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Ptolemaeus

Arabus et Latinus

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Vienna, Österreichische Nationalbibliothek, 5277

s. XVI1 (1520 for the first Ptolemaic section, cf. colophon f. 100v; 1525 for f. 231-236, cf. f. 236v). Or.: Johannes Vögelin’s notebook, mostly copied in his hand (including both Ptolemaic sections) probably in Vienna; f. 231-236 were copied by Georg Gotzmann of Aubing in Vienna (cf. f. 236v: ‘Viennae Pannoniae per G. G. Aubingen<sem> VIII calendarum Novembrium anno huius seculi quinto et vicesimo’). Prov.: family Fugger. The mention ‘Magistro Ratznperger zu… (?) gehort’ (f. 350r) does not seem to concern the present MS.

Paper, 385 f., one main hand (Johannes Vögelin ).

Mathematics, astronomy, optics and geography: table of contents in Vögelin’s hand (1r); ‘Regulae cosae vel algobre. Conditiones cira + vel – in additione…’ (2r-33r); ‘Sequitur ingeniosa ratio investigandi calculo annulum…’ (33v); ‘Modus preparandi virgam visoriam cubicam…’ (34r-36r); ‘Algorithmus de surdis quadratorum. In hoc algarithmo (!) quolibet…’ (37v); Levi ben Gerson, De sinibus, chordis et arcubus (38r-65v); notes by Vögelin, including onomancy ‘Scribe primo nomina ipsorum…’ and ‘Trapezuntium in Almagestum capitulo nono. Scientia chordarum…’ (66r); John of Gmunden, Compositio quadrantis novi seu magni cum eius practica (68r-90v); Ptolemaica (92r-100v); De inquisitione capacitatis (101r-110r); Pseudo-Messahallah, De compositione astrolabii, first part on construction, c. 17-18 ‘Proiectio sphaerae in planum. Concussio sive extensio immo potius proiectio sphaerae in planum…’ (110v-117r); astrological note ‘Ad cognoscendum omni die qualis sit aura, accipe a Sole in Saturnum…’ (117v); ‘Si quis voluerit componere torquetum, accipiat laminam de quacumque materia…’ (118r-119r); Franco de Polonia, Tractatus de turketo, incomplete (119r-123v); comm. on Jordanus of Nemore’s Elementa super demonstrationem ponderum (130r-137v); ‘Incipit tractatus specialis de modo demonstrandi iridem esse circularem secundum modum Aristotelis tertio Metheororum, quo continuatur et declaratur textus et demonstratio Aristotelis. Quod autem neque circulum…’ (137v-151r); De tribus notis (151v-154r); geometry ‘Artis cuiuslibet consummatio…’ (154r-164v); Jordanus of Nemore, De plana spera (164v-167v); Campanus of Novara, De proportione et proportionalitate (168r-170v); Menelaus, Spherica (171r-185r); Gernardus, Algorismus demonstratus (199r-223v); Tractatus de speculo parabolico ‘Parabolicum speculum est cuius superficiem concavam describit…’ (224r-230r); Zenodorus, De isoperimetris (231r-236v); notes on Alfraganus’s De scientia astrorum, c. 22-30 (237r-241v); scattered notes of arithmetic and astronomy in Latin and German (241v-246v), including a note on Almagest, V.15 ‘Circa caput decimum quintum libri quinti Magnae compositionis…’ (242r); ‘Instrumentum quo maximus dies discitur in qualibet regione cognita eius elevatione polari. Ptolemeus et in sua Magna compositione et in Geographia…’ (247v-248v); notes on Ptolemy’s Geographia (249r-270r); Claudius Clavus, geographical coordinates of northern-European cities and places (271r-276r, ed. Björnbo/Petersen, 216-233); notes on Ptolemy’s Geographia and related topics (276r-281r), including ‘De lineis semper appropinquantibus et nunquam concurrentibus. Omnium punctorum duorum in superficie…’ (276v-277r) and ‘Circa proportionies irrationales annotata. Omnis proportio rationalis vel est primaria…’ (277v-278r); ‘De diffinitionibus sinuum secundum Io<hannem> Blanchini’ (283r-284v); ‘Compositio tabulae sinus. Ex quo scientia sinuum necessaria est…’ (287r-287v), with table ‘Sequitur tabula sinus magistri Georgii de Peurbach’ (287v-289v); Tres Fratres Filii Moysi [Banū Mūsā], Verba filiorum Moysi filii Sekir, incomplete (297v-298v); medical recipes and notes in Latin and German (290r-296r); ‘Tabulam minutorum proportionalium componere…’ (296v-298v); Pseudo-Thebit Bencora, De motu octave spere (299r-302r); Ptolemaica (302r-305v); Thebit Bencora, De recta imaginatione spere et circulorum eius diversorum (305v-307r); Liber Ameti de proportione et proportionalitate (307v-320v); Jordanus of Nemore, De numeris datis, reworked (320v-327r) and followed by a commentary (327r-331r); ‘Pro regularum algabre cognitione est primo notandum quando duo signa…’ (331r-334v); Nicole Oresme, Algorismus proportionum (335r-336v); ‘Algorithmus quadratorum a quadratis. Reliquarumque ductionum…’ (337r-338v); scattered notes (339r); geographical coordinates of cities, with notes (340r-341r); ‘Horologium horarum inaequalium. Ad faciendum horologium horarum inaequalium…’ (341r-342r); notes of geometry (342r-343v); notes on Thomas Bradwardine’s Geometria speculativa (343v-346r); ‘Vögelin scribebat et inveniebat. Progressionum summas cupienti scire quaedam…’ (347r-349r); diagrams and notes of geometry and optics (351r-360v); comm. on Melenaus’s Spherica ‘Omnis trianguli ex arcubus circulorum magnorum super superficiem… Expletus est translatus tertius libri Milei de sphericis et cum eius expletione completus est totius liber eius’ (361r-378v); ‘Exempla super algorithmum de surdis’ (379r-391r); ‘Hec infrascripta scholia pertinent ad Mileum’ (381v-382r, cf. 361r-378v above); ‘De aliquibus speciebus cubicorum…’ (382r-382v); ‘Ars binomalis. Divisiones linearum ponere…’ (382v-384v); ‘Compositio instrumenti quo ad veram coniunctionem Solis et Lunae’ (385r-385v). Blank: 1v, 36v-37r, 66v-67v, 91, 124-129, 185v-198v, 230v, 247r, 270v, 281v-282v, 285-286v, 339v, 346v, 349v-350.

