Zmiany ilościowe i ich miara w traktacie O sześciu niedorzecznościach:
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| Format: | Buch |
| Sprache: | Polish |
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Łódź
Wydawnictwo Uniwersytetu Łódzkiego
2019
Łódź Centrum Filozofii Przyrody |
| Ausgabe: | Wydanie I. |
| Schriftenreihe: | Research on Science & Natural Philosophy
tom 3 |
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| Online-Zugang: | Inhaltsverzeichnis Register // Sachregister Register // Personenregister Literaturverzeichnis Abstract |
| Beschreibung: | Literaturverzeichnis Seite [193]-199 |
| Beschreibung: | 209 Seiten 24 cm |
| ISBN: | 9788381429764 8381429765 |
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Datensatz im Suchindex
| _version_ | 1804181743801991168 |
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| adam_text | Spis treści Przedmowa...................................................................... 7 Rozdział I Struktura dzieła O sņesciu niedorzecznościach.................... 11 Struktura traktatu...................................................... Kwestie o ruchu zmian ilościowych......................... 15 19 Rozdział II Zagadnienie szybkości ruchu powiększania................ 25 Artykuł pierwszy....................................................... Artykuł drugi............................................................. Artykuł trzeci............................................................. Podsumowanie........................................................... 33 34 35 39 Rozdział III Zagadnienie szybkości ruchu lokalnego....................... 41 Historia problemu...................................................... Kwestia o ruchu lokalnym........................................ Artykuł pierwszy.................................................. Artykuł drugi....................................................... Artykuł trzeci....................................................... Podsumowanie........................................................... 41 49 56 58 62 71
Spis treści 6 Anonim, O sześciu niedorzecznościach................. 73 Kwestia III Czy można wyznaczać szybkość ruchu powiększania?.... 75 Artykuł I Czy rozrzedzaniejest możliwe?....................................... 89 Artykuł II Czy rozpędzaniejest ruchem dojakiejś wielkośd?................ 97 Artykuł III Czy rozrzedzanie ząchodgi w tym, co jest rzadkie lub gęste......................................................................... 107 Kwestia IV Czy w ruchu lokalnym należy wyznaczać jakąś szybkość?............................................................... 117 Artykuł I Czy zwiększanie szybkości ruchu ciała ciężkiego ma swoją przyczynę?...................................................... 137 Artykuł II Czy szybkość ruchu dowolnej sfery wyznacza się za pomocą jakiegośpunktu lub odcinka?.......................................... 149 Artykuł III Czy szybkość każdegojednostajnie zmiennego ruchu lokalnego, rozpoczynającego się od nie-stopnia ruchu, jest równa jej stopniowi środkowemu?............................................... 167 Bibliografia....................................................................... 193 Indeks osób....................................................................... 201 Indeks pojęć...................................................................... 203 Summary........................................................................... 205
Indeks pojęć Całość 19,28,39, 81,82, 84, 86, 88-93, 95,99,103,153,154,155,160,162, 172,184 Ciało ciężkie 78,135,136,138,139,143, 147,148,156,157,190; c. rozciągłe 79; c. świecące 133 Ciepło 21,34, 36,52,100,128,131,133, 188,189 Ciężarek 137,141,142 Ciężkość 118,119,146,183 Czas 41,47,54,56, 66, 81, 99,109,130, 131 Część 132; cz. proporcjonalna 54,91,99, 103,108,181 Dążność 51,52,58, 68,118-120,140,141, 145,146,184; d. naturalna 43,69, 127,128 Definicja miejsca 28; d. proporcji ciągłej 45; d. szybkości ruchu 48 Droga 41,47, 62, 66,157 Eksperyment myślny (secundum imaginationem) 8,23, 35,47,52 Element 98; e. ciężki 43; e. lekki 43 Fizyka jakościowa 24 Kamień młyński 158 Kategorie 22 Koło 48,93 Kontinuum 67,83 Kres 84, 94,129,133; k. ruchu 54,134 Lekkość 118,119,184 Linia spiralna 104 Miejsce 47,75,190; m. naturalne 43,54,57, 117,120,130,140-143,145 Moc 119,122,123,127,137,177,185, 186,190; m. czynnika działającego 117; m. elementu doznającego 117; m. poruszania 52,121,126 Nadwyżka 50,53,70,117,120,124,171,196 Nieskończoność 55 Ogień 36, 68,84,123,129,138,189; najcieplejszy o. 85,92 Ogrzewanie 52,85 Opór 42,43-46,50,52-55,57,63,70,71, 117,119,122,123,127,129,132,138, 177,185,186,190,191; o. akcydentalny 57; o. całościowy 58; o. ośrodka 58, 69,118,121,125; o. wewnętrzny 121 Opóźnienie 41,47 Ośrodek 51,120,126,187 Gęstość ośrodka 29,118 Ilość 22,47 Jakość 22,47 Powietrze 52, 68,129,143 Powiększanie 26,28,30,31,32,76,77, 79-82, 94,102,103,164 Powstawanie 19
204 Prawa ruchu 21,42 Proporcja 44,46, 53,71, 75, 83,84,92, 122,124,127-130,132,139,178; p. ciągła 45 Próżnia 35,44,146 Przyspieszenie 41,47,114,140 Rachunek proporcji 38 Reguła 46,48 Rozpiętość 36,173,181; r. formy 36; r. rozrzedzania 36, 83; r. ruchu 63, 66,167,168,171,172,176,182 Rozrzedzanie 19, 20,25-29, 32-39, 57,77, 83-97,101,102,107,111,115,146; stopień r. 97, 98 Równania dynamiki 20 Ruch 23,36,46, 57, 84-89,100,102, 110,113,115,125-127,134,135, 137; r. jednostajny 95,111,114,142, 143,167,170,174,179,187,188,191; r.jedn. przyspieszony 63; r.jedn. zmienny 48,49, 60, 65,104,111, 167,173; r. lokalny 25, 27,43,48,49, 117,172,176,183; r. naturalny 43, 51, 69,117,120; r. niejednostajnie zmienny 48; r. okrężny 111,114; r. powiększania 36,88; r. przyspieszo ny 29, 62 Sfera 29, 65,77,114,149,155,156,160; s. gwiazd stałych 59,60,150,151, 161; s. gwiazd wędrujących 149; s. Księżyca 137,138,161; s. ognia 57, 92; s. powietrza 57,92,147; s. wody 57, 92 Indeks pojęć Siła 42, 44,45,50,53,54,63, 69, 70,117 Spalanie 36 Stopień 64, 65,102,174,175,176,178; s. gęstości 101; s. szybkości 49,62, 122,159,168-170,180 Stosunek (patrz proporcja) Stożek cienia 55,133,134 Strzała 148 Szybkość 19,20, 23, 26, 29,39,44, 46,48,50, 56-59, 66, 69-71,82, 85,93,99,100,124-131,139,140, 144-149,154,157,160,177-179,191; sz. chwilowa 41; sz. jednostajna 126,155; sz.jednostajniezmienna 153,180; sz. nieskończona 52, 54, 107,110,112,133,141; sz. sfery 59-61,149-163; sz. skończona 108, 109; sz. ruchu lokalnego 41,67; sz. r. powiększania 25,27,75,78,79; nasilanie sz. 42,113; szerokość sz. 62 Twierdzenie o
szybkości średniej 64 Waga 137 Wilgoć 52 Woda 68, 69,119,120,138,148 Wzrost 19 Zagęszczanie 25, 76,100,101,115 Ziemia 68,69, 92,119,120,123,124,148 Zimno 21,129,189 Zmiana ilościowa 19,25,26; z. jakościowa 19,25; z. miejsca 19 Zmniejszanie 19,31 Znak słowny 104,105
