Author.

HATTON, Edward (1707) [1701] The Merchant's Magazine: or, Trade Man's Treasury.... London: E.M. for Chr. Coningsby.

HAYES, Richard (1731) Modern Book-keeping, or, the Italian Method Improved; Containing Rules and Directions for Keeping ... Accompts by Double Entry. London.

[JONES, Edward Thomas] (1796) Jones English System of Book-keeping by Single or Double Entry, in Which It Is Impossible for an Error of the Most Trifling Amount to Be Passed Unnoticed; Calculated Effectually to Prevent the Evils Attendant on the Methods so Long Established; And Adapted to Every Species of Trade.... Bristol: R. Edwards.

JONES, Theodore (1840) Jones English System of Book-keeping for Schools. London: Theodore Jones & Co.

KATS, P. (1926) "Hugh Oldcastle and John Mellis", The Accountant, LXXIV (27 March), pp. 483-487.

KELLY, P. (1801) The Elements of Bookkeeping; Comprising a System of Merchants Accounts, Founded on Real Business, and Adapted to Modern Practice: With An Appendix on Exchanges, Including the Recent Alterations. Edinburgh.

KING, Thomas (1717) An Exact Guide to Book-keeping by Way of Debtor and Creditor: Done After the Italian Method.... London: S. Cruttenden.

LANERO FERNANDEZ, J. y E. ORTEGA MONTES (2006) "Algunas consideraciones historiograficas sobre la logica de la Partida Doble y la clasificacion de Cuentas", Pecvnia, 2, pp. 65-78.

LANERO FERNANDEZ, Juan (2004) El esplendor de la teneduria de libros: la partida doble en los tratados contables ingleses de la dinastia Tudor (1543-1588). Tesis Doctoral, Universidad de Leon.

LEWIS, James Henry (1869) The Quick and Easy Method of Teaching Book-keeping According to the English, Italian, and Scotch Systems of Single Entry and Double Entry Exemplified in Individual and Partnership Accounts, Both Domestic and Foreign. Forming a Branch of The Royal Lewisian System of Commercial Education. London: Printed for the Author and Sold at His Only Institution.

LISLE, George (1894) Elementary Book-keeping in Theory and Practice. With Numerous Examples and Exercises, Together with Solutions. London & Edinburgh: W. & R. Chambers, Limited.

LITTLETON, A.C. (1966) [1933] Accounting Evolution to 1900, New York: Russell & Russell.

MALCOLM, Alexander (1718) A New Treatise of Arithmetick and Book-keeping.... Edinburgh: John Mosman and William Brown.

--(1731) A treatise of Bookkeeping, or, Merchants Accounts; in the Italian Method of Debtor and Creditor.... The Whole Illustrated and Exemplified with Two Sets of Books, Containing Great Variety of Practice in All those Branches of Business. London: J. Osborn and T. Longman.

MANLY, Henry (1864) The Principles of Book.keeping by Double Entry, in A Series of Easy and Progressive Exercices. London: Edward Stanford.

MANZONI, Domenico (1540) Qvaderno Doppio col svo giornale, novamente composto, & diligentisimamente ordinato, secondo il costume di Venetia. Opera a ogni persona utilissima, & molto necessaria. Cvm gratia et privilegio del ilustrissimo Senato di Venetia, per Anni diece.

MATHESON, John (1818) The Theory and Practice of Book-keeping.... Remarks on Bills and Promissory Bills; The Nature of Trade.... London.

MELLIS, John (1588) A Briefe Instruction and maner how to keepe bookes of Accomptes after the order of Debitor and Creditor, & as well for proper Accompts partible, & c ... London: lohn Windet.

MORRISON, James (1813) The Elements of Book-keeping by Single & Double Entry. Comprising Several Sets of Books. Arranged According to Present Practice & Designed for the Use of Schools. To Which is Annexed An Introduction on Merchants Accounts with Engraved Specimens. London: Longman, Hurst, Rees, Orme, Brown & Green.

[NORTH, Roger] (1714) The Gentleman Accomptant: or An Essay to Unfold the Mistery of Accompts. By Way of Debtor and Creditor, Commonly Called Merchants Accompts, and Applying the Same to the Concerns of the Nobility and Gentry of England ... Done by a Person of Honour.... London: E. Curll.

