Abstract
The ideas propounded in the Elementa Jordani de ponderibus provoked very intense intellectual excitement during the Middle Ages. Philosophers, geometers and mechanicians vied with each other in discussing, commenting upon and developing these ideas. From the 13th century, the Elementa de ponderibus inspired treatises quite different from their source.
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References
Bibliothèque Nationale, Latin collection, No. 12247.
T. N.: The Latin reads, “As was evident in the next to last of the above demonstrations.”
T. N.: The Latin reads, “As it has been demonstrated by Euclid, Archimedes and others.”
Bibliothèque Nationale, Latin collection, Ms. 8680 A. The text of Ms. 7378 A, when compared to that of Ms. 8680 A, shows that the demonstrations had undergone several significant emendations. The fragment preserved in the “Codex Mazarineus” is a part of the unemended text in manuscript 8680 A.
T. N.: This is the book Duhem called earlier the Filotegni.
Bibliothèque Nationale, Latin collection, Ms. No. 7378 A.
T. N.: The Latin reads, “It has been demonstrated in books dealing with these matters.”
T. N.: Latin collection, Mss. Nos. 7310 and 10260.
T. N.: Latin collection, Ms. No. 7215.
Maximilian Curtze, Das angebliche Werk des Euklides über die Waage (Zeitschrift für Mathematik und Physik, XIX. Jahrgang, p. 263,1874).
Valentin Rose, Anecdota graeca et graeco-latina, liter Heft, 1870, — VII, Zwei Bruchstücke griechischer Mechanik. Philon und Heron.
T. N.: The Latin title reads, The Book on Weights by Jordanus, according to some, by Euclid. The Latin quote reads, “Here ends The Book on Weights, attributed by some to Euclid.
Maximilian Curtze, Zwei Beiträge zur Geschichte der Physik (Bibliotheca Mathematica, 3e Folge, Bd. I, p. 51; 1900).
Maximilian Curtze, Ueber die Handschrift, R. 40 2: Problematum Euclidis explicatio des Königl. Gymnasiums zu Thorn (Zeitschrift für Mathematik und Physik, XHIter Jahrgang, Supplément, p. 45, 1868). One can say the same about a piece entitled Liber de ponderibus vel de staterà Jordani, pointed out by Curtze in Ms. Db. 86, at the beginning of the XIVth century, kept in the Library of Dresden (Maximilian Curtze, Ueber eine Handschrift der K. Bibliothek zu Dresden: Zeitschrift für Mathematik und Physik, XXVIIIter Jahrgang, Supplément, p. 1; 1883).
This is the date attributed to it by Thurot (a) and confirmed by the Gothic handwriting. The catalogue in the Bibliothèque Nationale assigns Ms. 7378 A to the 14th century. As a matter of fact, other texts follow those which interest us here and are written in a different handwriting and almost certainly were copied in the 14th century. Thus, on sheet f. 52, one reads: Expliciunt canones tabularum astronomie sive tractatus de sinibus et cordis per Magistrum Johannem de Linieriis, ordinati et completi Parisiis anno ab Incarnatione Domini 1322. The same on sheet f. 63; Explicit pronosticatio Magistri Leonis Judei facta in Anno Domini 1341. Incipit pronosticatio Magistri Johannis de Muris super eodem. (T. N.: The Latin reads, Here end the rules of the astronomical tables or the Treatise on Sines & Cords by Master John of Linierius, completed in Paris, 1322. Here ends the Prognosis of Master Leon Judeus made in 1341. Here begins the Prognosis of Master John of Murs.) Chevalier (b) gives us the following information on John of Murs: musician and mathematician, Doctor at the Sorbonne, 1321.
(a) Thurot, Recherches historiques sur le Principe d’Archimède (Revue Archéologique, nouvelle série, Vol. XIX, p. 117,1869.)
(b) U. Chevalier, Bibliographie du moyen age, col. 1213.
