Abstract
A geographer wishing to describe a large river basin begins by making a rough draft of the course of the principal rivers which flow into the river basin. After that, he completes this provisional and tentative sketch by detailing all the meanderings of the thousand streams which feed into the main tributaries.
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References
Dr. Woepcke, Notice sur des traductions arabes de deux ouvrages perdus d’Euclide: Journal Asiatique, 4th series, Vol. XVIII, p. 217, 1851. (T.N.: The French title reads, Note on the Arabic Translations of Two Lost Works by Euclid.)
T. N.: The French title reads, The Book of Euclid on the Balance.
T.N.: The Beni Mouca or the Banu Musa, as the name is sometimes transcribed, were a family who devoted their lives to mathematics and translation.
Maximilian Curtze, Das angebliche Werk des Euklides über die Waage, Zeitschrift für Mathematik und Physik, XIXth, 1874, p. 263. (T. N.: The German title reads, The Alleged Work of Euclid on the Balance.)
Heiberg, Literargeschichtliche Studien über Euklid, Leipzig, 1882, p. 11. (T. N.: The German title reads, Literary and Historical Studies on Euclid.)
Steinschneider, Intorno al Liber Karastonis, Letter from Dr. Baldassare Boncompagni, Annali di Matematica, Vol. V, p. 54, 1863. (T. N.: The Italian reads, About the Liber Karastonis.)
Cf. Heiberg, Literargeschichtliche Studien über Euklid, p. 10.
Maximilian Curtze, Zwei Beiträge zur Geschichte der Physik, (Bibliotheca Mathematica, 3rd edition, Vol. I, p. 51, 1900.)
T. N.: The Latin title reads, The Book of Euclid on the Heavy and Light and on the Relation of Bodies to one Another.
Aristotle, The Physics, Book 7.
T. N.: The Latin title reads, Jordanus’ Treatise on Heaviness.
T. N.: The Latin title reads, Here begins Euclid’s Book on the Relative Heaviness and Lightness of Bodies.
Bibliothèque Nationale, Ms. 10260 (Latin collection).
T. N.: The Latin reads, “This is the end because nothing more can be found.”
T.N.: The Latin reads, “In this volume are contained the following books, in chapters and with figures.”
T. N.: The Latin reads, “Here begin the Elements of Jordanus on the Demonstration of Weights with charts and figures. Here begin excerpts from Thâbit on Weights. Here begins the Book of Euclid on Weights according to the circumference described by the extremities. Divinations. On Time-Reckoning.
Bibliothèque Nationale, Ms. 16649 (Latin collection).
T.N.: The Latin reads, Master François Guillebon of Paris, a Fellow of the Sorbonne and Doctor of Theology.
T. N.: The Latin reads, The Book of the Philosopher Arsamides on the measure of the circle.
T. N.: The Latin reads, “Here ends the Book of Arsamides. Written in 1519.”
T. N.: Cf. footnote #17.
Bibliothèque Nationale, Ms. 11247 (Latin Collection).
Montucla, Histoire des Mathématiques, Paris, Year VII, Vol. I, p. 217.
I was able to find this work in five compilations belonging to the Latin collection of the Bibliothèque Nationale as Mass. 7310, 7377B, 7434, 8680A, 10260. Steinschneider (a) found another copy in Ms. 184 of the Library of the Convent of Saint Mark in Florence and published its beginning and end. Maximilian Cürtze (b) pointed out the existence of the same work in two other manuscripts located in the Vatican Library: the Ms. Regina Suecorum 1233 and Ms. 2975. He found it again in Ms. R. No 402 of the Library of the Thorn gymnasium. He published the formulations of the theorems based on this last copy. We intend to provide an edition of the complete treatise.
Steinschneider, Intorno al Liber Karastonis, Lettera a D. Baldassare Boncompagni (Annali de Matematica, Vol. V, 1863, p. 54).
Maximilian Cürtze, Über die Handschrift R. 4°2, Problematum Euclidis explicate des Königl. Gymnasial Bibliothek zu Thorn (Zeitschrift für Mathematik und Physik XIIIter Jahrgang. Supplément, p. 45, 1868).
T. N.: The Latin title reads, The Book of Karaston, edited by Thâbit, the Son of Cora.
Wuestenfeld, Geschichte der Arabischen Aerzte und Naturforscher, Sr. 29, No. 71; Göttingen, 1840.
Moritz Cantor, Vorlesungen über die Geschichte der Mathematik, Bd. 1, p. 603; Leipzig, 1880.
B. Boncompagni, Della vita e delle opere di Gherardo Cremonese, Rome, 1851. (T. N.: The Italian title reads, On the Life and Work of Gerard of Cremona.)
Steinschneider, Intorno al Liber Karastonis, Lettera a D. Baldassare Boncompagni (Annali de Matematica, Vol. V, 1863, p. 54).