PEELE, James (1553) The maner and fourme how to kepe a perfecte reconyng, after the order of the moste worthie and notable accompte of Debitour and Creditour.... London: Richard Grafton.

--[1569] The Pathe waye to perfectnes, in thaccomptes of Debitour, and Creditour: in manner of a Dialogue.... London: Thomas Purfoote.

PERAGALLO, Edward (1938) Origin and Evolution of Double Entry Bookkeeping. A Study of Italian Practice from the Fourteenth Century.... New York: American Institute Co.

POSTLETHWAYT, Malachy (1751) The Merchant's Public Counting-House: Or, New Mercantile Institution: Wherein is shewn, the Necessity of Young Merchants Being Bred to Trade with Greater Advantages than They Usually Are. With a Practicable Plan for That Purpose. Also Some Remarks on the Benefit of This Institution to the Young Nobility and Gentry, and Such Who Are Intended for the Study of the Law, Second Edition. London: John and Paul Knapton.

QUIN, M. (1776) Quins Rudiments of Bookkeeping; Comprised in Six Plain Cases, and Attainable in as Many Days, Without the Help of a Teacher. Calculated for Persons of Either Sex, Grown to Maturity. With An Essay on the Fit Manner of Initiating Youth to Temperance and Moral Rectitude; By An Easy Arithmetical Scale. London: J. Bew.

ROE, R.B. (1825) An Introduction to Book-keeping ... London.

SARLL, Andrew (1899) [1881] Double Entry Book-keeping in Theory and Practice; Illustrated by Short and Graduated Exercices; Followed by Examination Papers Arranged in order of Their Difficulty.... London: George Gill & Sons, Ltd.

SHERIFF, Daniel (1850) The Whole Science of Double-Entry Book-keeping, Simplified by the Introduction of an Unerring Rule for Debtor and Creditor, Calculated to Insure a Complete Knowledge of the Theory and Practice of Accounts. Designed for the Use of Merchants, Clerks, and Schools. London: J. Brown & Co.

SNELL, Charles (1701) Rules for Book-keeping, According to the Italian Manner: Now in General Use. Directing Young Accomptants to the Books and Accompts, Where the Usual occurrences in Trade Are to Be Enter'd; and in the Stile proper for such Entrances. London: John Place.

SNELL, Charles (1718) The Merchants Counting-House: Or Wast-Book Instances, with Directions for Their Stating and Entrance.... London: Jonas Brown.

STEPHENS, Hustcraft (1735) Italian Book-keeping Reduced Into an Art: Being an Entire New and Compleat System of Accompts in General. Demonstrated in a Chain of Consequences from Clear and Self-Evident Principles. To Which is Added, The Greatest Variety of Merchants Accounts, with an Explanation of All the Terms of Art, Which have Commonly Been Madre Use of. Together with Proper Reflections on the Whole. London: W. Mears.

TAYLOR, William (1783) Complete System of Practical Arithmetic: With Various Branches in the Mathematics. Birmigham: Printed and Sold by the Author.

THORNTON, J. (1879) First Lessons in Book-keeping. London.

VAUTRO, P.C.L. (1828) A New System of Book Keeping; Calculated to Promote the Neccessary Reform of the Old Methods, by Following the Means Particularly Recommended by the Best english Authors. London.

VERNON, G.F. Carr (1893) Sets for Practice in Book-keeping. London: Charles Chappell.

W.P. (1596) The Pathway to Knowledge. Conteyning Certaine Briefe Tables of English Waights and Measures..., Written in Dutch and Translated into English by W.P.. London: William Barley.

WHITFIELD, E.E. (1900) Introduction to the Commercial Sciences. London: Rivingtons.

WICKS, J.H. (1797) Book-keeping Reformed.... Egham.

(1) [Roger North], The Gentleman Accomptant: or An Essay to Unfold the Mistery of Accompts. By Way of Debtor and Creditor, Commonly Called Merchants Accompts, and Applying the Same to the Concerns of the Nobility and Gentry of England.... Done by a Person of Honour ..., London: Printed for E. Curll, at the Dial and Bible against St. Dunstan's Church in Fleetstreet, 1714, p. 33.

