The Theories of Motion in the Middle Ages and in the Renaissance

Boccaletti, Dino

doi:10.1007/978-3-319-20134-4_2

Dino Boccaletti²

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Abstract

The period considered in this chapter (about ten centuries long) is that which, in its final part, is close to the time of Galileo and then, also in the light of the theories on the importance of some medieval works, it is essential to make clear in what context Galileo worked.

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Notes

1.
See Bernardino Baldi: Le Vite de’ Matematici—Edizione annotata e commentata della parte medievale e rinascimentale a cura di Elio Nenci —Milano, Franco Angeli, 1998.
2.
See Ernst Mach: The Science of Mechanics: A Critical and Historical Account of its Development—Translated by T. J. Mc Cormac—Open Court Classics 1988. (The first edition in German language was published in Prague in 1883).
3.
See P. Duhem: De l’accelération produite par une force constante—Notes pour servir à l’histoire de la Dynamique—Congrés international de philosophie (Geneva 1905), p. 859.
4.
One of the first works of this type was the Histoire de la Mécanique of René Dugas (Neuchâtel, 1950), which was published with a preface by Louis De Broglie and was translated in English some years later (the English translation was reprinted by Dover in 1988). To this, Dugas added La mécanique au XVII ^e siècle—Dès antécédents scolastique à la pensée classique (Neuchâtel, 1954).
5.
Unfortunately, Mayer’s work is almost unknown out of the exclusive circle of the specialists who deal with the history of philosophy and medieval science. Maier took her degree in Germany and then, after having completed her studies at Zurich and Berlin, passed in Italy in 1936 to look for manuscripts of Leibnitz (entrusted with a mandate by the Prussian Academy of Sciences). Starting from 1937 she resided in Italy almost consecutively and there published the greater part of her writings. She wrote always in German and this happened when by that time the scientific literature regarding the subjects she dealt with was for the most part in English language. Her writings were almost all published (in German language) by the Edizioni di Storia e Letteratura—Roma—since the fifties of the last century. Only some decades later an English translation of a selection of her essays on the medieval sciences and Galileo was published: On the Threshold of Exact Science—Selected Writings of Anneliese Maier on Late Medieval Natural Phylosophy, edited and translated with an Introduction by Steven D. Sargent —University of Pensilvania Press, 1982. For these reasons, as we said, her name has not crossed the border of the specialistic research and therefore the results of her research are known only through the quotations of the specialists.
6.
A. Favaro: Galileo Galilei e i “doctores parienses”—Rendiconti della Reale Accademia dei Lincei—Classe di scienze morali, storiche e filologiche. Serie Quinta. Vol. XXVII (1918), pp 139–150.
7.
In 1921, Favaro, on reviewing a work of a French author regarding the Italian though of XVI century, takes the opportunity to address accusations to Duhem. With regard to the studies of Duhem, he says: «… for having an exact enough opinion of the important question of which such studies show only one side, and perhaps the less important, it will not be inopportune to remind its highest origins, even if for this is necessary to unveil the back stage.» In substance, Duhem’s studies on the school of Parisian terminists and the consequent opinion on Galileo (only a continuator of theirs) would have been originated (through Cardinal Dechamps and abbot Mercier) by a directive of Pope Lion XIII for promoting the neo-scholasticism. See: A. Favaro—Galileo Galilei in una rassegna del pensiero italiano nel corso del secolo decimosesto—Archivio di storia della scienza, 2, 137–146 (1921).
8.