Indeks osób Strony zaznaczone kursywą wskazują odwołania do przypisów. Adam z Pipewelle 15,19,22,42,53, 72, 117 Albert z Saksonii 13 Arystoteles 7,14,19-22,25,28, 35,41, 42,44-46, 53,54, 64,101,111,124, 135,173 Avempace (Ibn Bäjja) 44 Awerroes (Averroes) 35, 64, 111, 124,135, 138 Basjan Polita (Bassanus Politus) 12 Błażej z Parmy 12,13 Bonetus Locatellus 12 Brodrick Georges C. 15 Campanus z Novary (Campanus de Novarra) 45,157 Caroti Stefano 11 Clagett Marshall 11,59 Crosby H. Lamar Jr. 61 Duhem Pierre 11,12 Emden Alfred B. 15 Euklides (Eukleides) 22,45 Franciszek z Meyronnes (Franciscus de Mayronis) 14 Gerard Odon (Gerardus Odonis) 13 Gerard z Brukseli (Gerardus Bruxellensis) 59,72 Grant Edward 24 Grellard Christophe 15 Hanke Miroslav 47 Jakuba od św. Marcina (Jacobus de Sancto Martino) 13 Jan Dumbleton (Johannes Dumbleton) 21 Jan z Casali (Johannes de Casali) 12,14 Jan z Holandii (lohannes de Hollandia) 14 Jordan z Nemore (Jordanus de Nemore) 22,135,144 Jung Elżbieta 7,12,19-21,35,44, 47,48, 55,57 Kajetan z Tieny (Gaetano da Thiene) 14 King Peter23 Komentator patrz Awerroes Kretzmann Barbara 21 Kretzmann Norman 21 Maier Annelise 11,12 Michałowska Monika 21 Mikołaj z Autrécourt (Nicolaus de Autricuria, Nicolaus de Ultricuria) 13,15 Mikołaj z Oresme (Nicolas Oresme) 12 Murdoch John, E. 23,46 Papiernik Joanna 8,11,12,17,18,21, 43,101 Pironet Fabienne 33 Podkoński Robert 21, 43,53,55 Ptolemeusz (Claudius Ptolemaeus) 59,150 Roger Bacon (Rogerus lub Rogerius Baconus, Baconis) 13 Roger Thomas 13 Rommevaux-Tani Sabine 11,12,15,19, 27,59, 64, 65, 67
202 Ryszard Kilvlngton (Ričardus Kilvington) 7, 8,12-14,19-22,25,26,33,34,42-46, 48,55,56,72,92,124,126,139,147 Ryszard Swineahead (Suisset, Suiseth) 53 Ryszard z Versellys (Ričardus de Verseile) 22, 59, 72 Spade Vincent P. 26 Spruyt Joke 33 Sylla Edith D. 23,24,46 Indeks osób Tomasz Bradwardine (Thomas Bradwardine) 7,8,12,13,15,19,21,22,42, 43,46-48,53,60-62,72,151,152,158 Walker Fernandez Gustavo 11,15 Walter Burley (Burlaeus, Burleus) 14 Wilson Curtis 19 Wilhelm Heytesbury (Gulielmus Hentisberus) 12-14,21,22,25-29,39,47,48, 62,78,79,81,117 Wilhelm Ockham (Gulielmus Occamus) 20
Bibliografìa RĘKOPISY Kraków, Biblioteka Jagiellońska, ms. 739. Oxford, Bodleian Library, Ms. Canon. Mise. 177. Oxford, Bodleian Library, Ms. Canon. Mise. 456. Paryż, Bibliothèque Nationale de France, Ms. lat. 6527. Paryż, Bibliothèque Nationale de France, Ms. Lat. 6559. Praga, Národní knihovna České republiky, VIII. G.19. Sewilla, Biblioteca Colombina, 7—7—13. Watykan, Biblioteca Apostolica Vaticana, Vat. lat. 3026. Wenecja, Biblioteca Nazionale Marciana, Cod. Lat. VIII.19 (=3267). WYDANIA STARODRUKOWE Anonymous, Tractatus de sex inconvenientibus, Venetiis: Bonetus Locatellus, 1505. Averroes, Commentarium in De melo, [w:] Aristotelis De melo, De generatione et corruptione, Mteorologicorum, De plantis eum Averrois Corduhensis variis in eosdem commentariis. M. A. Zimarae Contradictionum solutiones in libros De melo et in eos De generatione et corruptione. Haec autem quo pacto dige sta sint, ac castigata, versa pagina explicat, t. V, Venetiis: apud lunetas, M.D.LXII. Averroes, Commentarium in De generatione et corruptione, [w:] Aristotelis De coelo, De generatione et corruptione, Mteorologicorum, Deplantis cum Averrois Corduhensis variis in eosdem commentariis. M. A. Zimarae Contradictionum solutiones in libros De coelo et in eos De generatione et corruptione. Haec autem quo pacto digesta sint, ac castigata, versapagina explicat, lunetas, M.D.LXII. t. V, Venetiis: apud
194 Bibliografia Averroes, Commentarium in Metaphysicam, [w:] Aristotelis Methaphysicorum libri ХІПІ cumAverrois Cordubensis in eosdem commentariis et epitome Theophrasti Metaphysicorum liber. Marcii Anotnii Zimarae Contradictionum solutiones in hos Methaphysicorum libros. Quorum omnium recognitionem et additamentum, versa pagina estenditi t. VIII, Venetiis: apud lunetas, M.D.LXII. Averroes, Commentarium in Physicam, [w:] Aristotelis De physico auditu libri octo cum Averrois Cordubensis variis in eosdem commentariis. Que omnia, a summis huius etatis Philosophis, a mendis quamplurimis expurgata cernuntur. Marci Antoni] Zimarae Contradictionum in eosdem Libros Solutiones. Contenta vero in hoc võlumine, versa pagina ostendit., t. IV, Venetiis: apud lunetas M.D.LXII. Claudius Ptolemaeus, Almagestum Cl. Ptolemei Pheludiensis Alexandrini astronomorum principis opus ingens ac nobile omnes celorum motus continens, [trans. Gerard de Cremona], felicibus astris eat in lucern: duetu Petri Liechtenstein Coloniensis Germani... ex officina eiusdem litteraria, Venetiis: Petrus Liechtenstein, 1515. Guilelmus Hentisberus, Regulae solvendi sophismata, [w:], idem, De sensu com posito et diviso; Regulae solvendi sophismata, additis recollerta in regulas et expositione insolubilium Gaietani de Thienis; de scire et dubitare; De relativis; De incipit et disinit; De maximo et minimo, cum singulis expositionibus Gaietani de Thienis; De motu locali, vel De tribuspraedicamentis, cum expositionibus Messi ni, Angeli de Fossambruno et Bernardu Torinii; Sophismata, addita et recollecta Simonis de
Ledinaria; De veritate etfalsitate, Probationes conclusionum in regulis positarum, Venetiis: Bonetus Locatellus: impens Octaviani Scoti, 1494. WYDANIA KRYTYCZNE Anonymous, De motu locali, wyd. J. Papiernik, [w:] E. Jung, R. Podkoński, „Toward the Modern Theory of Motion. Oxford Calculators and the Interpretation of Aristotle”, („Research on Science Na tural Philosophy” voi. IV), Łódź 2020 (w druku). Averroes, Compendium libri Aristotelis De sensu et sensato, [w:] Compendia librorum Aristotelis qui Parva Natūralia vocantur; ed. Aemilia Ledyard Shields, adiuv. Henrico Blumberg, Cambridge, Mass.: Mediaeval Academy of America, 1949.
195 Bibliografia Campanus de Novara, Elementa, [w:] Campanus ofNovara and Euclid’s “Ele ments”, ed. By H.L.L. Busard, Stuttgart: Franz Steiner Verlag, 2005. Euclides, Elementorum libri priores XII ex Commandini et Gregorit versionibus latinis, edidit, pluribus in locis auxit et in depravatis emendavit Samuel [Horsley], episcopus Roffensis, Oxonii: e typographeo Clarendoniano, MD CCCII. Euclides, Optica, [w:] idem, Opera omnia, ediderunt I. L. Heibeg et H. Menge, voi. VII, Lipsiae: in aedibus B. G. Teubneri, MDCCCXC V. Guilelmus Heytesbury, De tribuspraedicamentis : de motu locali, ed. E. Jung, R. Podkoński, [w:] E. Jung, R. Podkoński, „Toward the Modern Theory of Motion. Oxford Calculators and the Interpretation of Aristotle”, („Research on Science Natural Philosophy” voi. IV), Łódź 2020 (w druku). Jordanus Nemorarius, Eiber Iordani Nemorarii... deponderibuspropositiones XIII et earunaem demonstrations՛, Elementa super demonstrationem ponderum De rationeponderis՛, ed. with introduction, translation and notes by E. Moody, [w:] The Medieval Science of Weights (Scientia de ponderi bus. Treatises ascribed to Euclid, Archimedes, Thabit ibn Qurra, Jordanus de edition and introduction M. Clagett, E. Moody, Madison: University of Wisconsin Press, 1952. Memore and Blasius of Tarma), Ees „Auctoritates Aristotelis”. En florilège médiéval. Etude historique et édition ed. J. Hamesse, Louvain: Publications Universitaires, 1974. Ričardus Kilvington, Etrum continuum sit divisibile in infinitum, ed. R. Pod koński, „Mediaevalia Philosophica Polonorum” (36/2) 2007, s. 123-175. Thomas
Bradwardine, Tractatus proportionum seu de proportionibus velocitatum in motibus, [w:] H.L. Crosby Jr., Thomas of Bradwardin. His „Trac critique, tatus de Troportionibus”. Its Significancefor the Development ofMathematical Physics, Madison: University of Wisconsin Press, 1955. TŁUMACZENIA Anonim, O sześciu niedorzecznościach, kwestia I i II, [w:] J. Papiernik, „Zmiany jakościowe i ich mira w traktacie O sześciu niedorzecznoś ciach”, („Research on Science Natural Philosophy” vol. I), Łódź 2019, s. 91-216.
