Abstract
The fragment De ponderoso et levi attributed to Euclid; the four propositions called Liber Euclidis de ponderibus secundum terminorum circumferentiam; the treatise De canonio; the Liber Karastonis published by Thâbit ibn Qurra: all of the above works as well as the Mechanical Problems of Aristotle seem to be the sole remnants of the Greek works on statics used by medieval mechanicians. They do not seem to have known of Archimedes’ method because they never use it in their works. As for the Arabs, they seem to have merely transmitted to the Western world the remnants of Alexandrian science.
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References
Montucla, Histoire des Mathématiques, Vol. I, p. 506; Paris, an VII.
Chasles, “Histoire de l’Algèbre. Sur l’époque où l’Algèbre a été introduite en Europe.” (Comptes Rendus, Sept. 6,1845, Vol. XIII, p. 507).
In hoc opere contenta: Jordani Nemorarii arithmetica decern libris demonstrata; Musica libris demonstrata quatuor, per Jacob. Fabrum Stapul.; Epitome in libros arithmeticos divi Severini Boetii; Ritmachie ludus qui et pugna numerorum appellatur. Parisiis. Jo. Higman et Volg. Hopil. 1496, in-folio, Gothic 72 ff. (T. N.: The Latin reads, Contained in this work: Arithmetic demonstrated in 10 books by Jordanus de Nemore; The Art of Music Demonstrated in 4 Books by Jacob Faber Stapulensis: Abstract for the Mathematical Books of the Divine Severinus Boetius: The Game of “Rithmomachie” which is also called the “Battle of Numbers.” Paris, 1496 in Gothic folio, pp. 71dd.) (Cf. Graesse, Trésor de livres rares et précieux, vol. III—J. Ch. Brunet, Manuel du libraire et de l’amateur de livres, p. 566).
Regiomontanus, Oratio in proelectiones Afragani, Norimbergae, 1537, in-4°. (T. N.: The Latin title reads, A Speech against the lectures of Afraganus, Nuremberg, 1537, in quarto.)
Cf. Chasles, “Histoire de l’Algèbre. Sur l’époque où l’Algèbre a été introduite en Europe,” (Comptes Rendus, Vol. XIII, 1845, p. 507).
T. N.: The Latin reads, “Jordanus published three very fine books on the properties of numbers.”
D. Francisci Maurolyci, Opuscula mathematica, Venetiis, 1575. Index lucubrationum. (N.T.: The Latin title reads, Francesco Maurolico, Treatise on Mathematics, Venice, 1575. With an Index of Erudite Works.) This list is reproduced in Libri, Histoire des Sciences mathématiques en Italie, Paris, 1840, Vol. III, p. 243.
Chasles, Histoire de l’Algèbre. Note sur la nature des opérations algébriques (dont la connaissance a été attribuée à tort à Fibonacci). Des droits de Viète méconnus (Comptes Rendus, 5 Mai 1841, Vol. XII, p. 743).
Treuttlein, Zeitschrift für Mathematik und Physik, Vol. XXIV, Supplément, pp. 135 and 136, 1879.
M. Curtze, Zeitschrift für Mathematik und Physik, Vol. XXXVI, Histor. litterar. Abtheilung, pp. 1, 41, 81, 121; 1891.
Cf. on this subject Treuttlein, Zeitschrift für Mathematik und Physik, Vol. XXIV, Supplément, p. 132; 1879. — Only recently was the attribution of the Algorithmus demonstratus to Jordanus questioned by M. G. Eneström in a work entitled, “1st Jordanus Nemorarius Verfasser der Schrift ‘Algorithmus demonstratus?” (Bibliotheca mathematica, 3 Folge, Vol. V, p. 9; 1904).
Maximilian Curtze, Jordani Nemorarii de triangulis libri quatuor (Mittheilung des Copernicus-Vereins für Wissenschaft und Kunst zu Thorn, 1887, Heft VI.). (T. N.: The Latin reads, Four Books on Triangles by Jordanus Nemorarius.)
Chasles, Aperçu historique, p. 516 — Weidler, Historia Astronomiae, 17 Al, p. 276.
Heilbrunner, Historia matheseos universae, 1742, p. 604. — Chasles, Aperçu historique,p. 517.
Moritz Cantor, Vorlesungen über die Geschichte der Mathematik, Vol. II, p. 54, 1892.
T. N.: The Latin reads, “Here begins the Treatise of Jordanus on Mirrors with a Commentary on the same.”
T. N.: The Latin reads, “Here ends the Book on Mirrors — Here begins the Elements of Jordanus on Weights.”
T. N.: The Latinized Greek reads, “a private person.”
Daunou, Histoire littéraire de la France, Vol. XVIII, p. 140, “Art. Jourdain le Forestier.”
T. N.: The Latin title reads, A Chronology of Famous Mathematicians.
Cf. on this subject, Moritz Cantor, Vorlesungen über die Geschichte der Mathematik, Vol. II, p. 599.