Raffaello Caverni: Storia del Metodo Sperimentale in Italia (six volumes)—Firenze, Stabilimento G. Civelli Editore (1891–1900). The work has had two anastatic reprints (Forni, Bologna 1970 and Johnson Reprint Corporation, New York/London, 1972).
9.
See: D. Boccaletti: Raffaello Caverni and the society for the progress of the sciences: an independent priest criticized by the lay scientists—Physis—vol. XLVIII (2011–2012) Nuova Serie—Fasc. 1–2.
10.
John Philoponus (about 490–570) was a Byzantine philosopher of Greek language (Neoplatonist and also Christian) and also director of the School of Alexandria.
11.
See: A Source Book in Greek Science by M. R. Cohen and I.E. Drabkin, Harvard University Press—1966, p. 217.
12.
Ibn-Badja is the first philosopher famous among the Arabs of Spain—he was born in Saragossa at the end of the XI century and died in Fez in 1138.
13.
It is of a great interest, on the discussions regarding the Aristotelian physics in the Middle Ages, the long essay of E. A. Moody: Galileo and Avempace—The dynamics of the leaning tower experiment—published in two parts in the Journal of the History of Ideas Vol. 12 (1951. 163–193, 375–422). We shall refer to this essay in Chap. III.
14.
See: Aristotle: Physics, (III, 1–200 b 30).
15.
P. Duhem: Études sur Léonard de Vinci—Troisième série—1913, pp 292–295.
16.
G. Eneström: Sur l’auteur d’un traité De Motu au quel Bradwardine a fait allusion en 1328—Archivio di storia della scienza 2, 133–136, 1921.
17.
M. Clagett: The Liber de Motu of Gerard of Brussels and the Origin of the Kinematics in the West-Osiris 12, 73–175, 1956. M. Clagett: Archimedes in the Middle Ages, vol. V—Madison Wisc., 1984.
18.
For this and a thorough discussion of the Liber de Motu, see E. Giusti: Alle origini della cinematica medievale: il Liber de Motu di Gherardo da Bruxelles (Bollettino di Storia delle Scienze Matematiche—vol. XVI, 199–240, 1996).
19.
See the final edition of Clagett quoted in footnote 17, p. 64: «The proportion between the velocities of points is the same as that between the lines described in the same time».
20.
See: J. Mazur: Zeno’s Paradox, Dutton, 2007. J. Mazur asserts that with Gerard one has to do, for the first time, with velocities considered as magnitudes and such an approach marks a turning point in the direction of the modern concept of istantaneous velocity. But neither Clagett, nor Giusti and not even Souffrin (who had dealt thoroughly with the concept of velocity) had made an assessment of this kind of the quoted passage of Gerard. The paper of Souffrin we refer to is the already quoted Sur l’histoire du concept de vitesse d’Aristote à Galilée—Medioevo—Rivista di Storia della Filosofia medievale—vol. XXIX (2004) pp 99–133.
21.
The editions in modern languages that one can look up are:
1. 1.
  H. Lamar Crosby : Thomas Bradwardine. His Tractatus de Proportionibus. Its Significance for the Development of Mathematical Physics (Madison, Wis., 1955).
2. 2.
  Thomas Bradwardine: Traité des Rapports entre Les Rapidités dans les Mouvements—suivi de Nicole Oresme: Sur les Rapports—Introduction, traduction, et commentaires de Sabine Rommevaux-Paris-Les Belles Lettres, 2010.
22.
To date complete translations in a modern language do not exist. For excerpts, one can see Clagett, op. cit., second part and Curtis A. Wilson : William Heytesbury-Medieval Logic and The Rise of Mathematical Physics (Madison, Wis., 1956).
23.
For a significant excerpt (in a modern language), see Clagett, op. cit. Chap. 5.3.
24.
Marshall Clagett: The Science of Mechanics in the Middle Ages—University of Wisconsin Press, 1959.
25.
See Clagett, op. cit. ibidem and also A Source Book in Medieval Science (edited by Edward Grant-Harvard University Press, 1974) p. 238.
26.
See Clagett, op. cit., ibidem.
27.
See Clagett, op. cit., ibidem and A Source Book in Medieval Science, op. cit. pp 239–240.
28.
For the overall work of Oresme and the scanty biographical data on him we refer to the article of Clagett in Charles Coulston Gillispie —Dictionary of Scientific Biography—Scribners, New York 1970—vol. 9, pp 223–230.