196 Bibliografía Arystoteles, Fizyka, tłum. К. Leśniak, [w:] Dzieła wszystkie, t. II, War szawa: PWN, 1990. Arystoteles, Krótkie rozprawypsychologic^no-biologicspe, tłum. P. Siwek, [w:] Dzieła wszystkie, t. III, Warszawa: PWN, 1992. Arystoteles, Metafizyka, tłum. K. Leśniak, [w:] Dfiełą wszystkie, t. II, Warszawa: PWN, 1990. Arystoteles, Meteorologika, tłum. A. Paciorek, [w:] Dzielą wszystkie, t. II, Warszawa: PWN, 1990. Arystoteles, O duszy, tłum. P. Siwek, [w:] Dzieła wszystkie, t. III, War szawa: PWN, 1992. Arystoteles, O niebie, tłum. P. Siwek, [w:] Dzieła wszystkie, t. II, Warsza wa: PWN, 1990. Arystoteles, O powstawaniu i niszczeniu, tłum. L. Regner, [w:] Dzieła wszystkie, t. II, Warszawa: PWN, 1990. Arystoteles, O świecie, tłum. A. Paciorek, [w:] Dfieła wszystkie, t. II, War szawa: PWN, 1990. Ryszard Kilvington, Kwestie o ruchu, [w:] E. Jung, Mrystotełes na nowo od czytany. Kyszarda Kilvingtona „Kwestie o ruchu”, Łódź: Wydawnictwo Uniwersytetu Łódzkiego, 2016. OPRACOWANIA Blaise de Farme Questiones circa Fractatum proportionum magistri Thome Braduardini,]. Biard, S. Rommevaux (eds), Paris 2005. Caroti S., Da Walter Burley al „Tractatus de sex inconvenientibus”. Fa tradizio ne inglese della discussione medievale „De reactione”, „Medioevo. Rivista di Storia della Filosofia Medievale”, 21 (1995), s. 257—374. Clagett M., „Nicole Oresme and the Medieval Geometry of Qualities and Motions. A Treatise on the Uniformity and Difformity of In tensities Known as Tractatus de configurationibus qualitatum et motuum”, Madison 1968. Crosby H.L., „Thomas of Bradwardine. His
Tractatus de Proportionibus. Its Significance for the Development of Mathematical Physics”, Madison 1955. Duhem P, „Etudes sur Léonard de Vinci”, է. 3, Paris: Libraire scientifi que A. Hermann et fils, 1913.
Bibliografia 197 Duhem P., Ea dialectique du Oxford et la Scolastique italienne, „Bulletin Italien” 12 (1912), s. 22-26, 101-103, 289-292. Duhem P., „Le système du monde; histoire des doctrines cosmologiqu es de Platon à Copernic; L’astronomie latine au Moyen Age (suite)”, III, Paris: librairie scientifique A. Hermann et fils, 1915. Grant E., „The Nature of Natural Philosophy in the Late Middle Ages” („Studies in Philosophy and the History of Philosophy”, Volume 52), Washington, D.C. 2010. Hanke M., Jung E., „William Heytesbury”, [w:] The Stanford Encyclopedia of Philosophy (Spring 2018 Edition), Edward N. Zalta (ed.), https:// plato.stanford.edu/archives/spr2018/entries/heytesbury/. Jung E., „Arystoteles na nowo odczytany. Ryszarda Kilvingtona „Kwe stie o ruchu”, Łódź: Wydawnictwo Uniwersytetu Łódzkiego, 2016. Jung E., Mathematics and the Secundum Imaginationem Procedure in Pdchard Kilvington, „Przegląd Tomistyczny” 22 (2016), s. 109—120. Jung E., „Między filozofią przyrody a nowożytnym przyrodoznaw stwem. Ryszard Kilvington i fizyka matematyczna w średniowie czu”, Łódź: Wydawnictwo Uniwersytetu Łódzkiego, 2002. Jung E., „Richard Kilvington”, [w:] The Stanford Encyclopedia ofPhilosophy (Winter 2016 Edition), Edward N. Zalta (ed.), https://plato.stanford.edu/archives/win2016/entries/kilvington/. Jung E., Świat widziany oczyma Arystotelesa a świat Galileusza, [w:] „ín tempore helli et pacis. Ludzie — Miejsca — Przedmioty”, T. Grabarczyk, A. Kowalska-Pietrzak, T. Nowak (red.), Warszawa 2011, s. 169—179. JungE., The New interpretation ofAristotle. Pdchard Kilvington,
Thomas Bradwardine and the New Patie of Motion, [w:] „Quantifying Aristotle. The Impact, Spread and Decline for Calculatores Tradition”, E. Sylla, D. Di Liscia (eds), Leiden: Brill 2020 (w druku). Jung E., Podkoński R., Pdchard Kilvington on Continuity, [w:] „Atomism in Late Medieval Philosophy and Theology”, C. Grellard, A. Ro bert (eds), Leiden-Boston: Brill, 2009, s. 65—84. Jung E., Podkoński R., „Toward the Modern Theory of Motion. Ox ford Calculators and the Interpretation of Aristotle”, („Research on Science Natural Philosophy” vol. IV), Łódź 2020 (w druku). King R, Mediaeval Thought-Experiments: The Metamethodology of Mediaeval Science, [w:] „Thought Experiments in Science and Philosophy”,
198 Bibliografia T. Horowitz, G.J. Massey (eds), Lanham: Rowman Littlefield Pub Incorporated, 1991, s. 43—64. Maier A., „An der Grenze von Scholastic und Naturwissenschaft. Studien zur Naturphilosophie des 14. Jahrhunderts”, ed. II, Roma: Edizioni di Storia e letteratura, 1952. Maier A., „Die Vorläufer Galileis im 14. Jahrhundert. Studien zur Na turphilosophie der Spätscholastik”, Roma: Edizioni di Storia e Let teratura, 1949. Murdoch J.E., The Analytical Character of Tate Medieval Teaming. Natu ral Philosophywithout Nature, [w:] „Approaches to Nature in the Middle Ages”, L.D. Roberts (ed.), Binghamton 1982, s. 171—213. Murdoch J.E., From Sodai into Intellectual Factors: An Aspect ofthe Unitary Cha racter ofTate Medieval Teaming, [w:] „The Cultural Context of Medieval Learning. Proceedings of the First International Colloquium on Philo sophy, Science, and Theology in the Middle Ages — September 1973”, J.E. Murdoch, E.D. Sylla (eds), Dordrecht 1975, s. 271-339. Murdoch J.E., Sylla E.D, The Science of Motion, [w:] „Science in the Middle Ages”, D.C. Lindberg (ed.), Chicago 1978. Papiernik J., Mow to measure different movements? The 14th century treatise „De sex inconvenientibus”, „Przegląd Tomistyczny” XXIII (2019), s. 445-462. Papiernik J., Metody matematyczne w badaniach զ zakresu filozofii przyrody. Problem szybkości powstawania form w XIV-wiecznym traktacie „De sex inconvenientibus”, „Przegląd Tomistyczny” XXIII (2017), s. 95-146. Papiernik J., „Zmiany jakościowe i ich miara w traktacie O sześciu niedo rzecznościach, („Research on Science Natural Philosophy” vol. I),
Łódź 2019. Pironet E, SpruytJ., „Sophismata”, The Stanford Encyclopedia ofPhilosophy (Winter 2019 Edition), Edward N. Zalta (ed.), https://plato.stanford. edu/archives/win2 019/entries/sophismata/. Podkoński R., „Richard Swinesheaďs Theory of Motion”, („Research on Science Natural Philosophy” vol. II), Łódź 2019. Podkoński R., „Suisetica inania. Ryszarda Swinesheada spekulatywna nauka o ruchu lokalnym”, Łódź 2017. Rommevaux S., Six inconvénients découlant de la regle du mouvement de Tho mas Bradwardine dans un texte anonyme du XlVe siècle, [w:] „L’homme au risque de l’infini. Mélanges d’histoire et de philosophie des sciences
Bibliografia 199 offerts à Michel Bky”, M. Malpangotto, V. Jullien, E. Nicolaïdis (eds), Turnhout: Brepols Publishers, 2013, s. 35—47. Rommevaux-Tani S., La détermination de la rapidité d’augmentation dans le De sex inconvenientibus: comparaison avec les développements sur le même sujet [w:] „Miroir de l’amitié. Mélanges offerts à Joël Biard”, Ch. Grellard (ed.), Paris: Vrin, 2017, s. 153—162. Rommevaux-Tani S., The study on local motion in the „Tractatus de sex inconvenientibus” an example of inheritance from the Oxford Calculators, [w:] „Quantifying Aristotle. The Rise and Decline of Oxford Calcula tors”, D. Di Liscia, E. Sylla (eds), Leiden 2020 (w druku). Rommevaux-Tani S., Un auteur anonyme du XlVe siècle, à Oxford, lecteur de Lierre de Maricourt, „Revue d’Histoire des Sciences”, 61 (2014/1), s. 5-33. Syliä E.D., Mathematical physics and imagination in the work of the Oxford Calculators: Koger Swineshead’s On Maturai Motion, [w:] „Mathematics and its implications to science and natural philosophy in the Middle Ages”, E. Grant, J. Murdoch (eds), Cambridge 1987, s. 85—96. Walker Fernandez G., A New Source of Nicholas ofAutrecourt’s Quaestio: The Anonymous Tractatus de sex inconvenientibus, „Bulletin de Philosop hie Medievale” 55 (2013), s. 57—69. Wilson C., „William Heytesbury. Medieval Logic and the Rise of Mat hematical Physics”, Madison 1956. de William Heytesbury,
Summary The presented book belongs to the tradition of the Oxford Calculators’ philosophy of nature, which started in the 1320s at Oxford University. Although, according to late medieval common practice, commenting on Aristotle’s libri naturales was obligatory and every student at Oxford University had to actively participate in natural philosophy classes, the comments did not slavishly follow the Philosopher’s works. The founders of this school, the so-called Oxford Calculators, namely Ri chard Kilvington and Thomas Bradwardine, offered a new interpre tation of Aristotle’s theory of motion, which in the history of science is known as the New Rule of Motion. In his questions on motion (Quaestiones de motu, translated into Polish as Kwestie o ruchu), written in 1326 at the latest, Richard Kilvington gave arguments and reasons why Aristotle’s theory of motion should be reinterpreted. Kilvington noticed that Aristotle’s rules of motion, presented in Book IV and VII of his Physics, would properly describe motion only by the continuous proportions and calculus of ratios, offered by Euclid in Book V of the Elements. Thomas Bardwardine, made use of Kilvington’s arguments, in his famous treatise On the Proportions of Speed in Motion (De proportibus velocitatum in тоРУиђ, written in 1328. He formulated this new rule of movement in a coherent and clear way. Kilvington/Bradwardine’s rule of motion described the mutual dependences between the speeds of motion and its causes, namely the acting powers and overcoming re sistances. Modern historians of medieval science present this rule
as follows: “The velocity of motion will vary arithmetically when the pro portions of force to resistance determining these velocities vary geo metrically. Thus, if a given proportion of force to resistance produces
206 Summary а given velocity, then when that proportion is squared, the velocity will be doubled.” From 1328 the New Rule of Motion was treated as the greatest achievement of the Oxford Calculators. Bradwardine’s treatise became a manual for “physics” and was used at universities across the whole of Europe until the 17th century. Kilvington’s questions were to remain unknown until the 20th century. The next generation of the Calculators, represented by William Heytesbury, the anonymous author of De sex inconvenientibus and John Dumbleton developed the theory of their predecessors. In his famous treatise Ruks ofsolving sophism (Regulae solvendi sophismatd), written in 1335, Heytesbury, in accord with Ockham nominalism, states that the real physical world consists only of subjects; point, line, surface, instant, time, and motion are conceptus mentis. Heytesbury seeks a mathematically precise de nomination or description of hypothetical phenomena, and he considers the entire range of imaginable cases and problems. Like in Kilvington’s works previously, the phrase secundum imaginationem frequently appears in the Regulae. The only requirement for an imaginable case is that it should not involve a formal logical contradiction. The result of this method is a kind of theoretical physics. Heytesbury was to offer another illustrio us theorem, which was later called the Mean Speed Theorem. It states that the distance traversed in a uniformly accelerated or decelerated mo tion in a given time is equal to the distance which would be traversed in the same time in a uniform movement of
which the speed is the arithmetic mean between the initial and final speed of the uniformly difform motion. This time the speeds of motion is related to the distance traversed and the time consumed during the motion, i.e., to the effects of the motion and not to its causes, like in the New Rule of Motion. Heytesbury’s rule was widely discussed during the 14th and 15th centu ries, and had later a crucial importance for the formulation of the law of free fall, according to which every latitude of motion uniformly acqui red or lost corresponds to its medium degree. Contemporary to William Heytesbury, John Dumbleton, the author of the last medieval encyclope dia presenting knowledge on logic and natural philosophy: Summa logicae andphilosophiae naturalis, was familiar with both these famous theorems and made a broad use of them in describing different type of motions (changes), such as local motion, augmentation, alteration and generation.
