Jordanus Nemorarius

Jordanus Nemorarius (also Jordanus de Nemore ) was a mathematician and mechanic of the early 13th century.

Demonstrations in Arithmetica

Life

His life dates have not survived, but from the mention of his writings in other dated works it can be concluded that he worked in the first half of the 13th century. In the Biblionomia catalog by Richard de Fournival from Amiens from 1246 to 1260, twelve of his works are listed. Some historians assume an identity with the Dominican Jordan of Saxony , but this cannot be conclusively proven. Frequently given dates of life are those of Jordanus von Sachsen. Apart from this identification with Jordan of Saxony, no references to him have been found in any contemporary list of clergy, so that he may not have been a clergyman.

In a manuscript there is a handwritten addition that points to a teaching at the University of Toulouse, but the attribution to Jordanus has been questioned.

The origin of the de Nemore suffix is unclear. A place with this name like Nemus cannot be identified with certainty according to Edward Grant (Dictionary of Scientific Biography) (e.g. Nemi (Latium) ), according to Moritz Cantor it refers to the Latin Nemus (forest) and is used by him to support his Identification with Jordan used by Saxony, in the sense of an origin from a wooded area. But the name could also come from his occupation with arithmetic (corrupted from de numero or de numeris ).

Works

He wrote numerous books on arithmetic , algebra , geometry, and astronomy . His students probably wrote down his works. His works were in frequent use until the 17th century. In his main work, the Liber de numeris datis , he explains, among other things, the solution of quadratic equations using a method that is similar to that of al-Chwarizmi , but is kept in a general form, as this is the first time that letter symbols replace concrete numbers.

It is of particular importance for the history of mechanics. He wrote the first correct description of the statics of weights on an inclined plane. After Pierre Duhem , Jordanus also used the principle of virtual work for the first time in his description of the lever.

A total of six works are definitely assigned to Jordanus Nemorarius:

• Communis et consuetus (Opus numerorum). According to Gustav Eneström a shorter, older version of the Demonstrationes de algorismo (see below). Linked to the work (and the longer version Demonstrationes de algorismo mentioned below) is a short treatise Tractatus minutiarum (after Eneström) on fractions.
• De elementis arismetice artis - first medieval book on number theory . It was printed in Paris in 1496 (and in several editions until 1514) with Jacques Lefèvre d'Étaples' own additions, comments and proofs .
• De plana spera (via stereographic projection ). It is based on the treatment of Claudius Ptolemy in his treatise Planisphaerium. It is shown for the first time in general that circles are mapped onto circles. It was printed in Basel in 1536 (Planispherium) and in Venice in 1558 by Federico Commandino .
• Elementa super demonstrationem ponderum (or Elementa de ponderibus ), about mechanics
• Liber de numeris datis (4 volumes, university textbook on algebra , linear and quadratic equations and systems of equations ).
• Liber philotegni de triangulis (on geometry)

Other works are also ascribed to Jordanus Nemorarius, although the assignment is not certain here:

• De isoperimetris (via isoperimetric figures)
• De proportionibus
• De ratione ponderis (on weights)
• Demonstrationes de algorismo (Explanation of the Arabic number system )

He had such an outstanding position in the teaching of arithmetic and statics in the Middle Ages that a lot appeared under his name that came from other hands and was later printed as a book, for example Algorithm demonstratus Jordani (Nuremberg 1534) based on an anonymous manuscript that found in the estate of Regiomontanus .

Excerpts of his mechanical writings (or writings attributed to Jordanus) appeared in the 16th century, for example by Peter Apian (Nuremberg 1533) and by Nicolo Tartaglia (Quesiti et inventioni diverse, first Venice 1546). Curtius Trojanus published Jordani Opusculum de ponderositate in Venice in 1565 from manuscripts in the Tartaglia estate (De ratione ponderis) .