29.
See Clagett, op. cit., ibidem and S. Rommevaux, op. cit. in footnote 21, pp LXII–LXVI.
30.
See Nicole Oresme and the Medieval Geometry of Qualities and Motions: A treatise on the Uniformity and Difformity of Intensities known as Tractatus de configurationibus Qualitatum et Motuum—edited and translated by Marshall Clagett—Madison, Wisc., 1968.
31.
See Nicole Oresme: De proportionibus Proportionum—ad Pauca Respicientes (ed. E. Grant)—Madison, Wisc., 1966. See also the edition in French language quoted in footnote 21.
32.
This interpretation has been suggested by Anneliese Maier in Die Vorläufer Galileis im 14 Jahrhundert , Roma 1949, p. 92. We refer the reader to Clagett’s work (op. cit. Chap. 7) and to the introduction of Sabine Rommevaux to the already quoted (see footnote 21) translation of Bradwardine’s treatise for further widening. Our very swift and schematic synthesis has only the aim of recording which was the conclusion achieved in the criticisms and corrections to the Aristotelian mechanics in the ambit of Mertonians. Swineshead and Dumbleton further elaborated into details the theory of Bradwardine (see Clagett, op. cit. Chap. 7).
33.
See the essay: The Significance of the theory of Impetus for Scholastic Natural Phylosophy (in the volume On the Threshold of Exact Science—Selected Writings of Anneliese Maier on Late Medieval Natural Phylosophy—University of Pennsylvania Press, 1982)—The first edition of this essay (in German) is of 1955.
34.
Pierre Duhem: Études sur Léonard de Vinci—Troisième série—Les Précurseurs parisiens de Galilée—Paris-Hermann, 1913.
35.
In the essay quoted in footnote 33, p. 77.
36.
Albertus Magnus, Physica VIII, tract. II, cap. 6 (Opera, ed. Borgnet, Paris 1890) «Every motion is originated by the victory of the motive force over the moveable and when that force operates, it is necessary that the passive potentiality of the thing moved is proportional to it.»
37.
Di Marchia was a Franciscan and follower of Duns Scoto (the doctor subtilis).
38.
Iohannis Buridani: Questiones super Libris quattuor de Caelo et Mundo—edited by E. A. Moody—Cambridge, Massachusset, 1942, Book II, question 12, p. 180. The translation of this excerpt (by M. Clagett) is taken from A Source Book in Medieval Science, op. cit. p. 282.
39.
Questiones super Libris quattuor de Caelo et Mundo, op. cit. Book II, question 13, pp 183–184. (Our translation).
40.
On Biagio Pelacani, besides Clagett op. cit., see also the articles of F. Barocelli and G. Federici Vescovini in Filosofia Scienza e Astrologia nel trecento europeo, a cura di Graziella Federici Vescovini e Francesco Barocelli—Il Poligrafo, Padova, 1992–.
41.
Ibidem. G. Federici Vescovini is the most authoritative scholar of the work of Biagio; she has dealt with it for several occasions, in books and articles.
42.
With regard of what could have been the influence of this work in the Study of Padua, see the interesting paper of Christopher J. T. Lewis : The Fortunes of Richard Swineshead in the time of Galileo—Annals of Science, 33 (1976), 561–584.
43.
See Mechanics in Sixteenth—Century Italy—Selection from Tartaglia, Benedetti, Guido Ubaldo & Galileo—Translated & Annotated by Stillman Drake & I.E. Drabkin—The University of Wisconsin Press, 1969—pp. 5–16.
44.
Most of the biographical notes about him come from autobiographical hints scattered in his works, particularly from Quesiti et Inventioni diverse (see the bibliographic reference further on).
45.
The reader can refer to the book (in Italian): Fabio Toscano—La formula segreta. Tartaglia, Cardano e il duello matematico che infiammò l’Italia del Rinascimento—Sironi, 2009. A French translation (Belin, Belin edition) is also available.
46.
Nova Scientia inventa da Nicolo Tartalea—in Vinegia, per Stephano da Sabio, ad instantia di Nicolo Tartalea brisciano, MDXXXVII.
47.