Summary 207 The treatise On sex inconveniencies (De sex inconvenientibus, also known as De sex inconvenientium) contains four main questions and three sub ordinated in each of them, thus it contains twelve questions in total. The treatise was written in between 1335 and 1339, most likely in Oxford, but the questions that make up this treatise, were discussed at Paris university. This work discusses the problem of motion in different type of changes, and more specifically the rules of motion describing speeds of motion in relations to its effects — distance tra versed and time. Thus the problems are considered here in regard with Heytesbury’s way of describing motion. Nevertheless, the ano nymous author of the treatise was also familiar with Bradwardine’s famous works. The vast majority of cases considered here use the secundum imaginationem procedure. The present book consists of two parts: the first presents a short history of the problems as pondered by the anonymous author of the treatise On sex inconveniences, and the second offers a translation into Polish of questions III and IV of this work. Both questions are devo ted to the problem of ‘measuring” the speed of augmentation and lo cal motion. While the second type of change, i.e., local motion does not raise any doubt that it is a motion properly defined as changes of place in time, the first type of motion i.e., augmentation may surprise modern readers. In accord with the Aristotelean and medieval defini tion of motion, however, also augmentation is a change which con sumes time, and thus it can be described
as motion. This time it may have been a motion either of the whole body, that having been spread or diminished takes up more or less space respectively, or a motion of the parts of the body that either move away from each other and then the body rarefies, or they approach each other, and then the body thickens. The process of rarefaction, and more specifically the speed in this process is the crucial problem of question III. Searching for the rule of changes of speed in local motion is not surprising for modern readers at all, since from the 17th century in schools we have been taught rules describing local motion. In comparison to all the texts composed in the Middle Ages, the structure of this particular treatise is unconventional. The author pre sents four main questions, then three possible answer to each, then
208 Summary six inconveniences against each opinion, then three subordinated questions, in which one always finds six inconveniences and argu ments pro and contra them, then he gives his answer and finally he gives arguments contra inconveniences and he presents the solution of the main problem. In question III on rarefaction titled: “Whether a body moves faster during augmentation”? (Otrum augmentatum in augendo velocitet motuum suurni), he discusses three possible solutions of the main problem, and he raises three doubts in the form of a question as well: 1) “Whether rarefaction is possible”? (Otrum rarefaction ispossibilis})՛, 2) “Whether ra refaction is a motion to some quantity”? {JJtrum rarefaction sit motus ad aliquem quantitateml)·, 3) “Whether a body which is rarefied or dense is a cause of rarefaction”? (JJtrum rarefaction sit per rarum et densuml). An anonymous author refers here to William Heytesbury, but he final ly rejects his opinion. The answers to three subordinated questions and to the main one are always affirmative, thus his opinion, in short, states that rarefaction is the properly defined motion of augmenta tion, therefore it takes time and, since it is a motion which results in the increasing of a body, it can be described by the continuous change of places. Only a material body which has parts, and as such is rare or dense can be the subject of such motion. The author states that during rarefaction a body moves faster and faster with constant acceleration, and the speed in such motion should be described by the fastest point of moving, i.e., an
increasing body. In question IV on local motion titled: “Whether there is a certain speed in local motion”? (JJtrum in motu locali sit certa servanda velocitasi), an anonymous author also discusses three possible solutions of the problem, and he raises three doubts: 1) “Whether the acceleration of a heavy body occurs from some definite cause”? {JJtrum velocitatio mo tus gravis sit ab aliqua certa causal)·, 2) “Whether the speed of motion of a celestial sphere can be described by a point or by a space”? {JJtrum ve locitatio motus tempore cuiuslibet spere penes punctum tantum vei spácium aliquod attendabiturl)·, 3) “Whether the velocity of a uniformly difform local motion beginning at no degree is equal to its middle degree”? {JJtrum velocitas omnis motus localis uniformiter difformis incipiens a non gradu sit equalis suo medio grádmi). As earlier the answers to the questions are affirmative,
Summary 209 and the anonymous author declares that the discussions and final so lutions of three subordinated questions would help to solve the main problem. He repeats, after Richard Kilvington and Adam de Pipewelle, that: “the acceleration of a falling body, in its descents, comes from several causes, though one is more significant than the others [...] the decrease in the resistance is the principal cause and the con tinuation of the motion, the proximity, the impulse of the medium, the accidental heaviness, and the natural inclination are the secondary causes.” While answering the second question, he states that the ve locity of a celestial sphere depends on the fastest point described on the radius of the sphere. This time he refers to Thomas Bradwardine’s Chapter IV of the treatise on the proportion of speeds in motion. The third subordinated question presents three different opinions of how to “measure” the speed in accelerated or decelerated motion {motus uni formly difform). The author finally accepts William Heytesbury’s above mentioned mean speed theorem. The presented Polish translation of the treatise On sex inconvenientibus testifies to the development of the mechanical theories invented by Richard Kilvington, Thomas Bradwardine and William Heytsbury — the most important figures from amongst the first generation of Oxford Calculators.
