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Liber de triplici motus by Alvarus Thomas

 
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500 Years

> Versão Portuguesa

Alvarus Thomas or Álvaro Tomás (fl. 1509), a Portuguese master at the University of Paris at the beginning of the sixteenth century, is still a poorly known historical figure. In his Liber de triplici motu he presented a comprehensive and sophisticated analysis of the theory of proportions and of the science of motion of his time, in the characteristic form of the Calculatory tradition. Besides some interesting criticism of contemporary physical theories, this work is also relevant from the point of view of mathematics since Thomas achieves some surprising results in the study of infinite series.

He published this book in 1509, exactly 500 years ago, under the title "Book on the three [kinds of] movement, with added [treatise on] ratios, by Master Alvarus Thomas of Lisbon, Explaining in Part Swineshead's Philosophical [i.e. Physical] Calculations".

 

Liber de triplici motu proportionibus annexis magistri Alvari Thomae Ulixbonensis philosophicas Suiseth calculationes ex parte declarans,

Explicit liber de triplici motu compositus per Magistrum Aluarum Thomam vlixbonensem Regentem Parrhisius in Collegio Coquereti. Anno domini. 1509. Die Februarii. 11

Impressum Parris[iis]: per Guillermum Anabat ... ex[p]ensis Po[n]seti le Preux, [1509]

 

Copies (with frontispice type 1):

> Digitalized copy (B General A Res. 52/4/27) at Biblioteca de la Universidad de Sevilla

> Digitalized copy from the Digital Research Library, Archimedes Project

 

Digitalized frontispice type 2:

> Digitalized copy of the 2 first and 2 last pages (B. GENERAL BG/13232) from the Biblioteca de la Universidad de Salamanca

 

 

 

 

Preface to the Liber de triplici motu

Prohemium

Preclara Philonis in libro Sapientie extat sententia deum maximum optimumque rerum omnium natura constantium opificem, cunctorum substantiam atque compaginem numero, mensura, ac pondere procreasse atque disposuisse; cui applaudit illud prophete qui profert numero seculum. Cui etiamt [sic] astipulatur divus ille Plato in Thimeo, magna auctoritate commendans deum numeris mundum fabricasse. Quam sententiam Aurelius Augustinus libro De Civitate Dei commendat. Quapropter intima, secretioraque nature atque minerve penetralia, rerumque omnium naturalium reconditas passiones, ac motus qui numeris consistunt perscrutari atque rimari volentes, arithmeticam atque geometriam aut saltem harum scientiarum quedam requisita documenta necessum est anteponant. Et non abs re quidem, quoniam non solum elementaris hec regio et naturalia illa entia que in ea natura procreanda censuit his numeris et geometricis ponderibus constant, verumetiam ethereus ille celorum globus (ut inquit Plinius et Aristoteles) Pythagore sententia arithmeticis proportionibus, musicisque tonis circumvoluitur. Inquit enim saturnum dorio moveri, mercurium pthogo, iovem phrygio. Quantam videlicet arithmetica scientia habeat ad philosophiam universasque disciplinas, luculentur in libro De Legibus divus Plato ostendit inquiens Legislator civibus omnibus precipiat ne a numerorum ordine quo ad possunt discedant. Nam nulla alia disciplina ad rei familiaris gubernationem, ad rem publicam, ad artes denique universas, tantam habeat vim, quantam huiusmodi numerorum cognitio. Sonnolentos, etiam a natura rudes, excitat, et dociles, memores, solertesque facit, preter naturam suam divina arte proficientes. Inconcussa enim et inviolata est arithmetice atque geometrie scientia, cuius veritati sacratissime sanctiones auctoritatem prebent inquientes arithmeticam et geometriam in se veritatem continere et quamvis pietatis scientie non sint, sunt tamen maximo adminculo atque adiumento ipsi scientie pietatis ut preclare Aurelius ille Augustinus in libro De Doctrina Christiana sacris comprobat rationibus. Has enim sapiens ille Salomon dicit pedissequas, atque ancillas theologie, quas iubet vocari ad turrim, et ad menia civitatis. His enim prostergatis, qui ad theologisandum et philosophandum progreditur (si divo Severino Boetio credimus) superflue conatur. Ad philosophiam utique temere his mathemathicis omissis documentis accedentes, philosophia ipsa sacrilegos, suique minimis invasores vestem sua frusta lacerantes (teste Boetio) appellat. Et ut verum fatear hinc est quod nostris temporibus ob harum disciplinarum defectum balbutiens atque concutiens visa est philosophia. Plurimum enim apud Grecos philosophia valuit primatumque obtinuit, quia (ut inquit Cicero) in summo honore apud illos geometria fuit nihilque apud eos mathematicis illustrius. Non immerito igitur speculationibus physicis triplicis motus tractaculum proportionum ex mathematicis codicibus depromptum duximus preponedum et quantum ingenioli nostri vires suppetunt absolvendum.

