[János Bolyai]: Appendix. Scientiam Spatii absolute veram exhibens: a veritate aut falsitate Axiomatis XI. Euclidei (a priori haud unquam decidenda) independentem; adjecta ad casum falsitatis, quadratura circuli geometrica. Auctore Johanne Bolyai de eadem, Geometrarum in Exercitu Caesareo Regio Austriaco Castrensium Capitaneo.
An English translation of the work: The science absolute of space, independent of the truth or falsity of Euclid’s axiom XI (which can never be decided a priori) / by John Bolyai ; translated from the Latin by George Bruce Halsted. – 4th ed. – Austin, Texas, 1896.
János Bolyai's work appeared as an appendix to his father’s, Farkas (Wolfgang) Bolyai’s monumental two-volume book Tentamen (Maros Vásárhelyini, 1832, 1833), which summarized the mathematical knowledge of the time. Appendix appeared in the first volume in 1832 but was also published as a preprint in 1831. (The imprimatur of Tentamen – on the versos of the volumes’ title pages – is dated October 12, 1829.)
Appendix was written in Latin, in a concise, elegant and rigorous style. János Bolyai presents his discoveries of absolute geometry, which is independent of Euclid’s axiom of parallelism and, replacing the axiom of parallelism by its negation, of hyperbolic geometry. The text is divided into 43 sections (§ 1 through § 43). Though this is the only subdivision of the book, two major parts may be distinguished in its contents: the treatment of absolute geometry, and of non-Euclidean (hyperbolic) geometry.
This copy of Appendix once belonged to the author, János Bolyai, and contains autographic notes and figures drawn by him and a manuscript title page by his father, Farkas Bolyai.
The Hungarian Academy of Sciences bought this copy of Appendix from architect Ferenc Schmidt (1827-1901) or heirs in 1901. (Schmidt authored the biography of Farkas and János Bolyai, thus making them more widely known.)
Description of the publication and the copy
The copy is in its publisher’s wrappers. A label on the front cover of the grey wrappers reads „Bolyai A.3.”, the item number in what was called the Bolyai cabinet of the Library of the Academy.
Size of the publication: 26,  p.,  leaf of plates, quarto, height 20 cm. Signatures: A-C4 D2. It consists of 14 leaves, which are numbered 4 through 26 from leaf 2 verso through leaf 13 verso (p. 4-26). The first leaf begins with Explicatio signorum, its verso is blank; the text begins on leaf 2 recto: § 1. (Fig. 1.) Si rectam …; ends on leaf 13 verso (p. 26): … quod tamen occasioni // magis idoneae reservatur.; leaf 14 (unnumbered): Errata …; ends on the verso: … lege sectio. At the end of the book, pasted inside the lower cover of the wrappers, there is a fold-out leaf of plates, light blue paper with the printed figures; marked at bottom left: „Steph. Vizi sc.”; the title at top right: Tabula Appendicis; verso is blank.
These leaves, including the fold-out leaf of plates with the printed figures, are the same as in Appendix published with Tentamen.
Appendix, as it appeared in Tentamen – as well as in other separate copies – has its own title page with the long title shown above. In the present copy, this title page is missing, it is replaced by a leaf with the title written by Farkas Bolyai:
Appendix Prima. Scientia Spatii absolute vera; nulli quoad parallelas supposito Axiomati (Euclideo vel alii simili) innixa. Auctore Johanne Bolyai de eadem, Geometrarum in Exercitu Caesareo Regio Austriaco Castrensium Locumtenente Primario Auctoris Filio.
Schmidt confirmed it in red ink: „Handschrift Wolfgang Bolyai. Fr. Schmidt.” – János Bolyai also made some notes here in pencil.
The preceding fly-leaf – the same light blue paper as used for the leaf of plates with the printed figures – bears on its recto a variant of the title in János Bolyai’s hand:
Appendix, Scientiam Spatii absolute veram exhibens; a veritate aut falsitate Axiomatis XI. Euclidei (a priori haud unquam decidenda) independentem; adjecta ad casum falsitatis quadratura circuli geometrica. Auctore Johanne Bolyai de Eadem, Geometrarum in Exercitu Caesareo Regio Austriaco Castrensium Capitaneo. Agropoli sive Maros-Vásárhelyini 1832. Typis Collegii Reformatorum per Josephum et Simeonem Kali de Felső-Vist.
Ferenc Schmidt’s note in red ink at the top of the page: „Handschrift von Johan Bolyai.”
The present shelfmark is written in pencil on the verso: 545.091; underneath a stamp identifying the item in the Academy Library’s accession journal: 1901. év 296.; underneath a printed label: „354. Bolyai János: Appendix. (A nyomtatott munka B.J. saját kezű bejegyzéseivel.) 27 levél. Bolyai A.3. Tud. Akadémia.”
The light blue paste-down – the other half of the fly-leaf – is filled with János Bolyai’s Note in German: „Anmerkung”, rejecting the opinions of his incompetent critics. Schmidt’s note at top left in red ink: Johan Bolyai.
Following leaf 13 (page 26), a loose leaf is inserted, numbered „) 27 )”, printed with three lines altogether (its verso is blank):
omnes. Ax XI Eucl. demonstrandi necessario irritos // fuisse): at muneris ratio huic amplius vacare haud // permittens, alii occasioni reservare jubet.
At the end of the book, preceding the leaf of plates with the printed figures, another fold-out of white paper is pasted in, containing the figures drawn by János Bolyai himself in Indian ink, as well as his corrections to Figs. 4 and 13 and an additional Fig. 23 in pencil. There is a note on it in pencil: „Original Zeichnung Jo. Bolyai.” His corrections and the additional figure are included in the printed figures.
This copy of Appendix seems to have been compiled from two copies or versions later some time. The second (inner) title page, pages 1 through 24, page 27 and the leaf of plates with the figures in Bolyai’s hand must have been parts of the same unit. These leaves were pierced, starting from the lower cover of the wrappers, resulting in a pattern of about 30 pricks on them. This might have arisen from the disinfection process by fumigation during the cholera epidemic in 1831.
The book is now preserved and kept in a new acid-free case covered with leather. (Its former half-cloth library binding was removed after the digital pictures were taken.)
This copy of János Bolyai’s Appendix was submitted for inclusion in UNESCO’s Memory of the World Register in 2009.
description | wrappers1 | title page1 | title page2 | 1 | 2-3 | 4-5 | 6-7 | 8-9 | 10-11 | 12-13 | 14-15 | 16-17 | 18-19 | 20-21 | 22-23 | 24-25 | 26-27 | errata1 | errata2 | tabula1 | tabula2 | tabula3 | wrappers2