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Spis treści Przedmowa. 7 Rozdział I Struktura dzieła O sņesciu niedorzecznościach. 11 Struktura traktatu. Kwestie o ruchu zmian ilościowych. 15 19 Rozdział II Zagadnienie szybkości ruchu powiększania. 25 Artykuł pierwszy. Artykuł drugi. Artykuł trzeci. Podsumowanie. 33 34 35 39 Rozdział III Zagadnienie szybkości ruchu lokalnego. 41 Historia problemu. Kwestia o ruchu lokalnym. Artykuł pierwszy. Artykuł drugi. Artykuł trzeci. Podsumowanie. 41 49 56 58 62 71
Spis treści 6 Anonim, O sześciu niedorzecznościach. 73 Kwestia III Czy można wyznaczać szybkość ruchu powiększania?. 75 Artykuł I Czy rozrzedzaniejest możliwe?. 89 Artykuł II Czy rozpędzaniejest ruchem dojakiejś wielkośd?. 97 Artykuł III Czy rozrzedzanie ząchodgi w tym, co jest rzadkie lub gęste. 107 Kwestia IV Czy w ruchu lokalnym należy wyznaczać jakąś szybkość?. 117 Artykuł I Czy zwiększanie szybkości ruchu ciała ciężkiego ma swoją przyczynę?. 137 Artykuł II Czy szybkość ruchu dowolnej sfery wyznacza się za pomocą jakiegośpunktu lub odcinka?. 149 Artykuł III Czy szybkość każdegojednostajnie zmiennego ruchu lokalnego, rozpoczynającego się od nie-stopnia ruchu, jest równa jej stopniowi środkowemu?. 167 Bibliografia. 193 Indeks osób. 201 Indeks pojęć. 203 Summary. 205
Indeks pojęć Całość 19,28,39, 81,82, 84, 86, 88-93, 95,99,103,153,154,155,160,162, 172,184 Ciało ciężkie 78,135,136,138,139,143, 147,148,156,157,190; c. rozciągłe 79; c. świecące 133 Ciepło 21,34, 36,52,100,128,131,133, 188,189 Ciężarek 137,141,142 Ciężkość 118,119,146,183 Czas 41,47,54,56, 66, 81, 99,109,130, 131 Część 132; cz. proporcjonalna 54,91,99, 103,108,181 Dążność 51,52,58, 68,118-120,140,141, 145,146,184; d. naturalna 43,69, 127,128 Definicja miejsca 28; d. proporcji ciągłej 45; d. szybkości ruchu 48 Droga 41,47, 62, 66,157 Eksperyment myślny (secundum imaginationem) 8,23, 35,47,52 Element 98; e. ciężki 43; e. lekki 43 Fizyka jakościowa 24 Kamień młyński 158 Kategorie 22 Koło 48,93 Kontinuum 67,83 Kres 84, 94,129,133; k. ruchu 54,134 Lekkość 118,119,184 Linia spiralna 104 Miejsce 47,75,190; m. naturalne 43,54,57, 117,120,130,140-143,145 Moc 119,122,123,127,137,177,185, 186,190; m. czynnika działającego 117; m. elementu doznającego 117; m. poruszania 52,121,126 Nadwyżka 50,53,70,117,120,124,171,196 Nieskończoność 55 Ogień 36, 68,84,123,129,138,189; najcieplejszy o. 85,92 Ogrzewanie 52,85 Opór 42,43-46,50,52-55,57,63,70,71, 117,119,122,123,127,129,132,138, 177,185,186,190,191; o. akcydentalny 57; o. całościowy 58; o. ośrodka 58, 69,118,121,125; o. wewnętrzny 121 Opóźnienie 41,47 Ośrodek 51,120,126,187 Gęstość ośrodka 29,118 Ilość 22,47 Jakość 22,47 Powietrze 52, 68,129,143 Powiększanie 26,28,30,31,32,76,77, 79-82, 94,102,103,164 Powstawanie 19
204 Prawa ruchu 21,42 Proporcja 44,46, 53,71, 75, 83,84,92, 122,124,127-130,132,139,178; p. ciągła 45 Próżnia 35,44,146 Przyspieszenie 41,47,114,140 Rachunek proporcji 38 Reguła 46,48 Rozpiętość 36,173,181; r. formy 36; r. rozrzedzania 36, 83; r. ruchu 63, 66,167,168,171,172,176,182 Rozrzedzanie 19, 20,25-29, 32-39, 57,77, 83-97,101,102,107,111,115,146; stopień r. 97, 98 Równania dynamiki 20 Ruch 23,36,46, 57, 84-89,100,102, 110,113,115,125-127,134,135, 137; r. jednostajny 95,111,114,142, 143,167,170,174,179,187,188,191; r.jedn. przyspieszony 63; r.jedn. zmienny 48,49, 60, 65,104,111, 167,173; r. lokalny 25, 27,43,48,49, 117,172,176,183; r. naturalny 43, 51, 69,117,120; r. niejednostajnie zmienny 48; r. okrężny 111,114; r. powiększania 36,88; r. przyspieszo ny 29, 62 Sfera 29, 65,77,114,149,155,156,160; s. gwiazd stałych 59,60,150,151, 161; s. gwiazd wędrujących 149; s. Księżyca 137,138,161; s. ognia 57, 92; s. powietrza 57,92,147; s. wody 57, 92 Indeks pojęć Siła 42, 44,45,50,53,54,63, 69, 70,117 Spalanie 36 Stopień 64, 65,102,174,175,176,178; s. gęstości 101; s. szybkości 49,62, 122,159,168-170,180 Stosunek (patrz proporcja) Stożek cienia 55,133,134 Strzała 148 Szybkość 19,20, 23, 26, 29,39,44, 46,48,50, 56-59, 66, 69-71,82, 85,93,99,100,124-131,139,140, 144-149,154,157,160,177-179,191; sz. chwilowa 41; sz. jednostajna 126,155; sz.jednostajniezmienna 153,180; sz. nieskończona 52, 54, 107,110,112,133,141; sz. sfery 59-61,149-163; sz. skończona 108, 109; sz. ruchu lokalnego 41,67; sz. r. powiększania 25,27,75,78,79; nasilanie sz. 42,113; szerokość sz. 62 Twierdzenie o
szybkości średniej 64 Waga 137 Wilgoć 52 Woda 68, 69,119,120,138,148 Wzrost 19 Zagęszczanie 25, 76,100,101,115 Ziemia 68,69, 92,119,120,123,124,148 Zimno 21,129,189 Zmiana ilościowa 19,25,26; z. jakościowa 19,25; z. miejsca 19 Zmniejszanie 19,31 Znak słowny 104,105
Indeks osób Strony zaznaczone kursywą wskazują odwołania do przypisów. Adam z Pipewelle 15,19,22,42,53, 72, 117 Albert z Saksonii 13 Arystoteles 7,14,19-22,25,28, 35,41, 42,44-46, 53,54, 64,101,111,124, 135,173 Avempace (Ibn Bäjja) 44 Awerroes (Averroes) 35, 64, 111, 124,135, 138 Basjan Polita (Bassanus Politus) 12 Błażej z Parmy 12,13 Bonetus Locatellus 12 Brodrick Georges C. 15 Campanus z Novary (Campanus de Novarra) 45,157 Caroti Stefano 11 Clagett Marshall 11,59 Crosby H. Lamar Jr. 61 Duhem Pierre 11,12 Emden Alfred B. 15 Euklides (Eukleides) 22,45 Franciszek z Meyronnes (Franciscus de Mayronis) 14 Gerard Odon (Gerardus Odonis) 13 Gerard z Brukseli (Gerardus Bruxellensis) 59,72 Grant Edward 24 Grellard Christophe 15 Hanke Miroslav 47 Jakuba od św. Marcina (Jacobus de Sancto Martino) 13 Jan Dumbleton (Johannes Dumbleton) 21 Jan z Casali (Johannes de Casali) 12,14 Jan z Holandii (lohannes de Hollandia) 14 Jordan z Nemore (Jordanus de Nemore) 22,135,144 Jung Elżbieta 7,12,19-21,35,44, 47,48, 55,57 Kajetan z Tieny (Gaetano da Thiene) 14 King Peter23 Komentator patrz Awerroes Kretzmann Barbara 21 Kretzmann Norman 21 Maier Annelise 11,12 Michałowska Monika 21 Mikołaj z Autrécourt (Nicolaus de Autricuria, Nicolaus de Ultricuria) 13,15 Mikołaj z Oresme (Nicolas Oresme) 12 Murdoch John, E. 23,46 Papiernik Joanna 8,11,12,17,18,21, 43,101 Pironet Fabienne 33 Podkoński Robert 21, 43,53,55 Ptolemeusz (Claudius Ptolemaeus) 59,150 Roger Bacon (Rogerus lub Rogerius Baconus, Baconis) 13 Roger Thomas 13 Rommevaux-Tani Sabine 11,12,15,19, 27,59, 64, 65, 67
202 Ryszard Kilvlngton (Ričardus Kilvington) 7, 8,12-14,19-22,25,26,33,34,42-46, 48,55,56,72,92,124,126,139,147 Ryszard Swineahead (Suisset, Suiseth) 53 Ryszard z Versellys (Ričardus de Verseile) 22, 59, 72 Spade Vincent P. 26 Spruyt Joke 33 Sylla Edith D. 23,24,46 Indeks osób Tomasz Bradwardine (Thomas Bradwardine) 7,8,12,13,15,19,21,22,42, 43,46-48,53,60-62,72,151,152,158 Walker Fernandez Gustavo 11,15 Walter Burley (Burlaeus, Burleus) 14 Wilson Curtis 19 Wilhelm Heytesbury (Gulielmus Hentisberus) 12-14,21,22,25-29,39,47,48, 62,78,79,81,117 Wilhelm Ockham (Gulielmus Occamus) 20