 

[Transcription made from the exemplar at the Biblioteca Nacional de Portugal, Lisbon]

 

Monday, 28th September

Alvarus Thomas Workshop
CIUCHT, Lisbon
More information...

 

 

> Preface of the Liber

> Bibliography

> Census of exemplars

 


Frontispice (type 1), black and red print, of Liber de triplici motus, Paris, 1509


Alternative frontispice (type 2) of Liber de triplici motus, Paris, 1509

     
     

Bibliography

S T U D I E S

  • Pascal Brioist & Jean-Jacques Brioist, "Harriot, lecteur d'Alvarus Thomas et de Niccolo Tartaglia", in Joël Biard et Sabine Rommevaux eds., Mathématiques et théorie du mouvement. XIVe-XVIe siècles, (Villeneuve d'Ascq: Presse Universitaire du Septentrion, Collection: Histoire des sciences, 2008), p. 147-172
  • Carlos Correia de Sá, "A soma de séries na obra De triplici Motu de Álvaro Tomás", Encontro Luso-Brasileiro de História da Matemática, 2004
  • Pierre Duhem, Études sur Léonard de Vinci, ceux qu'il a lus et ceux qui l'ont lu. Troisième série. Les précurseurs parisiens de Galilée, Paris, A. Hermann et fils, 1913
  • Luís de Matos, Les Portugais à l'Université de Paris entre 1500 et 1550 (Coimbra: Universidade de Coimbra, 1950)
  • Henrique Leitão, "Notes on the life and work of Álvaro Tomás", Bulletin do CIM [Centro Internacional de Matemática], n. 9, Dezembro de 2000, p. 10-15
  • Henrique Leitão, "Álvaro Tomás, calculator português em Paris", Ciência em Portugal: Personagens e Episódios, http://www.instituto-camoes.pt/cvc/ciencia/e44.html
  • Matthias Schemmel, The English Galileo: Thomas Harriot's Work on Motion as an Example of Preclassical Mechanics, Boston Studies in the Philosophy of Science , Vol. 268, Berlin, Springer, 2008. Partially digitalized here.
  • Edith Sylla, "Mathematics in the Liber de triplici motu of Alvarus Thomas of Lisbon", in The practice of Mathematics in Portugal, Coimbra, 2004, p. 109-161
  • Edith Sylla, "Alvarus Thomas and the role of Logic and Calculations in sixteenth century Natural Philosophy", in Stefano Caroti ed., Studies in Medieval Natural Philosophy, Biblioteca di Nuncius Studi e Testi, Florence, Olschki, 1989, p. 257-298
  • William A. Wallace, "The calculators in the sixteenth century", in William A. Wallace ed., Prelude to Galileo. Essays on Medieval and sixteenth-century sources of Galileo's thought, Boston Studies in the Philosphy of Science, vol. 62, Dordrecht, Boston, Reidel, 1981, p. 78-90
  • William A. Wallace, "The Enigma of Domingo de Soto: Uniformiter difformis and Falling Bodies in Late Medieval Physics", Isis, vol. 59, no. 4, 1968, p. 384-401, particularly p. 394-395.
  • Heinrich Wieleitner, "Zur Geschichte der unendlichen Reihe im Christlichen Mittelalter", Bibliotheca Mathematica, Dritte Folge, Vol. 14, (1914), p. 150-168