Lit.Tabulae codicum manu scriptorum praeter Graecos et Orientales in Bibliotheca Palatina Vindobonensi asservatorum, IV: Cod. 5001-6500, Wien, 1870, 82-85; A. A. Björnbo, C. S. Petersen, Der Däne Claudius Claussøn Swart (Claudius Clavus). Der älteste Kartograph des Nordens, der erste Ptolemäus-Epigon der Renaissance, Innsbruck, 1909, 45-47; Katalog der datierten Handschriften in lateinischer Schrift in Österreich, IV: F. Unterkircher, Die datierten Handschriften der österreichischen Nationalbibliothek von 1501 bis 1600, I, Wien, 1976, 51; B. B. Hughes, Jordanus de Nemore: De numeris datis, Berkeley-Los Angeles-London, 1981, 44.

92r‑100v

‘Tractatus de quantitate trium solidorum. Capitulum primum de distantia Lunae a terra. <Q>uia tria corpora solida particularium quia quod modicum distat nihil distare videtur. Explicit tractatus de quantitate trium solidorum corporum secundum sententiam Ptolo<mei> in Almag<esti> anno 1520 in die animarum.’

= Johannes Andree Schindel, Tractatus de quantitate trium solidorum (C.1.15). A few marginal notes by the scribe (Vögelin).

302r‑305v

‘Thebit praecognitiones Almagesti. Thebit ben Corah De hiis quae indigent expositione antequam legatur Almagesti. Aequator diei est circulus maior qui describitur supra 2 polos mundi — propinqui oppositioni Solis erunt retrogradi. Explicit Thebit De hiis quae indigent expositione antequam legatur Almagesti, et dicitur Aequator diei.’