(2) Vease Juan Lanero Fernandez, El esplendor de la teneduria de libros: la partida doble en los tratados contables ingleses de la dinastia Tudor (1543-1588), Tesis Doctoral, Universidad de Leon, 2004.

(3) John Mellis, A Briefe Instruction and maner how to keepe bookes of Accomptes after the order of Debitor and Creditor, & as well for proper Accompts partible, & c ..., Imprinted at London by Iohn Windet, dwelling at the Signe of the White Beare, nigh Baynards Castle, 1588, capitulo IX.

(4) P. Kats, "Hugh Oldcastle and John Mellis," The Accountant, LXXIV (27 March 1926), pp. 483-487.

(5) James Peele, The maner and fourme how to kepe a perfecte reconyng, after the order of the moste worthie and notable accompte of Debitour and Creditour ..., Imprinted at London, by Richard Grafton, printer to the Kinges Maiestie, 1553, capitulo IV.

(6) James Peele, The Pathe waye to perfectnes, in th'accomptes of Debitour, and Creditour: in manner of a Dialogue ..., Imprinted at London, in Paules Churchyarde. By Thomas Purfoote, dwellinge at the signe of Lucrece, [1569].

(7) Richard Dafforne, The Merchants Mirrour: Or Directions for the Perfect Ordering and Keeping of His Accounts; Framed by way of Debitor and Creditor, after the (so termed) Italian-manner: containing 250 Rare Questions, with their Answers, in forme of a Dialogue, London: Printed by R. Young, for Nicolas Bourne, at the South-entrance of the Royall Exchange, 1635.

(8) Johannes Buingha, Oprecht Fondament Ende principalen inhout van het Italiaens Boeck-houden. Om van alle Partyen den Rechten Debiteur, ende Crediteur te stellen, die selve int cort op tgroot Boeck, over te draghen: Mitsgaders een grontlijcke onderrichtinghe, om een y eghelijcx Reeckeninghe in Debito, ende Credito van t'groot Voeck wel te verstaen, zijride t'voornaemste des Boeck-houdens, t'Amstelredam: By Willem lansz, Stam Boeckvercooper, 1627.

(9) Richard Dafforne, The Apprentices Time-Entertainer Accomptantly: Or A Methodical means to obtain the Exquisite Art of Accomptantship: Digested in Three Parts ..., London: Printed by W. Godbid, for Robert Horne and are to be sold at his shop at the South Entrance of the Royal Exchange in Corn-hill, 1670, [1640].

(10) Edward Hatton, The Merchant's Magazine: or, Trade Man's Treasury ..., London: Printed by E.M. for Chr. Coningsby at the Ink-Bottle near St Dunstan's Church in Fleestreet; and Dan. Midwinter at the Rose and Crown in St. Paul's Churchyard, 1707 [1701].

(11) Charles Snell, Rules for Book-keeping, According to the Italian Manner: Now in General Use. Directing Young Accomptants to the Books and Accompts, Where the Usual Occurrences in Trade Are to Be Enter'd; and in the Stile proper for such Entrances, London: Printed for John Place, at Furnivals-Inn-Gate in Holborn, 1701.

(12) Charles Snell, The Merchants Counting-House: Or Wast-Book Instances, with Directions for Their Stating and Entrance ..., London: Printed for Jonas Brown, at the Black Swan without Temple-Bar, 1718.

(13) William Taylor, Complete System of Practical Arithmetic: With Various Branches in the Mathematics, Birmigham: Printed and Sold by the Author, 1783.

(14) James Henry Lewis, The Quick and Easy Method of Teaching Book-keeping According to the English, Italian, and Scotch Systems of Single Entry and Double Entry Exemplified in Individual and Partnership Accounts, Both Domestic and Foreign. Forming a Branch of The Royal Lewisian System of Commercial Education, London: Printed for the Author and Sold at His Only Institution, 1869, p. xvi.

(15) John Collins, An Introduction to Merchants Accounts Containing Five Distinct questions of Accounts ..., London: Printed by James Flesher for Nicholas Bourn, at the South entrance of the Royal Exchange, 1653.