Bibliografìa RĘKOPISY Kraków, Biblioteka Jagiellońska, ms. 739. Oxford, Bodleian Library, Ms. Canon. Mise. 177. Oxford, Bodleian Library, Ms. Canon. Mise. 456. Paryż, Bibliothèque Nationale de France, Ms. lat. 6527. Paryż, Bibliothèque Nationale de France, Ms. Lat. 6559. Praga, Národní knihovna České republiky, VIII. G.19. Sewilla, Biblioteca Colombina, 7—7—13. Watykan, Biblioteca Apostolica Vaticana, Vat. lat. 3026. Wenecja, Biblioteca Nazionale Marciana, Cod. Lat. VIII.19 (=3267). WYDANIA STARODRUKOWE Anonymous, Tractatus de sex inconvenientibus, Venetiis: Bonetus Locatellus, 1505. Averroes, Commentarium in De melo, [w:] Aristotelis De melo, De generatione et corruptione, Mteorologicorum, De plantis eum Averrois Corduhensis variis in eosdem commentariis. M. A. Zimarae Contradictionum solutiones in libros De melo et in eos De generatione et corruptione. Haec autem quo pacto dige sta sint, ac castigata, versa pagina explicat, t. V, Venetiis: apud lunetas, M.D.LXII. Averroes, Commentarium in De generatione et corruptione, [w:] Aristotelis De coelo, De generatione et corruptione, Mteorologicorum, Deplantis cum Averrois Corduhensis variis in eosdem commentariis. M. A. Zimarae Contradictionum solutiones in libros De coelo et in eos De generatione et corruptione. Haec autem quo pacto digesta sint, ac castigata, versapagina explicat, lunetas, M.D.LXII. t. V, Venetiis: apud
194 Bibliografia Averroes, Commentarium in Metaphysicam, [w:] Aristotelis Methaphysicorum libri ХІПІ cumAverrois Cordubensis in eosdem commentariis et epitome Theophrasti Metaphysicorum liber. Marcii Anotnii Zimarae Contradictionum solutiones in hos Methaphysicorum libros. Quorum omnium recognitionem et additamentum, versa pagina estenditi t. VIII, Venetiis: apud lunetas, M.D.LXII. Averroes, Commentarium in Physicam, [w:] Aristotelis De physico auditu libri octo cum Averrois Cordubensis variis in eosdem commentariis. Que omnia, a summis huius etatis Philosophis, a mendis quamplurimis expurgata cernuntur. Marci Antoni] Zimarae Contradictionum in eosdem Libros Solutiones. Contenta vero in hoc võlumine, versa pagina ostendit., t. IV, Venetiis: apud lunetas M.D.LXII. Claudius Ptolemaeus, Almagestum Cl. Ptolemei Pheludiensis Alexandrini astronomorum principis opus ingens ac nobile omnes celorum motus continens, [trans. Gerard de Cremona], felicibus astris eat in lucern: duetu Petri Liechtenstein Coloniensis Germani. ex officina eiusdem litteraria, Venetiis: Petrus Liechtenstein, 1515. Guilelmus Hentisberus, Regulae solvendi sophismata, [w:], idem, De sensu com posito et diviso; Regulae solvendi sophismata, additis recollerta in regulas et expositione insolubilium Gaietani de Thienis; de scire et dubitare; De relativis; De incipit et disinit; De maximo et minimo, cum singulis expositionibus Gaietani de Thienis; De motu locali, vel De tribuspraedicamentis, cum expositionibus Messi ni, Angeli de Fossambruno et Bernardu Torinii; Sophismata, addita et recollecta Simonis de
Ledinaria; De veritate etfalsitate, Probationes conclusionum in regulis positarum, Venetiis: Bonetus Locatellus: impens Octaviani Scoti, 1494. WYDANIA KRYTYCZNE Anonymous, De motu locali, wyd. J. Papiernik, [w:] E. Jung, R. Podkoński, „Toward the Modern Theory of Motion. Oxford Calculators and the Interpretation of Aristotle”, („Research on Science Na tural Philosophy” voi. IV), Łódź 2020 (w druku). Averroes, Compendium libri Aristotelis De sensu et sensato, [w:] Compendia librorum Aristotelis qui Parva Natūralia vocantur; ed. Aemilia Ledyard Shields, adiuv. Henrico Blumberg, Cambridge, Mass.: Mediaeval Academy of America, 1949.
195 Bibliografia Campanus de Novara, Elementa, [w:] Campanus ofNovara and Euclid’s “Ele ments”, ed. By H.L.L. Busard, Stuttgart: Franz Steiner Verlag, 2005. Euclides, Elementorum libri priores XII ex Commandini et Gregorit versionibus latinis, edidit, pluribus in locis auxit et in depravatis emendavit Samuel [Horsley], episcopus Roffensis, Oxonii: e typographeo Clarendoniano, MD CCCII. Euclides, Optica, [w:] idem, Opera omnia, ediderunt I. L. Heibeg et H. Menge, voi. VII, Lipsiae: in aedibus B. G. Teubneri, MDCCCXC V. Guilelmus Heytesbury, De tribuspraedicamentis : de motu locali, ed. E. Jung, R. Podkoński, [w:] E. Jung, R. Podkoński, „Toward the Modern Theory of Motion. Oxford Calculators and the Interpretation of Aristotle”, („Research on Science Natural Philosophy” voi. IV), Łódź 2020 (w druku). Jordanus Nemorarius, Eiber Iordani Nemorarii. deponderibuspropositiones XIII et earunaem demonstrations՛, Elementa super demonstrationem ponderum\ De rationeponderis՛, ed. with introduction, translation and notes by E. Moody, [w:] The Medieval Science of Weights (Scientia de ponderi bus. Treatises ascribed to Euclid, Archimedes, Thabit ibn Qurra, Jordanus de edition and introduction M. Clagett, E. Moody, Madison: University of Wisconsin Press, 1952. Memore and Blasius of Tarma), Ees „Auctoritates Aristotelis”. En florilège médiéval. Etude historique et édition ed. J. Hamesse, Louvain: Publications Universitaires, 1974. Ričardus Kilvington, Etrum continuum sit divisibile in infinitum, ed. R. Pod koński, „Mediaevalia Philosophica Polonorum” (36/2) 2007, s. 123-175. Thomas
Bradwardine, Tractatus proportionum seu de proportionibus velocitatum in motibus, [w:] H.L. Crosby Jr., Thomas of Bradwardin. His „Trac critique, tatus de Troportionibus”. Its Significancefor the Development ofMathematical Physics, Madison: University of Wisconsin Press, 1955. TŁUMACZENIA Anonim, O sześciu niedorzecznościach, kwestia I i II, [w:] J. Papiernik, „Zmiany jakościowe i ich mira w traktacie O sześciu niedorzecznoś ciach”, („Research on Science Natural Philosophy” vol. I), Łódź 2019, s. 91-216.
196 Bibliografía Arystoteles, Fizyka, tłum. К. Leśniak, [w:] Dzieła wszystkie, t. II, War szawa: PWN, 1990. Arystoteles, Krótkie rozprawypsychologic^no-biologicspe, tłum. P. Siwek, [w:] Dzieła wszystkie, t. III, Warszawa: PWN, 1992. Arystoteles, Metafizyka, tłum. K. Leśniak, [w:] Dfiełą wszystkie, t. II, Warszawa: PWN, 1990. Arystoteles, Meteorologika, tłum. A. Paciorek, [w:] Dzielą wszystkie, t. II, Warszawa: PWN, 1990. Arystoteles, O duszy, tłum. P. Siwek, [w:] Dzieła wszystkie, t. III, War szawa: PWN, 1992. Arystoteles, O niebie, tłum. P. Siwek, [w:] Dzieła wszystkie, t. II, Warsza wa: PWN, 1990. Arystoteles, O powstawaniu i niszczeniu, tłum. L. Regner, [w:] Dzieła wszystkie, t. II, Warszawa: PWN, 1990. Arystoteles, O świecie, tłum. A. Paciorek, [w:] Dfieła wszystkie, t. II, War szawa: PWN, 1990. Ryszard Kilvington, Kwestie o ruchu, [w:] E. Jung, Mrystotełes na nowo od czytany. Kyszarda Kilvingtona „Kwestie o ruchu”, Łódź: Wydawnictwo Uniwersytetu Łódzkiego, 2016. OPRACOWANIA Blaise de Farme Questiones circa Fractatum proportionum magistri Thome Braduardini,]. Biard, S. Rommevaux (eds), Paris 2005. Caroti S., Da Walter Burley al „Tractatus de sex inconvenientibus”. Fa tradizio ne inglese della discussione medievale „De reactione”, „Medioevo. Rivista di Storia della Filosofia Medievale”, 21 (1995), s. 257—374. Clagett M., „Nicole Oresme and the Medieval Geometry of Qualities and Motions. A Treatise on the Uniformity and Difformity of In tensities Known as Tractatus de configurationibus qualitatum et motuum”, Madison 1968. Crosby H.L., „Thomas of Bradwardine. His
Tractatus de Proportionibus. Its Significance for the Development of Mathematical Physics”, Madison 1955. Duhem P, „Etudes sur Léonard de Vinci”, է. 3, Paris: Libraire scientifi que A. Hermann et fils, 1913.