D I C T I O N A R Y   E N T R I E S

  • F. Gama Caeiro, "Tomás, Álvaro", in: Enciclopédia Luso-Brasileira de Cultura (Lisboa: Editorial Verbo, 1963-1985), Vol. 17, p. 1643
  • Francisco Gomes Teixeira, "Alvaro Tomaz e Gaspar Nicolas, aritmeticos", in História das Matemáticas em Portugal (Lisboa: Academia das Ciências de Lisboa, 1934), p. 95-97
  • J. Rey Pastor, Los Matematicos Españoles del Siglo XVI (Toledo: Biblioteca Scientia, 1926), p. 82-89
  • William Wallace, "Thomaz, Alvaro", in C. C. Gillispie ed., Dictionary of Scientific Biography (New York: Charles Scribner's Sons, 1970-1980), Vol. 13, p. 350
 
     

Census of extant copies

[under construction]

  • Queen Mother Library, Aberdeen University, United Kingdom (1)
  • University of Michgan Library, Ann Arbor, US (1):
  • Staats- und Stadtbibliothek Augsburg, Augsburg, Germany (1):
    • Shelfmark 2 Ink adl 9
  • Staatsbibliothek Berlin, Germany (1?):
  • Bibliothèque Mériadeck Patrimoine, Bordeaux, France (1):
    • Shelfmark magasin fonds patrimoniaux S 348
  • Royal Observatory Library, Edinburgh, United Kingdom (1?)
  • Biblioteca Pública de Évora, Portugal (3):
    • Séc. XVI 1003
    • Séc. XVI 1019
    • Res 649
  • Biblioteca Pública del Estado, Girona, Catalunya, Spain (1):
    • Shelfmark A/22
  • Universitätstbibliothek Heidelberg, Germany (1?)
  • Kongelige Bibliotek, Universitetsbiblioteket, København, Denmark (1):
  • Universitäts- und Stadtbibliothek Köln, Alemanha (1)
  • Universitätstbibliothek Leipzig (Biblioteca Albertina), Germany (1):
    • Shelfmark Philos.53/2
  • Biblioteca Nacional de Portugal, Lisbon (1):
  • Biblioteca da Ajuda, Lisbon, Portugal (1)
  • Private collection, Lisbon, Portugal (1)
  • British Library [formerly British Museum], London (1):
  • Biblioteca Nacional de Madrid, Spain (1?)
  • Bayrische Staatsbibliothek, München, Germany (2?):
  • Nürnberg Staatsbibliothek, Germany (1?)
  • Biblioteca General de Navarra, Pamplona (1):
    • Shelfmark 109-11-2/62
  • Bibliothèque Nationale de France, Paris (2?):
    • Shelfmark RES- V- 619
    • Shelfmark RES- R- 146
  • Biblioteca Universitaria Alessandrina, Rome (1):
    • Frontispice type 2, Shelfmark D.g.15.f2 (Inventario: LA 1004301)
  • Biblioteca de la Universidad de Salamanca, Spain (1):
  • Biblioteca Capitular y Colombina, Sevilla, Spain (1):
    • Shelfmark 13-6-15
  • Biblioteca General y Archivo Histórico de Sevilla, Spain (1):
  • Kungl. biblioteket är Sveriges nationalbibliotek [Swedish National Library], Stockholm, Sweden (1):
  • University of Toronto Library (Thomas Fisher Library), Canada (1):
    • Shelfmark Thomas Fisher Rare Book sci 06559 or sci 02472
  • Bibliothèque d'Étude et du Patrimoine, Toulouse, France (1):
  • Universitätstbibliothek Tübingen, Germany (1):
  • Österreichische Nationalbibliothek, Viena, Austria (1):
  • Biblioteca Apostolica Vaticana, Vatican (1?)
  • Herzogin Anna Amalia Bibliothek, Weimar, Germany (1)
  • Biblioteca Universitaria Universidad de Zaragoza, Spain (1):
    • Shelfmark H-2-57(1)

Number of identified copies TOTAL: 34

 

 
     

S.Gessner
H.Leitão

 

 
            
           
  Última actualização 18-09-09