T. N.: The Latin title reads, The Third Work.
Chasles, Histoire de VAlgèbre. “Note sur la nature des opérations algébriques (dont la connaissance a été attribuée à tort à Fibonacci). — Des droits de Viète méconnus” (Comptes Rendus, May 5, 1841, Vol. XII, p. 743).
Libri, Histoire des Sciences mathématiques en Italie, Vol. IV, p. 490; 1841.
Chasles, Histoire de TAlgèbre. Sur l’époque où VAlgèbre a été introduite en Europe” (Comptes Rendus, Sept. 6,1841, Vol. XIII, p. 107).
T. N.: The Latin title reads, The Book on Weights by the Illustrious Jordanus Nemorarius.
Treuttlein, Zeitschrift für Mathematik und Physik. Supplement zur historisch-litterarischen Abtheilung des XXIV Jahrganges. Abhandlungen zur Geschichte der Mathematik, 1879, p. 125.
Maximilian Curtze, Mittheilung des Copernicus- Vereins für Wissenschaft und Kunst zu Thorn, 1887, Heft VI.
Id., Maximilian Curtze, Mittheilung des Copernicus- Vereins für Wissenschaft und Kunst zu Thorn, 1887, Heft VI. (T. N.: The Latin title reads, Four Books on Triangles by Jordanus Nemorarius.)
T. N.: “Nemorarius” perhaps derives from the Latin word for forest, “nemus, (gen.) nemoris.”
T. N.: Duhem probably means the city of Hildesheim near Dassel.
T. N.: The Latin title reads, Mathematical Delights.
R.P. Denifle, a letter addressed to Maximilian Curtze and included by the latter in his work.
Moritz Cantor, Vorlesungen über die Geschichte der Mathematik, Vol. II, p. 53.
Bibliothèque Nationale (Latin collection): No. 16644 (XIIIth century) Jordani de Nemore Arismetica — No. 7364 (XIVth century) Jordani de Nemore Elementorum Arismetice distinctiones decern — No. 16198 (XIV century) Jordani de Nemore Elementorum Arismetice — No. 14737 (XV century) Jordani de Nemore Elementa Arismetice. (T. N.: The Latin title reads, The Elements of Arithmetic of Jordanus de Nemore.)
M. Curtze, “Die angebliche Werke des Euklides über die Waage” (Zeitschrift für Mathematik und Physik, XIX. Jahrgang, p. 263, 1874).
Nemus, the Latin form for “Nemi.” Cf. De Vit, Totius latinitatis onomasticon, Prati, MDCCCLXXXLVII, Vol. IV, p. 651.
T. N.: “Moment” in this context is to be understood, in the manner of Archimedes, as the product of force and perpendicular distance to the pivot point.
T. N.: This is Duhem’s translation of the Greek original. Cf. Aristotle’s Minor Works, Mechanical Problems, 848b, 11.
Aristotle, Mechanical Problems,III.
T. N.: Due to the excess weight of the lever to the right of the point of support there exists a restoring moment.
T. N.: In this case, the unbalanced moment will cause the lever to rotate about point A (Fig. 19) until it assumes the configuration shown in Figure 18, if the rotation is unimpeded.
Bibliothèque Nationale (Latin collection), No. 10252.
T. N.: The Latin title reads, Algorism of Integers by John of Sacrobosco. Finished in Naples, by Arnold of Brussels, Feb. 11, 1476, before sunrise.
Bibliothèque Nationale, Latin collection, No. 10267.
T. N.: The Latin reads, “The End. Completed April 1468. Here end the rules for the tables of the illustrious mathematician and Doctor of Arts, John of Bianchine, a soldier in the service of the most efficacious benefactor, the illustrious Borso, Duke of Modena and Reggio, Count of Rovigo, Marquis of Este and Ferrara, completed by Arnold of Brussels, of the Duchy of Brabant, in April 1468 in the city of Naples.”
T. N.: The Latin reads, Brussels, at 40° of latitude.
De Saint-Genois, Biographie Belge, 1866.
Bibliothèque Nationale, Latin collection, No. 11247.
Bibliothèque Mazarine, No. 3642 (formerly 1258).
Bibliothèque Nationale, Latin collection, No. 16649.
T. N.: The Latin reads, “We have made this construction in the Preambles.”
T. N.: The Latin reads, “As was stated in the Filotegni. So we have stated in the Filotegni.”
We should note here that one of the references to the Filotegni is in a fragment of the 13th century kept in the Bibliothèque Mazarine. The copy of this text which belonged to François Guillebon reads, Philotegne.
T. N.: The Latin reads, “This has been demonstrated in books dealing with these matters.”
We called attention to the fact that the translator of the De canonio replaced in his figures the Greek letter eta, with an i. In the same way, Jordanus writes Filotegni for the Greek.
T. N.: The Latin reads, “positional gravity.”
T. N.: The Latin reads, The motion of every heavy body is towards the center, with its force and power tending downward and resisting contrary motion… Every falling body is heavier when its motion is straight toward the center. A body is heavier positionally when in a given position, the descent is less oblique. The descent is more oblique to the same extent that it projects less on the vertical.
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Duhem, P. (1991). Statics During the Middle Ages Jordanus de Nemore. 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_6
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