Bibliografia 197 Duhem P., Ea dialectique du Oxford et la Scolastique italienne, „Bulletin Italien” 12 (1912), s. 22-26, 101-103, 289-292. Duhem P., „Le système du monde; histoire des doctrines cosmologiqu es de Platon à Copernic; L’astronomie latine au Moyen Age (suite)”, III, Paris: librairie scientifique A. Hermann et fils, 1915. Grant E., „The Nature of Natural Philosophy in the Late Middle Ages” („Studies in Philosophy and the History of Philosophy”, Volume 52), Washington, D.C. 2010. Hanke M., Jung E., „William Heytesbury”, [w:] The Stanford Encyclopedia of Philosophy (Spring 2018 Edition), Edward N. Zalta (ed.), https:// plato.stanford.edu/archives/spr2018/entries/heytesbury/. Jung E., „Arystoteles na nowo odczytany. Ryszarda Kilvingtona „Kwe stie o ruchu”, Łódź: Wydawnictwo Uniwersytetu Łódzkiego, 2016. Jung E., Mathematics and the Secundum Imaginationem Procedure in Pdchard Kilvington, „Przegląd Tomistyczny” 22 (2016), s. 109—120. Jung E., „Między filozofią przyrody a nowożytnym przyrodoznaw stwem. Ryszard Kilvington i fizyka matematyczna w średniowie czu”, Łódź: Wydawnictwo Uniwersytetu Łódzkiego, 2002. Jung E., „Richard Kilvington”, [w:] The Stanford Encyclopedia ofPhilosophy (Winter 2016 Edition), Edward N. Zalta (ed.), https://plato.stanford.edu/archives/win2016/entries/kilvington/. Jung E., Świat widziany oczyma Arystotelesa a świat Galileusza, [w:] „ín tempore helli et pacis. Ludzie — Miejsca — Przedmioty”, T. Grabarczyk, A. Kowalska-Pietrzak, T. Nowak (red.), Warszawa 2011, s. 169—179. JungE., The New interpretation ofAristotle. Pdchard Kilvington,
Thomas Bradwardine and the New Patie of Motion, [w:] „Quantifying Aristotle. The Impact, Spread and Decline for Calculatores Tradition”, E. Sylla, D. Di Liscia (eds), Leiden: Brill 2020 (w druku). Jung E., Podkoński R., Pdchard Kilvington on Continuity, [w:] „Atomism in Late Medieval Philosophy and Theology”, C. Grellard, A. Ro bert (eds), Leiden-Boston: Brill, 2009, s. 65—84. Jung E., Podkoński R., „Toward the Modern Theory of Motion. Ox ford Calculators and the Interpretation of Aristotle”, („Research on Science Natural Philosophy” vol. IV), Łódź 2020 (w druku). King R, Mediaeval Thought-Experiments: The Metamethodology of Mediaeval Science, [w:] „Thought Experiments in Science and Philosophy”,
198 Bibliografia T. Horowitz, G.J. Massey (eds), Lanham: Rowman Littlefield Pub Incorporated, 1991, s. 43—64. Maier A., „An der Grenze von Scholastic und Naturwissenschaft. Studien zur Naturphilosophie des 14. Jahrhunderts”, ed. II, Roma: Edizioni di Storia e letteratura, 1952. Maier A., „Die Vorläufer Galileis im 14. Jahrhundert. Studien zur Na turphilosophie der Spätscholastik”, Roma: Edizioni di Storia e Let teratura, 1949. Murdoch J.E., The Analytical Character of Tate Medieval Teaming. Natu ral Philosophywithout Nature, [w:] „Approaches to Nature in the Middle Ages”, L.D. Roberts (ed.), Binghamton 1982, s. 171—213. Murdoch J.E., From Sodai into Intellectual Factors: An Aspect ofthe Unitary Cha racter ofTate Medieval Teaming, [w:] „The Cultural Context of Medieval Learning. Proceedings of the First International Colloquium on Philo sophy, Science, and Theology in the Middle Ages — September 1973”, J.E. Murdoch, E.D. Sylla (eds), Dordrecht 1975, s. 271-339. Murdoch J.E., Sylla E.D, The Science of Motion, [w:] „Science in the Middle Ages”, D.C. Lindberg (ed.), Chicago 1978. Papiernik J., Mow to measure different movements? The 14th century treatise „De sex inconvenientibus”, „Przegląd Tomistyczny” XXIII (2019), s. 445-462. Papiernik J., Metody matematyczne w badaniach զ zakresu filozofii przyrody. Problem szybkości powstawania form w XIV-wiecznym traktacie „De sex inconvenientibus”, „Przegląd Tomistyczny” XXIII (2017), s. 95-146. Papiernik J., „Zmiany jakościowe i ich miara w traktacie O sześciu niedo rzecznościach, („Research on Science Natural Philosophy” vol. I),
Łódź 2019. Pironet E, SpruytJ., „Sophismata”, The Stanford Encyclopedia ofPhilosophy (Winter 2019 Edition), Edward N. Zalta (ed.), https://plato.stanford. edu/archives/win2 019/entries/sophismata/. Podkoński R., „Richard Swinesheaďs Theory of Motion”, („Research on Science Natural Philosophy” vol. II), Łódź 2019. Podkoński R., „Suisetica inania. Ryszarda Swinesheada spekulatywna nauka o ruchu lokalnym”, Łódź 2017. Rommevaux S., Six inconvénients découlant de la regle du mouvement de Tho mas Bradwardine dans un texte anonyme du XlVe siècle, [w:] „L’homme au risque de l’infini. Mélanges d’histoire et de philosophie des sciences
Bibliografia 199 offerts à Michel Bky”, M. Malpangotto, V. Jullien, E. Nicolaïdis (eds), Turnhout: Brepols Publishers, 2013, s. 35—47. Rommevaux-Tani S., La détermination de la rapidité d’augmentation dans le De sex inconvenientibus: comparaison avec les développements sur le même sujet [w:] „Miroir de l’amitié. Mélanges offerts à Joël Biard”, Ch. Grellard (ed.), Paris: Vrin, 2017, s. 153—162. Rommevaux-Tani S., The study on local motion in the „Tractatus de sex inconvenientibus” an example of inheritance from the Oxford Calculators, [w:] „Quantifying Aristotle. The Rise and Decline of Oxford Calcula tors”, D. Di Liscia, E. Sylla (eds), Leiden 2020 (w druku). Rommevaux-Tani S., Un auteur anonyme du XlVe siècle, à Oxford, lecteur de Lierre de Maricourt, „Revue d’Histoire des Sciences”, 61 (2014/1), s. 5-33. Syliä E.D., Mathematical physics and imagination in the work of the Oxford Calculators: Koger Swineshead’s On Maturai Motion, [w:] „Mathematics and its implications to science and natural philosophy in the Middle Ages”, E. Grant, J. Murdoch (eds), Cambridge 1987, s. 85—96. Walker Fernandez G., A New Source of Nicholas ofAutrecourt’s Quaestio: The Anonymous Tractatus de sex inconvenientibus, „Bulletin de Philosop hie Medievale” 55 (2013), s. 57—69. Wilson C., „William Heytesbury. Medieval Logic and the Rise of Mat hematical Physics”, Madison 1956. de William Heytesbury,
Summary The presented book belongs to the tradition of the Oxford Calculators’ philosophy of nature, which started in the 1320s at Oxford University. Although, according to late medieval common practice, commenting on Aristotle’s libri naturales was obligatory and every student at Oxford University had to actively participate in natural philosophy classes, the comments did not slavishly follow the Philosopher’s works. The founders of this school, the so-called Oxford Calculators, namely Ri chard Kilvington and Thomas Bradwardine, offered a new interpre tation of Aristotle’s theory of motion, which in the history of science is known as the New Rule of Motion. In his questions on motion (Quaestiones de motu, translated into Polish as Kwestie o ruchu), written in 1326 at the latest, Richard Kilvington gave arguments and reasons why Aristotle’s theory of motion should be reinterpreted. Kilvington noticed that Aristotle’s rules of motion, presented in Book IV and VII of his Physics, would properly describe motion only by the continuous proportions and calculus of ratios, offered by Euclid in Book V of the Elements. Thomas Bardwardine, made use of Kilvington’s arguments, in his famous treatise On the Proportions of Speed in Motion (De proportibus velocitatum in тоРУиђ, written in 1328. He formulated this new rule of movement in a coherent and clear way. Kilvington/Bradwardine’s rule of motion described the mutual dependences between the speeds of motion and its causes, namely the acting powers and overcoming re sistances. Modern historians of medieval science present this rule
as follows: “The velocity of motion will vary arithmetically when the pro portions of force to resistance determining these velocities vary geo metrically. Thus, if a given proportion of force to resistance produces
206 Summary а given velocity, then when that proportion is squared, the velocity will be doubled.” From 1328 the New Rule of Motion was treated as the greatest achievement of the Oxford Calculators. Bradwardine’s treatise became a manual for “physics” and was used at universities across the whole of Europe until the 17th century. Kilvington’s questions were to remain unknown until the 20th century. The next generation of the Calculators, represented by William Heytesbury, the anonymous author of De sex inconvenientibus and John Dumbleton developed the theory of their predecessors. In his famous treatise Ruks ofsolving sophism (Regulae solvendi sophismatd), written in 1335, Heytesbury, in accord with Ockham nominalism, states that the real physical world consists only of subjects; point, line, surface, instant, time, and motion are conceptus mentis. Heytesbury seeks a mathematically precise de nomination or description of hypothetical phenomena, and he considers the entire range of imaginable cases and problems. Like in Kilvington’s works previously, the phrase secundum imaginationem frequently appears in the Regulae. The only requirement for an imaginable case is that it should not involve a formal logical contradiction. The result of this method is a kind of theoretical physics. Heytesbury was to offer another illustrio us theorem, which was later called the Mean Speed Theorem. It states that the distance traversed in a uniformly accelerated or decelerated mo tion in a given time is equal to the distance which would be traversed in the same time in a uniform movement of
which the speed is the arithmetic mean between the initial and final speed of the uniformly difform motion. This time the speeds of motion is related to the distance traversed and the time consumed during the motion, i.e., to the effects of the motion and not to its causes, like in the New Rule of Motion. Heytesbury’s rule was widely discussed during the 14th and 15th centu ries, and had later a crucial importance for the formulation of the law of free fall, according to which every latitude of motion uniformly acqui red or lost corresponds to its medium degree. Contemporary to William Heytesbury, John Dumbleton, the author of the last medieval encyclope dia presenting knowledge on logic and natural philosophy: Summa logicae andphilosophiae naturalis, was familiar with both these famous theorems and made a broad use of them in describing different type of motions (changes), such as local motion, augmentation, alteration and generation.