(16) Domenico Manzoni, Qvaderno Doppio col svo giornale, novamente composto, & diligentisimamente ordinato, secondo il costume di Venetia. Opera a ogni persona utilissima, & molto necessaria. Cvm gratia et privilegio del Ilustrissimo Senato di Venetia, per Anni diece, 1540.

(17) James Peele, The maner and fourme, ed. cit.

(18) Richard Dafforne, The Merchants Mirrour, ed. cit.

(19) P. Kelly, The Elements of Bookkeeping; Comprising a System of Merchants Accounts, Founded on Real Business, and Adapted to Modern Practice: With An Appendix on Exchanges, Including the Recent Alterations, Edinburgh: 1801.

(20) Geo H. Boutler, A Course of Bookkeeping by Double and Single Entry, As Applied to Inland and Foreign Trade, Containing the Most Recent Improvements Both in the Method of Teaching, and in the Practice of the Art. Adapted to the Use of Schools or Self-Instruction, London: Printed and Published by John Mabley, 143, Strand, 1847, p. ii.

(21) I. Carpenter, A Most Excellent Instruction for the Exact and Perfect Keeping Merchants Bookes of Accovnts, By Way of Debitor and Creditor, after the Italian Manner: Most Vsefvll for all Merchants, Factors, And Tradesmen ..., London: Printed by I.B. for Iames Boler, and are to be sold at the signe of the Marigold in Pauls Churchyard, 1632, p. 57.

(22) Thomas Browne, The Accurate Accomptant or London-Merchant.... Also a Journal and Leager.... With An Addition of An Accompt Partable, Wherein Four Persons Are Mentioned to Joyn in Partnership Upon Two Several Designs: in Both Which, They All Have Different and Unequal Parts. With A Question Concisely Stated And Resolved..., London: William Godbid for John Hancock, 1670.

(23) M. Quin, Quin's Rudiments of Bookkeeping; Comprised in Six Plain Cases, and Attainable in as Many Days, Without the Help of a Teacher. Calculated for Persons of Either Sex, Grown to Maturity. With An Essay on the Fit Manner of Initiating Youth to Temperance and Moral Rectitude; By An Easy Arithmetical Scale, London: Printed and Sold by J. Bew, Pater-noster Row; also by W. Davenhill, Cornhill, and J. Walter, Charing Cross, 1776, pp. 10-11.

(24) Thomas King, An Exact Guide to Book-keeping by Way of Debtor and Creditor: Done After the Italian Method ..., London: S. Cruttenden, 1717.

(25) R. Hamilton, A Short System of Arithmetic and Bookkeeping. With A Supplement; Containing Answers to the Arithmetical Questions, London: Printed for C. Elliot & T. Kay, No. 332, Strand; and Edinburgh: C. Elliot, 1788; "Directions to Teachers", p. vi.

(26) John Matheson, The Theory and Practice of Book-keeping.... Remarks on Bills and Promissory Bills; The Nature of Trade..., London: 1818, p. 73.

(27) Richard Dafforne, The Merchants Mirrour, ed. cit.

(28) Richard Dafforne, The Apprentices Time-Entertainer, ed. cit.

(29) Alexander Malcolm, A treatise of Bookkeeping, or, Merchants Accounts; in the Italian Method of Debtor and Creditor.... The Whole Illustrated and Exemplified with Two Sets of Books, Containing Great Variety of Practice in All those Branches of Business, London: Printed for J. Osborn and T. Longman, in Pater-noster-Row; F. Fayram and E. Symon, at the Royal Exchange, 1731, p. 35.

(30) Robert Hamilton, An Introduction to Merchandize. Containing A Compleat System of Arithmetic. A system of Algebra. Book-keeping in various forms. An Account of the Trade of Great Britain, and the Laws and Practices which Merchants are Chiefly Interested In, 2 vols., Edinburgh: Printed for the Author; Sold by T. Cadell, London, and John Balfour, Edinburgh, 1777, vol. I, p. 29.

(31) J.H. Wicks, Book-keeping Reformed ..., Egham: 1797. "Dedication".

(32) R.G.C. Hamilton and John Ball, Book-Keeping, Oxford: At the Clarendon Press, 1869.

(33) J. Thornton, First Lessons in Book-keeping, London: 1879.

