PAL

Ptolemaeus Arabus et Latinus

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Work C.1.17

Giovanni Bianchini
Flores Almagesti

A series of ten tractatus, dealing with arithmetic (I), algebra (II), De proportionibus (III) and astronomical matters from the first six books of the Almagest (IV-X), written by Giovanni Bianchini (c. 1410-1469) in Ferrara from c. 1440 until at least 1456. The manuscripts display differences in content and organisation.

Text

‘(Cracow, BJ, 558) (1r-12r) [I] Tractatus primus de arismeticha per Iohannem de Blanchinis. Liber primus. Incipit prohemium. Arismetrica (corr. in Arithmetica) dico quod determinatur per numeros, et duas noto diffinitiones numerorum — nec resultabit error sensibilis in aliquo calculo astrologie. (12r-15v) [II] Tractatus secundus Iohannis de Blanchinis de demonstrationibus cum regulis agregatis. De practica regularum argebre capitulum primum. In tota practica regularum argebre quattuor demonstrationibus — radix diminuta medietate cuborum valet res. (16r-25r) [III] Tractatus tertii Iohannis de Blanchinis. Diffinitiones. Si duo numeri ad invicem multiplicentur et productum per primum multiplicantem — versus protionis AE, quod est ultima conclusio. (25r-29v) [IV] [Blank space for title] Omnes recte linee et trianguli orthoghonii inter lineas eque distantes — et tot pedes sint blasis. (30r-47v) [V] Incipiunt demonstrationes necessarie ad figuram retoris liber tertius. Si ab uno puncto angulariter due recte linee protrahantur — tractatus quarti huius fiet eadem conclusio. (48r-80v) [VI] Liber primus tractatus sextus Iohannis de Bianchinis. Distantiam centri deferentis Solis a centro mundi atque verum locum augis Solis demonstrative invenire. Describam circulum zodiaci supra quem sit ABQL circa centrum — ut per operationes non committatur error. (80v-94r) [VII] Tractatus septimus. Liber secundus. Distantia centri deferentis, centrum epicicli acc… (?) quantitates semidiametri ipsius deferentie demonstrare. Demonstratum est per Ptholomeum in libro Almagesti — in demonstratione eclipsium et figura ipsorum pungenda. (94v-100r) [VIII] Tractatus octavus. Liber I. De minutis cass… (?) ad longitudines longiores et propinquiores demonstratio. In hiis que precesserunt, demonstratum est quod semidiameter Solis — in lineis rectis inclusorum tam quibus quibus perficietur opus nutu Dei gloriosi. (100v-110r) [IX] De imperfecta compositione tabularum hucusque observatarum aspectus Lune invenienda. In precedentibus demonstratum est diversitatem aspectus Lune — operare prout in sequentibus dabo exemplum eclipsis Lune futura. (110r-116r) [X] Eclipsis Solis futuri que erit in anno 1460 a nativitate domini de mense Iulii ad situm Ferrarie perscrutari. Primo queram coniunctionem veram luminarium per tabulas de motibus planetarum alias per me constructas — et si excesserit minuta 50 erit grisia cum albedine.’

Bibl.

L. A. Birkenmajer, ‘Flores Almagesti. Ein angeblich verloren gegangener Traktat Giovanni Bianchini’s Mathematikers und Astronomen von Ferrara aus dem XV. Jahrhundert’, Bulletin International de l’Académie des Sciences de Cracovie, Classe des Sciences (1911), 268-278; L. Thorndike, ‘Giovanni Bianchini in Paris Manuscripts’, Scripta Mathematica 16 (1950), 5-12 and 169-180: 6-8 and 169-171; L. Thorndike, ‘Giovanni Bianchini in Italian Manuscripts’, Scripta Mathematica 19 (1953), 5-17: 10-13; G. Rosińska, ‘The ‘Italian Algebra’ in Latin and How it Spread to Central Europe: Giovanni Bianchini’s De Algebra (ca. 1440)’, Organon 26-27 (1997), 131-145; J. Chabás, B. R. Goldstein, The Astronomical Tables of Giovanni Bianchini, Leiden-Boston, 2009, 19; H. Zepeda, The Medieval Latin Transmission of the Menelaus Theorem, PhD dissertation, University of Oklahoma at Norman, 2013, 323-329; G. Van Brummelen, ‘The End of an Error: Bianchini, Regiomontanus, and the Tabulation of Stellar Coordinates’, Archive for History of Exact Sciences 72 (2018), 547-563: 551-552 and passim; J. Chabás, B. R. Goldstein, ‘The Tabulae eclypsium by Giovanni Bianchini’, Aestimatio NS 2.1 (2021), 1-41: 5-6 and passim.

Modern ed.

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MSS

Bologna, BU, 198 (293), s. XV, f. 3r-125v

Cracow, BJ, 558, s. XV, 1r-116rImages

Cracow, BJ, 601, s. XV, f. 62r-68v

Paris, BnF, lat. 10253, s. XV, f. 6r-138v

Perugia, BCA, 1004 (M. 27), s. XV, f. 1r-77r

Vatican, BAV, Reg. lat. 1904, s. XV-XVI, f. 1r-56r

Vatican, BAV, Vat. lat. 2228, s. XV, f. 16r-51v and 78r-120r