Nova Scientia, f. 4r. (The translation is taken from Mechanics in Sixteenth—Century Italy, op. cit. p. 74).
48.
Ibidem. f. 1r. (Mechanics … op. cit. p. 70).
49.
Ibidem, f. 4r. (Ibidem, p. 75).
50.
La Nova Scientia, Stampata in Venetia per Nicolo de Bascarini a instantia de l’Autore. 1550. See the anastatic reprint by Arnaldo Forni Editore, 1984.
51.
See La Nova Scientia, op. cit. f. 4r,v. ( Mechanics … op. cit. pp 75–76).
52.
See: Albert od Saxony—Questiones subtilissime in libros de celo et mundo Aristotelis—Venice 1492, (ff. 32r–33v)—The quotation is taken from Clagett, op. cit. chap. 9.
53.
See: Mechanics in Sisteenth—Century Italy, op. cit., p. 76.
54.
La Nova Scientia, op. cit. f. 5r. ( Mechanics … op. cit. pp 75–76).
55.
Ibidem, f. 5v. (Mechanics … op. cit. p. 78).
56.
Ibidem, f. 6v. (Mechanics … op. cit. p. 79).
57.
Ibidem, f. 7r. (Mechanics … op. cit. p. 80).
58.
Ibidem, f. 10v. (Mechanics … op. cit. p. 84).
59.
Ibidem, f. 11r. (Mechanics … op. cit. pp 84–85).
60.
Ibidem, ff. 16v, 17r. (Mechanics … op. cit. p. 91).
61.
Quesiti et inventioni diverse de Nicolo Tartalea Brisciano in Venetia per Venturino Ruffinelli, ad instantia et requisitione, et a proprie spese da Nicolo Tartalea, autore, 1546. The first edition of 1546 was followed by others until the definitive edition Quesiti et inventioni diverse de Nicolo Tartaglia—in Venetia per Nicolo de Bascarini, ad instantia et requisitione, et a proprie spese de Nicolo Tartaglia Autore. Nell’anno di nostra salute. MDLIIII. An anastatic reprint of this edition is available with introduction and notes by Arnaldo Masotti—La nuova cartografica, Brescia 1959.
62.
Guillaume Libri: Histoire des sciences mathématiques en Italie, depuis la renaissance des lettres jusqu’à la fin du XVII ^e siècle (Paris 1838–41).
63.
Libri, op. cit. tome troisième, p. 123.
64.
Ibidem, p. 131.
65.
Caverni, op. cit., tomo I, p. 103.
66.
Caverni, op.cit. tomo IV, p. 97.
67.
Ibidem.
68.
Giovanni Vailati: Le speculazioni di Giovanni Benedetti sul moto dei gravi—Atti della R. Accademia delle Scienze di Torino, vol. XXXIII, 1898 (Reprinted in: Giovanni Vailati—Scritti a cura di Mario Quaranta—Arnaldo Forni Editore, 1987—vol. II, pp 143–160).
69.
Resolutio Omnium Euclidis Problematum Aliorumque ad hoc necessario inventorum una tantummodo circini data apertura, Per Joannem Baptistam De Benedictis inventa. Venetiis MDLIII.
70.
Taken from the eighth page (the pages are not numbered) of the dedication to abbot Gabriele Guzman of the Resolutio: «…ceterum quia cuique quod suum est reddi debet, nam pium et iustum est, Nicolaus Tartaleas mihi quattuor primos libros Euclidis solos legit, reliqua omnia privato labore et studio investigavi: volenti namque scire nihil est difficile».
71.
Still today, the most complete study on this regard is given by the memoir of Giovanni Bordiga: Giovanni Battista Benedetti filosofo e matematico veneziano del secolo XVI—Atti dell’Istituto Veneto di Scienze, Lettere ed Arti, Tomo LXXXV, Parte seconda, pp 585–754 (1925–1926)—reprinted in 1985, with a bibliographic updating by Pasquale Ventrice on the occasion of the workshop on «Giovan Battista Benedetti e il suo tempo». In addition one can consult the entry of him (by Stillman Drake) in the vol. 1 (1970), pp. 604–609, of the Dictionary of Scientific Biography op. cit.
72.
With regard to this, the most important studies are due to Carlo Maccagni (of whom we quote Le speculazioni giovanili “de motu” di Giovan Battista Benedetti (Pisa, Domus Galilaeana, 1967) and to Enrico Giusti (of whom we quote Gli scritti «de motu» di Giovan Battista Benedetti—Bollettino di Storia delle Scienze Matematiche, vol. XVII (1997) fasc. 1, pp 51–103.
73.
See footnote 69.
74.
For this, see: C. Maccagni Le speculazioni giovanili «de motu» … op cit. pp XXVII–XXXII. The book of Maccagni also contains excerpts of the dedicatory letter of the Resolutio omnium Euclidis problematum and the text of the two editions of the subsequent work Demonstratio ….
75.