Individual evidence

1. ↑ The twelve works are: Philotegni (De triangulis), De ratione ponderum, De ponderum proportione, De quadratura circuli, Practica (Algorismus), Practica de minutiis, Experimenta super algebra, Arithmetica, De numeris datis, Quedam experimenta super progressione numerorum, Liber de proportionibus, Suppletiones plane spere. De quadratura circuli is probably identical to part of De triangulis.
2. ^ Marshall Clagett, Archimedes in the Middle Ages (Madison, Wis., 1964)
3. ^ Edward Grant in Dictionary of Scientific Biography. For the interpretation of the name as a corrupted reading of De numero , he quotes Oscar Klein Who was Jordanus Nemorarius? , Nuclear Physics , Vol. 57, 1964, pp. 345-350
4. ↑ Eneström on a short algorism script ascribed to Jordanus Nemorarius, Bibliotheca mathematica, 3rd series, volume 8, 1907/08, pp. 135–153
5. ↑ There she calls Eneström Demonstratio de minutiis
6. ↑ Eneström The Fractional Calculation of Jordanus Nemorarius , Bibliotheca mathematica, 3rd series, Volume 14, 1913/14, pp. 41–54
7. ↑ Busard: Jordanus de Nemore, 'De elementis arithmetice artis': A medieval treatise on number theory. Parts I, II , Stuttgart, 1991
8. ^ Edited by EA Moody, Marshall Clagett, The Medieval Science of Weights (Scientia de ponderibus) , Madison, Wisconsin 1952
9. ↑ Edited by Barnabas B. Hughes, Jordanus de Nemore, De numeris datis , Berkeley-Los Angeles-London, 1981, and P. (eter) Treutlein Der Traktat des Jordanus Nemorarius “De numeris datis” , Treatises on the History of Mathematics, No. 2, Leipzig 1879, pp. 125–166, Maximilian Curtze Commentar on the "Tractatus de numeris datis" by Jordanus Nemorarius , Journal of Mathematics and Physics, Hist.-lit. Abt., Vol. 36, 1891, pp. 1-23, 41-63, 81-95, 121-138
10. ↑ Two versions are known. The longer, younger version was published by Maximilian Curtze Jordani Nemorarii Geometria vel De triangulis libri IV , Mitteilungen des Coppernicus-Verein, 6 (1887). Marshall Claggett published both versions in Archimedes in the Middle Ages , Volume 4
11. ^ HLL Busard: The tracts De proportionibus by Jordanus Nemorarius and Campanus , Centaurus, Volume 15, 1971, pp. 193-227
12. ^ Edited by EA Moody, Marshall Clagett, The Medieval Science of Weights (Scientia de ponderibus) , Madison, Wisconsin 1952
13. ^ Gustav Eneström on the 'Demonstratio Jordani de algorismo,' , Bibliotheca mathematica, 3rd series, Volume 7 1906/1907, pp. 24–37

literature

• Edward Grant : Jordanus de Nemore . In: Charles Coulston Gillispie (Ed.): Dictionary of Scientific Biography . tape 7 : Iamblichus - Karl Landsteiner . Charles Scribner's Sons, New York 1973, p. 171-179 .
• HLL Busard , Jordanus de Nemore, 'De elementis arithmetice artis': A medieval treatise on number theory. Parts I, II , Stuttgart, 1991
• Moritz Cantor , Franz Stanonik :  Jordanus Nemorarius . In: Allgemeine Deutsche Biographie (ADB). Volume 14, Duncker & Humblot, Leipzig 1881, pp. 501-504.
• Marshall Clagett , Archimedes in the Middle Ages , Madison, Wis., 1964
• BB Hughes, Jordanus de Nemore, De numeris datis , Berkeley-Los Angeles-London, 1981
• EA Moody and M. Clagett (Eds.), The medieval science of weights (Scientia de ponderibus), Treatises ascribed to Euclid, Archimedes, Thabit ibn Qurra, Jordanus de Nemore, and Blasius of Parma , Madison, Wis., 1952
• Jens Hoyrup Jordanus de Nemore, 13th Century Mathematical Innovator , Archive for History of Exact Science, Volume 38, 1988, pp. 307-363.
• Jens Hoyrup Jordanus de Nemore: a case study on 13th century mathematical innovation and failure in cultural context , Philosophica, Volume 42, 1988, pp. 43-77
• Pierre Duhem, article in Catholic Encyclopedia 1911

Web links

• Internet facsimile of a print of the Elementa super demonstrationem ponderum from 1565
• John J. O'Connor, Edmund F. Robertson :  Jordanus Nemorarius. In: MacTutor History of Mathematics archive .