Mathematical Treasure: János Bolyai’s Appendix to Tentamen juventutem studiosam in elementa matheseos purae

The Hungarian mathematician János Bolyai (1802–1860) produced his own system of non-Euclidean geometry, which was completed by 1823 but not published until 1832, when it was printed as an appendix to his father Farkas’s larger work, Tentamen juventutem studiosam in elementa matheseos purae, elementaris ac sublimioris, methodo intuitiva, evidentiaque huic propria, introducendi (An attempt to introduce the young student to the pure, elementary and sublime elements of mathematics, by an intuitive method, and with proofs proper to this). This privately-published work was poorly printed by an obscure college publisher in a run of about 150 copies in Marosvásárhely, a small city in Hungary. The work remained obscure for many years, but once it was revealed, it brought Bolyai the mathematical recognition he deserved. Today, this book is extremely rare.

János’s appendix begins on page 503. He defined his terminology and then presented a highly symbolic argument.

These images are from the copy owned by the Dibner Library of the Smithsonian Institution Libraries. Rights and reproduction information may be found here.

Index to Mathematical Treasures