T. N.: The Latin title reads, The Book on Weights by the illustrious Jordanus de Nemore, containing thirteen propositions with their demonstrations as well as extremely elegant explications of many other matters, now published with Imperial privilege by Peter Apian, mathematician of Ingolstadt, licensed for thirty years, 1533.
T. N.: The Latin reads, “Another commentary follows.”
Bibliothèque Nationale, Latin collection, No. 7378 A.
This is the date assigned to the manuscript by Thurot (Recherches historiques sur le Principe dArchimède (Revue Archéologique, nouvelle série, Vol. XIX, p. 117, 1869)). The handwriting of this manuscript is clearly from the 13th century.
Bibliothèque Nationale, Latin collection, No. 8680 A.
Jordani, Opusculum de ponderositate,Nicolai Tartaleae studio correctum novisque figuris auctum. Venetiis, apud Curtium Trojanum, MDLXV. (T. N.: The Latin reads, A Treatise on Weight by Jordanus, corrected and enlarged with new figures by Nicolo Tartaglia. Venice, Curtius Trojanus, 1565.
T. N.: The Latin words “pondus,” “mundus,” “regula” and “responsa” mean “weight,” “world,” “rule” and “answer” respectively.
T. N.: Duhem, in his Études sur Léonard de Vinci, changed this designation to the Precursor of Simon Stevin.
T. N.: The Latin title reads, On the Common Principles of all Natural Phenomena.
Liber primus, Prop. II. — Edition of Curtius Trojanus, Quaestio II.
Liber primus, Prop. VIII — Edition Curtius Trojanus, Quaestio VIII.
Liber tertius, Propositiones I et II. — Editions of Curtius Trojanus, Quaestiones XXIII et XXIV.
Liber tertius, Propositio V. — Edition of Curtius Trojanus, — Quaestio XXVII. The scribe introduced errors in this proposition so that the author’s ideas are sometimes rendered unintelligible.
Liber primus, Propositio VIII. Edition of Curtius Trojanus, Quaestio VIII.
Liber primus, Propositio VIII, et Liber tertius, Propositio III. Edition of Curtius Trojanus, Quaestiones VIII et XXV.
Liber primus, Propositio IX. Edition of Curtius Trojanus, Quaestio IX.
Liber primus, Propositio IX. Edition of Curtius Trojanus, Quaestio IX.
T. N.: Duhem has written “el” where one should read “It”.
Cf.: Affò, Scrittori parmigiani Parma, 1789: Vol. II pp. 112, 118, 123.
Tiraboschi, Storia delle lettere italiane.1807, Vol. VI, I, pp. 335–339.
Gherardi, Di alcuni materiali per la storia della facoltà matematica nell’antica università di Bologna, Bologna. 1846.
T. N.: Italian for, “A distinguished philosopher and mathematician.”
Bassiani politi Laudens, De numero modalium; — Ejusdem, Tractatus proportionum. — Nicolai Hören, Proportiones; — Ejusdem, De latitudinibus formarum. — Blasii de Parma, De latitudinibus formarum; De sex inconvenientibus. — Joannis de Lasali, De velocitate motus alterationis Blasii de Parma, De tactu corporum durorum. Venetiis, mandato et sumptibus heredum Oct. Scoti Modoetiens, per Bonetium Locatelfum Bergom. Kal. Sept. MDV.
Bibliothèque Nationale, Latin collection, No. 10252.
T. N.: The Latin reads, Song of Weights or of Weights and Measures.
T. N.: The Latin reads, The Minor Latin Poets.
T. N.: Latin for, “Since the science of weights is subordinate to geometry as well as to natural philosophy…”
T. N.: Latin for, “The science of weights is rightly said to be subordinated to natural philosophy.” Duhem seems to ignore the essential difference between these two quotes.
T. N.: The Latin reads, “Now, with the weight having been given, I wish to obtain a knowledge of the arms.”
T. N.: The Latin reads, “However, let the philosophers consider it.”
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Duhem, P. (1991). The Statics of the Middle Ages (Continued) the School of Jordanus. In: The Origins of Statics. Boston Studies in the Philosophy of Science, vol 123. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3730-0_7
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