Jordanus (Jordanis) de Nemore

The name given in manuscripts of the thirteenth and fourteenth centuries to a mathematician who in the Renaissance period was called Jordanus Nemorarius. A number of his works are extant, but nothing is known of his life. It is customary to place him early in the thirteenth century. Emile Chasles, the geometrician, concluded from a study of the "Algorismus Jordani" that its author lived not later than the twelfth century. In the fourteenth century the English Dominican Nicolas Triveth, in a chronicle of his order, attributed the "De ponderibus Jordani" and the "De lineis datis Jordani" to Jordanus Saxo, who, in 1222, succeeded St. Dominic as master general of the Friars Preachers. Since then, the identity of Jordanus Saxo with Jordanus Nemorarius has been accepted by a great many authors; it seems difficult to maintain this opinion, however, as the Dominican superior general never adds de Nemore to his name, and the mathematician never calls himself Saxo. The literal translation of Jordanus de Nemore (Giordano of Nemi) would indicate that he was an Italian. Jordanus had a great vogue during the Middle Ages . In the "Opus Majus", under "De communibus naturæ", Roger Bacon quotes his "De ponderibus", as well as a commentary which had been written on it at that period. Thomas Bradwardine and the logicians who succeeded him in the school of Oxford likewise make a great deal of use of the writings of Jordanus. During the Renaissance his "De ponderibus" powerfully influenced the development of the science of statics.

The treatises composed by Jordanus de Nemore are: (1) "Algorismus", a theory of the elementary operations of arithmetic. An "Algorithmus demonstratus Jordani" was printed at Nuremberg in 1534, by Petreius for Johannes Schöner. The "Algorithmus" reproduced an anonymous manuscript found among the papers of Regiomontanus. It was erroneously attributed to Jordanus, and had really been composed in the thirteenth century by a certain Magister Gernardus (Duhem in "Bibliotheca mathematica", 3rd series, VI, 1905, p. 9). The genuine "Demonstrato Algorismi" of Jordanus, which E. Chasles had already examined, has been rediscovered by M. A. A. Bjornbö (G. Eneström in "Bibliotheca mathematica", 3rd series, VII, 1906, p. 24), but is still unpublished. (2) "Elementa Arismeticæ": this treatise on arithmetic, divided into distinctiones , was printed at Paris in 1496 and in 1514, to the order of Lefèvre d'Etaples , who added various propositions to it. (3) "De numeris datis", published in 1879 by Treutlein ("Zeitschr. Math. Phys.", XXIV, supplem., pp. 127-66) and again in 1891 by Maximillian Curtze (ibid., XXXVI, "Histor. liter. Abtheilung", pp. 1-23, 41-63, 81-95, 121-38). (4) "De triangulis".--Jordanus himself gave this treatise the name of Philotechnes (Duhem in "Bibliotheca mathematica", 3rd series, V, 1905, p. 321; "Archiv für die Geschichte der Naturwissenschaften und der Technik", I, 1909, p. 88). It was published by M. Curtze ("Mittheil. der Copernicusvereins für Wissenschaft und Kunst", VI--Thorn, 1887). (5) "Planispherium".--This work on map-drawing gives, for the first time, the theorem: The stereographic projection of a circle is a circle. It was printed by Valderus, at Basle, in 1536, in a collection containing the cosmographical works of Ziegler, Proclus, Berosius, and Theon of Alexandria, and the "Planisphere" of Ptolemy. (6) "De Speculis", a treatise on catoptics, still unedited. (7) "De ponderibus", or better, "Elementa super demonstrationem ponderis", a treatise on statics, in nine propositions, still unpublished, seems to have been composed as an introduction to a fragment on the Roman balance attributed to one Charistion, contemporary and friend of Philo of Byzantium (second century, B.C.). This fragment has survived under two forms: (a) a Latin version directly form the Greek, entitled "De canonio"; (b) a ninth-century commentary by the Arab mathematician Thâbit ibn Kurrah, translated into Latin by Gerard of Cremona .

Most of the propositions of the "De ponderibus Jordani" are gravely erroneous. But the last offers a remarkable demonstration of the principle of the lever, introducing the method of virtual work for the first time in mathematical history. Towards the end of the fourteenth century, or the beginning of the fifteenth, an anonymous author expanded the demonstrations in Jordanus's treatise; in this enlarged form, the treatise, combined with the "De cannio", is found in many manuscripts under the title "Liber Euclidis de ponderibus". There is also an anonymous commentary on the "De ponderibus", based on ideas apparently borrowed from Aristotle's "Quæstiones mechanicæ". This Aristotelean commentary is mentioned by Roger Bacon in his "Opus majus"; together with an enlarged edition of the "Liber Euclidis de ponderibus", it was printed at Nuremberg, in 1533, by Johannes Petreius, under the direction of Petrus Apianus, under the title "Liber Jordani Nemorarii, viri clarissimi, de ponderibus". In the thirteenth century an anonymous author undertook to write a preamble to a fragment on mechanics, this fragment being of Hellenic origin, and, apparently, later than Hero of Alexandria. For this purpose he resumed Jordanus's work, correcting, however, its errors in mechanics. The method of virtual work, employed by Jordanus to justify the law of equilibrium of the straight lever, supplies this anonymous writer with some admirable demonstrations for the law of equilibrium of the bent lever and for the apparent weight of a heavy body on an inclined plane. This preamble is found in many manuscripts, with the Hellenic fragment. In 1554 it was cynically plagiarized by Nicolò Tartaglia in his "Quesiti et inventioni diverse"; the manuscript text, found in Trataglia's papers, was published at Venice, in 1565, by Antius Trojanus, under the title: "Jordani Opusculum de ponderositate, Nicolai Tartaleæ studio correctum" (A Brief Work of Jordanus, on Ponderosity, carefully corrected by Nicolò Tartaglia ).

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