(34) G.F. Carr Vernon, Sets for Practice in Book-keeping, London: Sold by Charles Chappell, 3 Brecknock Road, N.W., 1893; "Preface".

(35) Edward Peragallo, Origin and Evolution of Double Entry Bookkeeping. A Study of Italian Practice from the Fourteenth Century.... New York: American Institute Co., 1938, p. 1.

(36) W.P., The Pathway to Knowledge. Conteyning Certaine Briefe Tables of English Waights and Measures ..., Written in Dutch and Translated into English by W.P., London: William Barley, 1596.

(37) Richard Dafforne, The Merchants Mirrour, ed. cit., p. 9.

(38) Alexander Malcolm, A Treatise of Book-keeping, ed. cit., p. 13.

(39) James Peele, The Pathe waye, ed. cit., "A dialogue betwene the Scholemaster and the Scholler ...".

(40) Benjamin Donn, The Accountant and Geometrician: Containing the Doctrine of Circulating Decimals, Loga rithms, Book-keeping and Plain Geometry ..., London: 1765.

(41) Edmond Degrange, La tenue des livres rendue facile, ou nouvelle methode d'enseignement a l'usage des personnes destinees au commerce, avec une nouvelle methode pour tenir des livres en double partie, par le moyen d'un seul registre dont tous les comptes balancent journellement. Sixtieme edition, revue, cossignee et augmentee, Paris: Hocquart & Bordeaux, chez l'auteur et chez Filiatre [&] de l'l'mprimerie de J. Foulquier, 1806, p. 9. Sobre la importancia y repercusion de la aportacion de Degrange, vease J. Lanero Fernandez y E. Ortega Montes, "Algunas consideraciones historiograficas sobre la logica de la Partida Doble y la clasificacion de Cuentas", Pecvnia, 2 (2006), pp. 65-78; pp. 74-75.

(42) Cfr. A.C. Littleton, Accounting Evolution to 1900, New York: Russell & Russell, 1966 [1933], pp. 46-47.

(43) Ibid.

(44) Edmond Degrange, La tenue des livres rendue facile, ed. cit., pp. 6-9.

(45) James Henry Lewis, The Quick and Easy Method of Teaching Book-keeping, ed. cit., p. 41. La italica es del autor.

(46) Philip Crellin, Bookkeeping for Teachers and Pupils With Accounts in Illustration, Exercices for Practice and A Glossary of Commercial Terms, London: Whittaker & Co., White Hart Street, E.C., 1892, p. 26.

(47) Richard Hayes, Modern Book-keeping, or, the Italian Method Improved; Containing Rules and Directions for Keeping ... Accompts by Double Entry, London: 1731, p. 4.

(48) Citado en B.F. Foster, The Origin and Progress of Book-keeping: Comprising an Account of All the Works on This Subject, Published in the English Language, from 1543 to 1852, with Remarks, Critical and Historical, London: Printed for John Souter: Published by C.H. Law, 131, Fleet Street; Aylott and Jones 8, Paternoster Row; John Vandenbergh, 161A, Strand, 1852, pp. 13-14.

(49) En la actualidad se reconoce que el Profesor de Morgan fue quien dio los primeros pasos en contabilidad matricial.

(50) Augustus de Morgan, Elements of Arithmetic, Sixth Edition, London: Edward Stanford, 55, Charing Cross, S.W., 1876, pp. 181-2.

(51) James Collier, Bookkeeping by Double Entry: Familiarly Explained Together with Copious and Graduated Exercises, and a New Method for Dealing with Small Debts, London: Relfe Brothers, 6 Charterhouse Buildings, Aldersgate, E.C., 1884, pp. 5-6.

(52) Ibid., pp. 10-11.

(53) Ibid., p. 11.

(54) S. Dyer, A Common Sense Method of Double-Entry Bookkeeping on First Principles. As Suggested by De Morgan, 2 vols., London: George Philip & Son, 32 Fleet Street, E.C., 1897.

(55) [Edward Thomas Jones], Jones English System of Book-keeping by Single or Double Entry, in Which It Is Impossible for an Error of the Most Trifling Amount to Be Passed Unnoticed; Calculated Effectually to Prevent the Evils Attendant on the Methods so Long Established; And Adapted to Every Species of Trade ..., Bristol: Printed by R. Edwards and sold by the author: by Grosvenor and Chater, Stationers, 1796, p. 26.