«Olim cum adhuc una essemus, magno me opere orasti obsecratusque es aliqua de motibus naturalibus speculatione sollicita conscriberem, idem quantum possibile est Mathematicis demonstrationibus muniens.»
76.
The demonstration, based on the Archimedes’ principle had been perhaps suggested by the reading of the first treatise of Archimedes translated by Tartaglia in 1551.
77.
E. Giusti, op. cit. in 72) p. 60.
78.
Ibidem, p. 69.
79.
Ibidem, p. 75.
80.
Excerpts of this work and also of the Resolutio, and the text of **Demonstratio are translated in English in the book Mechanics in Sixteenth—Century Italy by Stillman Drake & I.E. Drabkin—The University of Wisconsin Press, 1969.
81.
E. Giusti, op. cit. p. 94.
82.
Diversarum Speculationum, op. cit. p. 184—«Aristoteles 8 cap. primi lib. De coelo, dicere non deberet quanto propius accedit corpus ad terminum ad quem, tanto magis fit velox; sed potius, quanto longius distat a termino a quo tanto velocius existit quia tanto maior sit semper impressio, quanto magis movetur naturaliter corpus, et continuo novum impetum recipit cum in se motus causam contineat, quae est inclinatio ad locum suum eundi, extra quem per vim consistit. » (Translation from Mechanics … op. cit. p. 217).
83.
“The most authoritative”.
84.
P. Duhem: Études sur Léonard De Vinci—troisième série—op. cit. pp 214–227.
85.
Alexandre Koyré: À l’Aube de la science classique, Paris, Hermann—1939, pp 41–54.
86.
«Nempe omne corpus grave, aut sui natura, aut vi motum, in se recipit impressionem et impetum motus, ita ut separatum a virtute movente per aliquod temporis spatium ex seipso moveatur. nam si secundum naturam motu cieatur, suam velocitatem semper agebit, cum in eo impetus et impressio semper ageantur, quia coniuctam habet perpetuo virtutem moventem. Unde manu movendo rotam, ab eaque eam removendo rota statim non quiescet, sed per aliquod temporis spatium circumverteretur.» Diversarum Speculationum … op. cit. pp 286–287. (Mechanics … op. cit. p. 230).
87.
From Galileo to his father Vincenzio (… I’m keeping very well and attend to study and to learn with Signor Mazzoni, who greets you. And not having anything also to tell, I end. From Pisa, the ninth of October 1590…). From Guidobaldo Del Monte to Galileo (… I rejoice at the fact that you are getting along well with Signor Mazzoni, not without envy from me, who would sometimes be with both and take pleasure of his talks: give my best regards and a long hand-kissing to Signor Mazzoni …. From Monte Barroccio, the eighth of December 1590 …) E. N. X, pp 44–45.
88.
Jacopo Mazzoni: In Universam Platonis, et Aristotelis Philosophiam Praeludia, sive de comparatione Platonis & Aristotelis—Venetiis, MCXCVII. There is a critical edition of this book edited by Sara Matteoli and with an introduction of Anna De Pace —M. D’Auria Editore—2010.
89.
E. N. II, pp 193–202.
90.
R. Caverni: La Storia del Metodo Sperimentale in Italia, op. cit. Tomo IV, p. 275.
91.
Bernard Gille: Les ingénieurs de la Renaissance (Hermann, Paris, 1964).
92.
See, in E. N. II, the Breve instruzione all’architettura militare and the Trattato di fortificazione.
93.
Besides in E. N. II, see Il Compasso geometrico e militare di Galileo Galilei edited by Roberto Vergara Caffarelli, Edizioni ETS, 1992 and Galileo Galilei—Operations of the Geometric and military compass—Smithsonian Institute Press, 1978. ( Facsimile reprint translated with an introduction by S. Drake).
94.
E. N. VIII (Discorsi e Dimostrazioni matematiche intorno a due nuove scienze), p. 49. (Drake p. 11).
95.
Antonio Favaro: Galileo Galilei e lo studio di Padova, II, reprint of the original work of 1883, Editrice Antenore—Padova, 1996, p. 70.

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Boccaletti, D. (2016). The Theories of Motion in the Middle Ages and in the Renaissance. In: Galileo and the Equations of Motion. Springer, Cham. https://doi.org/10.1007/978-3-319-20134-4_2

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