Summary 207 The treatise On sex inconveniencies (De sex inconvenientibus, also known as De sex inconvenientium) contains four main questions and three sub ordinated in each of them, thus it contains twelve questions in total. The treatise was written in between 1335 and 1339, most likely in Oxford, but the questions that make up this treatise, were discussed at Paris university. This work discusses the problem of motion in different type of changes, and more specifically the rules of motion describing speeds of motion in relations to its effects — distance tra versed and time. Thus the problems are considered here in regard with Heytesbury’s way of describing motion. Nevertheless, the ano nymous author of the treatise was also familiar with Bradwardine’s famous works. The vast majority of cases considered here use the secundum imaginationem procedure. The present book consists of two parts: the first presents a short history of the problems as pondered by the anonymous author of the treatise On sex inconveniences, and the second offers a translation into Polish of questions III and IV of this work. Both questions are devo ted to the problem of ‘measuring” the speed of augmentation and lo cal motion. While the second type of change, i.e., local motion does not raise any doubt that it is a motion properly defined as changes of place in time, the first type of motion i.e., augmentation may surprise modern readers. In accord with the Aristotelean and medieval defini tion of motion, however, also augmentation is a change which con sumes time, and thus it can be described
as motion. This time it may have been a motion either of the whole body, that having been spread or diminished takes up more or less space respectively, or a motion of the parts of the body that either move away from each other and then the body rarefies, or they approach each other, and then the body thickens. The process of rarefaction, and more specifically the speed in this process is the crucial problem of question III. Searching for the rule of changes of speed in local motion is not surprising for modern readers at all, since from the 17th century in schools we have been taught rules describing local motion. In comparison to all the texts composed in the Middle Ages, the structure of this particular treatise is unconventional. The author pre sents four main questions, then three possible answer to each, then
208 Summary six inconveniences against each opinion, then three subordinated questions, in which one always finds six inconveniences and argu ments pro and contra them, then he gives his answer and finally he gives arguments contra inconveniences and he presents the solution of the main problem. In question III on rarefaction titled: “Whether a body moves faster during augmentation”? (Otrum augmentatum in augendo velocitet motuum suurni), he discusses three possible solutions of the main problem, and he raises three doubts in the form of a question as well: 1) “Whether rarefaction is possible”? (Otrum rarefaction ispossibilis})՛, 2) “Whether ra refaction is a motion to some quantity”? {JJtrum rarefaction sit motus ad aliquem quantitateml)·, 3) “Whether a body which is rarefied or dense is a cause of rarefaction”? (JJtrum rarefaction sit per rarum et densuml). An anonymous author refers here to William Heytesbury, but he final ly rejects his opinion. The answers to three subordinated questions and to the main one are always affirmative, thus his opinion, in short, states that rarefaction is the properly defined motion of augmenta tion, therefore it takes time and, since it is a motion which results in the increasing of a body, it can be described by the continuous change of places. Only a material body which has parts, and as such is rare or dense can be the subject of such motion. The author states that during rarefaction a body moves faster and faster with constant acceleration, and the speed in such motion should be described by the fastest point of moving, i.e., an
increasing body. In question IV on local motion titled: “Whether there is a certain speed in local motion”? (JJtrum in motu locali sit certa servanda velocitasi), an anonymous author also discusses three possible solutions of the problem, and he raises three doubts: 1) “Whether the acceleration of a heavy body occurs from some definite cause”? {JJtrum velocitatio mo tus gravis sit ab aliqua certa causal)·, 2) “Whether the speed of motion of a celestial sphere can be described by a point or by a space”? {JJtrum ve locitatio motus tempore cuiuslibet spere penes punctum tantum vei spácium aliquod attendabiturl)·, 3) “Whether the velocity of a uniformly difform local motion beginning at no degree is equal to its middle degree”? {JJtrum velocitas omnis motus localis uniformiter difformis incipiens a non gradu sit equalis suo medio grádmi). As earlier the answers to the questions are affirmative,
Summary 209 and the anonymous author declares that the discussions and final so lutions of three subordinated questions would help to solve the main problem. He repeats, after Richard Kilvington and Adam de Pipewelle, that: “the acceleration of a falling body, in its descents, comes from several causes, though one is more significant than the others [.] the decrease in the resistance is the principal cause and the con tinuation of the motion, the proximity, the impulse of the medium, the accidental heaviness, and the natural inclination are the secondary causes.” While answering the second question, he states that the ve locity of a celestial sphere depends on the fastest point described on the radius of the sphere. This time he refers to Thomas Bradwardine’s Chapter IV of the treatise on the proportion of speeds in motion. The third subordinated question presents three different opinions of how to “measure” the speed in accelerated or decelerated motion {motus uni formly difform). The author finally accepts William Heytesbury’s above mentioned mean speed theorem. The presented Polish translation of the treatise On sex inconvenientibus testifies to the development of the mechanical theories invented by Richard Kilvington, Thomas Bradwardine and William Heytsbury — the most important figures from amongst the first generation of Oxford Calculators. |
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| author | Jung, Elżbieta 1956- |
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| author_facet | Jung, Elżbieta 1956- |
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| building | Verbundindex |
| bvnumber | BV046884128 |
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| edition | Wydanie I. |
| format | Book |
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| id | DE-604.BV046884128 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T15:19:03Z |
| indexdate | 2024-07-10T08:56:31Z |
| institution | BVB |
| isbn | 9788381429764 8381429765 |
| language | Polish |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032294072 |
| oclc_num | 1197709850 |
| open_access_boolean | |
| owner | DE-12 |
| owner_facet | DE-12 |
| physical | 209 Seiten 24 cm |
| psigel | BSB_NED_20210427 gbd_0 |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | Wydawnictwo Uniwersytetu Łódzkiego Centrum Filozofii Przyrody |
| record_format | marc |
| series | Research on Science & Natural Philosophy |
| series2 | Research on Science & Natural Philosophy |
| spelling | Jung, Elżbieta 1956- Verfasser (DE-588)1217074074 aut Zmiany ilościowe i ich miara w traktacie O sześciu niedorzecznościach Elżbieta Jung Wydanie I. Łódź Wydawnictwo Uniwersytetu Łódzkiego 2019 Łódź Centrum Filozofii Przyrody 209 Seiten 24 cm txt rdacontent n rdamedia nc rdacarrier Research on Science & Natural Philosophy tom 3 Literaturverzeichnis Seite [193]-199 Zusammenfassung auf Englisch Aristoteles v384-v322 (DE-588)118650130 gnd rswk-swf Bewegung (DE-588)4006311-2 gnd rswk-swf Naturphilosophie (DE-588)4041408-5 gnd rswk-swf Aristoteles / (384-322 p.n.e.) / krytyka i interpretacja Filozofia przyrody Zmiana (filozofia) Ruch (filozofia) Aristoteles v384-v322 (DE-588)118650130 p Naturphilosophie (DE-588)4041408-5 s Bewegung (DE-588)4006311-2 s DE-604 Erscheint auch als Online-Ausgabe 978-83-8142-977-1 Research on Science & Natural Philosophy tom 3 (DE-604)BV046884122 3 Digitalisierung BSB München 25 - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032294072&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung BSB München 25 - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032294072&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Register // Sachregister Digitalisierung BSB München 25 - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032294072&sequence=000005&line_number=0003&func_code=DB_RECORDS&service_type=MEDIA Register // Personenregister Digitalisierung BSB München 25 - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032294072&sequence=000007&line_number=0004&func_code=DB_RECORDS&service_type=MEDIA Literaturverzeichnis Digitalisierung BSB München 25 - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032294072&sequence=000009&line_number=0005&func_code=DB_RECORDS&service_type=MEDIA Abstract |
| spellingShingle | Jung, Elżbieta 1956- Zmiany ilościowe i ich miara w traktacie O sześciu niedorzecznościach Research on Science & Natural Philosophy Aristoteles v384-v322 (DE-588)118650130 gnd Bewegung (DE-588)4006311-2 gnd Naturphilosophie (DE-588)4041408-5 gnd |
| subject_GND | (DE-588)118650130 (DE-588)4006311-2 (DE-588)4041408-5 |
| title | Zmiany ilościowe i ich miara w traktacie O sześciu niedorzecznościach |
| title_auth | Zmiany ilościowe i ich miara w traktacie O sześciu niedorzecznościach |
| title_exact_search | Zmiany ilościowe i ich miara w traktacie O sześciu niedorzecznościach |
| title_exact_search_txtP | Zmiany ilościowe i ich miara w traktacie O sześciu niedorzecznościach |
| title_full | Zmiany ilościowe i ich miara w traktacie O sześciu niedorzecznościach Elżbieta Jung |
| title_fullStr | Zmiany ilościowe i ich miara w traktacie O sześciu niedorzecznościach Elżbieta Jung |
| title_full_unstemmed | Zmiany ilościowe i ich miara w traktacie O sześciu niedorzecznościach Elżbieta Jung |
| title_short | Zmiany ilościowe i ich miara w traktacie O sześciu niedorzecznościach |
| title_sort | zmiany ilosciowe i ich miara w traktacie o szesciu niedorzecznosciach |
| topic | Aristoteles v384-v322 (DE-588)118650130 gnd Bewegung (DE-588)4006311-2 gnd Naturphilosophie (DE-588)4041408-5 gnd |
| topic_facet | Aristoteles v384-v322 Bewegung Naturphilosophie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032294072&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032294072&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032294072&sequence=000005&line_number=0003&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032294072&sequence=000007&line_number=0004&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032294072&sequence=000009&line_number=0005&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV046884122 |
| work_keys_str_mv | AT jungelzbieta zmianyiloscioweiichmiarawtraktacieoszesciuniedorzecznosciach |