(56) Daniel Sheriff, The Whole Science of Double-Entry Book-keeping, Simplified by the Introduction of an Unerring Rule for Debtor and Creditor, Calculated to Insure a Complete Knowledge of the Theory and Practice of Accounts. Designed for the Use of Merchants, Clerks, and Schools, London: Printed by J. Brown & Co., Paternoster-Row, 1850.

(57) B.F. Foster, The Origin and Progress of Book-keeping, ed. cit., p. 31.

(58) James Collier, Bookkeeping by Double Entry, ed. cit., pp. 10-11.

(59) C.F. Sprague, The Bookkeeper, New York, 1882. Citado en A.C. Littleton, Accounting Evolution to 1900, ed. cit., p. 59.

(60) Roger North, The Gentleman Accomptant, ed. cit., pp. 10-11.

(61) Malachy Postlethwayt, The Merchant's Public Counting-House: Or, New Mercantile Institution: Wherein is shewn, the Necessity of Young Merchants Being Bred to Trade with Greater Advantages than They Usually Are. With a Practicable Plan for That Purpose. Also Some Remarks on the Benefit of This Institution to the Young Nobility and Gentry, and Such Who Are Intended for the Study of the Law, Second Edition, London: Printed for John and Paul Knapton, in Ludgate-Street, 1751, pp. 24-5.

(62) Benjamin Donn, The Accountant and Geometrician, ed. cit., "Preface".

(63) Alexander Malcolm, A New Treatise of Arithmetick and Book-keeping ..., Edinburgh: Printed by John Mosman and William Brown, for John Paton Bookseller and are to be sold at his Shop in the Parliament-Closs, 1718, "Preface".

(64) James Bryce, A Treatise of Book-keeping by Double and Single Entry, Edinburgh: Adam and Charles Black, 1860.

(65) B.F. Foster, Double Entry Elucidated, Fifth Edition, London: Printed for John Souter, Published by C.H. Law 131, Fleet Street; Aylott and Jones, 8, Paternoster Row, John Vadenbergh, 161A, Strand, 1852, p. 76.

(66) Philip Comins, The Science of Commerce; or, A New and Universal System of Practical Mercantile Business and Book-keeping Combined, by Double Entry ..., Dublin: 1814, p. 30.

(67) R.B. Roe, An Introduction to Book-keeping ..., London: 1825, "Preface".

(68) Theodore Jones, Jone's English System of Book-keeping for Schools, London: Published by Theodore Jones & Co., 8, Moorgate Street, 1840, p. 2.

(69) The Rev. Dr. Brewer, An Entire System of Book-keeping by Double Entry: Compiled from Invoices by London Merchants and Adopted to Modern Practice for the Use of Schools and Private Tuition, London: Jarrold and Sons, 47, St. Paul's Churchyard, 1850.

(70) James Dimelow, Practical Book-keeping Made Easy. A Series of Practical Book-keeping, Including An Entirely New Mode of Teaching It (...) for the Use of Commercial Schools and for Self-Tuition, London & Glasgow: William Collins, Sons & Co., 1876.

(71) Citado en B.F. Foster, The Origin and Progress of Book-keeping, ed. cit., p. 51.

(72) B.F. Foster, Counting-House Instruction. Remarks on the Ordinary Modes of Teaching Writing and Book-keeping, London: 1846, p. 4.

(73) A.C. Littleton, Accounting Evolution to 1900, ed. cit., p. 181.

(74) James Morrison, The Elements of Book-keeping by Single & Double Entry. Comprising Several Sets of Books. Arranged According to Present Practice & Designed for the Use of Schools. To Which is Annexed An Introduction on Merchants Accounts with Engraved Specimens, London: Printed for Longman, Hurst, Rees, Orme, Brown & Green, 1813, p. 20.

(75) Augustus de Morgan, Elements of Arithmetic, ed. cit., p. 181.

(76) Henry Manly, The Principles of Book.keeping by Double Entry, in A Series of Easy and Progressive Exercices, London: Edward Stanford, 6, Charing Cross, S.W., 1864.