T. N.: The Latin reads, “Eratosthenes is written in the title. But, at the beginning of the book the author is named differently by the man by whom the book was translated and toward the end, he is expressly called Karaston.”
T. N.: In his History of Mechanics René Dugas believes like Duhem that the Greek geometer Charistion, a contemporary of Philo of Byzantium in the second century B.C., is the author.
Steinschneider, Intorno al Liber Karastonis. Lettera a D. Baldassare Boncompagni (Annal di Matematica, Vol. V, 1863, p. 54).
Heiberg, Literargeschichtliche Studien über Euklid, Leipzig, 1882, p. 11.
Maximilian Curtze, “Das angebliche Werk des Euklides über die Waage” (Zeitschrift für Mathematik und Physik, XIXth Jahrgang, p. 263, 1874.)
Montucla, Vol. I, p. 314; Paris Year VII.
T. N.: Cf. footnote 39 below.
J. Graesse, Trésor de livres rares et précieux, Vol. V.
Geschichte der Künste und Wissenschaften seit der Wiederherstellung derselben bis an das Ende des achtzehnten Jahrhunderts. VIIts Abtheilung: Geschichte der Mathematik, von A. G. Kastner, Bd. II, p. 688; 1797.
T. N.: The Latin title reads, A Book on Diverse Matters of Astronomy by Ptolemy, which he dedicated to his son Heriston, dealing compendiously with diverse matters contained in the table at the beginning of that book, 1508. Edited by Peter Liechtenstein.
T. N.: The Latin reads, Here ends the Book on Diverse Matters by Ptolemy of Alexandria, illustrious Prince of Geometers. 1509. Venice. Ed. by Peter Liechtenstein of Cologne, Germany.
Steinschneider, Hebraic Bibliography, Vol. VII, p. 92, 1864.
Cf. Moritz Cantor, History of Mathematics, Vol. I, p. 604; Leipzig, 1880.
Bailly, Dictionnaire grec-français, Paris, 1895.
Simplicii in Aristotelis Physicorum libros quatuor posteriores commentaria; Commentarla in Physicorum VII, 5 (Edition Diels, Berlin, 1895, p. 1110). (T. N.: The Latin title reads, Simplicius, Commentaries on the Last Four Books of Aristotle’s Physics, Commentary on the Physics, VII, 5.)
Bailly, Dictionnaire grec-français, Paris, 1895.
T. N.: The usual English translation is, “Give me a place to stand and I will move the earth.”
Tzetzes, On the Millennia (Corpus Poetarum Graecorum, Vol. II, Geneva 1614) — Tzetzes lived in Constantinople from 1120 to ca. 1180.
Pappi Alexandrini, Collectionis quae supersunt, edidit F. Hultsch. Lib. VIII, Propos. XI, p. 1060; Berlin. 1888.
A. J. Vincent, Géométrie pratique des Grecs (Notices et Extraits des Manuscrits de la Bibliothèque Impériale, Vol. XIX, 2nd partie, p. 330) — Carra de Vaux, Les Mécaniques ou l’Elévateur de Héron d’Alexandrie, published for the first time based on the Arab version of Qustâ ibn Lûkâ. Book I, art. 1, Paris, 1894.
Mathematicorum Hypomnematum de Statica, conscriptus a Simone Stevino brugensi, Liber III, De Staticae praxi, p. 101. (T. N.: The Latin title reads, The Mathematical Memoires on Statics of Simon Stevin of Brugge. Book III, On the Practice of Statics, p. 101.)
T. N.: The Latin reads, “Moreover, this chapter is based upon the work called The Book of Euclid.” There is some disagreement between translations of this Latin phrase. In the Science of Weights on pp. 88 and 89, Moody and Clagett’s translation implies that the Liber Karastonis is physically “joined” to the Liber Euclidis while Duhem’s translation says that the Liber Karastonis is “based upon” the Liber Euclidis. Duhem’s rendering is truer to the Latin.
Thurot, “Recherches historiques sur le Principe d’Archimède” (Revue Archéologique, nouvelle série, Vol. XIX, 1869, p. 117.)
The treatise by the pseudo-Archimedes might also be a fragment of the On Weights.
Bibliothèque Nationale, Ms. 16649 (Latin collection).
T. N.: Neither term is a legitimate Latin word.
And even “tetragonium” in the 13th century text, No. 3642 of the Bibliothèque Mazarine.
T. N.: The Latin reads, “It has been shown in the books which speak about these things that there is no difference whether a weight db is uniformly distributed along the whole line db or whether it is suspended at a point in the middle of the interval.”
T. N.: The Latin reads, “It has been demonstrated thus by Euclid, Archimedes and others and this is the point around which everything else turns.”
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Duhem, P. (1991). The Alexandrian Sources of Medieval Statics. 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_5
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