(77) George Lisle, Elementary Book-keeping in Theory and Practice. With Numerous Examples and Exercises, Together with Solutions, London & Edinburgh: W. & R. Chambers, Limited, 1894.

(78) E.E. Whitfield, Introduction to the Commercial Sciences, London: Rivingtons, 34, King Street, Covent Garden, 1900, pp. 118-9.

(79) Andrew Sarll, Double Entry Book-keeping in Theory and Practice; Illustrated by Short and Graduated Exercices; Followed by Examination Papers Arranged in Order of Their Difficulty ..., London: George Gill & Sons, Ltd., Warwick Lane, Paternoster Row, 1899, [1881].

(80) Hustcraft Stephens, Italian Book-keeping Reduced Into an Art: Being an Entire New and Compleat System of Accompts in General. Demonstrated in a Chain of Consequences from Clear and Self-Evident Principles. To Which is Added, The Greatest Variety of Merchants Accounts, with an Explanation of All the Terms of Art, Which have Commonly Been Madre Use of. Together with Proper Reflections on the Whole, London: Printed for W. Mears, at the Lamb on Ludgate-Hill, 1735.

(81) Ibid., "Preface", p. vi.

(82) Ibid., "The Introduction", p. 2.

(83) Ibid., "The Introduction", p. 4.

(84) Ibid., p. 7.

(85) Ibid., p. 10.

(86) Ibid., p. 13.

(87) John Williamson Fulton, British-Indian Book-keeping. A New System of Double Entry and Progressive Adjustment; Exemplified in a Variety of Compendious Methods, for the Practical Purposes as well of the Private Gentleman as of the Merchant. The whole Calculated to Supply a Desideratum in the Art, by a Perspicuous Process, never before adverted to ..., London: Printed by G. Auld, Greville-Street, Hatton-Garden, and Sold by Vernor & Hood, Poultry, 1800, p. vi.

(88) Ibid., pp. 8-9.

(89) Ibid., p. 9.

(90) F.W. Cronhelm, Double Entry by single, A New Method of Book-keeping, Applicable to All Kinds of Business; and Exemplified in Five Sets of Books, London: Printed for the Author by Bensley and Sons, Bolt-Court, Fleet Street; and Published by Longman, Hurst, Rees, Orme, and Brown, Paternoster-Row, 1818.

(91) Ibid., p. vi.

(92) Ibid., p. 5.

(93) Ibid., pp. 7-8.

(94) Ibid., p. 8.

(95) Ibid., pp. 8-9. Resulta sorprendente que esta idea de una ecucion fundamental no la desarrollaran los matematicos. Pierre Jocet escribio su tratado Theorie agebrique et ideologique de la tenue des livres en 1898 y desarrollo una estructura de ecuaciones partiendo de su equation fondamentale, que tiene muchas semejanzas con la de Cronhelm. Cfr. Charles H. Griffin and Thomas H. Williams, "A Comparative Analysis of Accounting and Mathematics", Accounting Review, 37 (No. 3, Jul., 1963), pp. 410-4.

(96) Ibid., p. 9.

(97) P.C.L. Vautro, A New System of Book Keeping; Calculated to Promote the Neccessary Reform of the Old Methods, by Following the Means Particularly Recommended by the Best English Authors, London: Printed for the Author; and Sold by S. Salva, 124, Regent Street, Boosey and Sons, 4, Old Broad Street; and J. Richardson, 91, Royal Exchange, 1828.

(98) J.H. Chauvier, The Perfect Book-keeper, A New Method of Book-keeping, by Double Entry ..., London: 1849.

(99) R.Y. Barnes, A Treatise of Book-keeping; Showing the Advantages of a Clear, Distinct, and Accurate Method of Accounts; and Explaining the Principles of a New and Improved System, Adapted to Meet the Wants of the Entire Trading Community; and by the Use of Which Perfect Bookkeeping May Be Obtained in All Businesses, Small as well as Large, with Ease and Profit, London: John Haddon & Co., 3, George Yard, Lombard Street, 1867.

(100) Percy Child, Book-keeping and Accounts, London: R.E. Thomas and Co., 24, White St., Finsbury, E.C., 1891.
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Author:Lanero Fernandez, J.; Ortega Montes, E.
Publication:Pecunia
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Date:Dec 1, 2006
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