Depicts Bolyai János signature, extract from his work "The Appendix" in Latin, inscriptions and engraver's privy mark below.

The extract is: "Presenting a knowledge of space that is absolutely true: independent of the truth or falsity of Euclid's Axiom XI (which can never be determined a priori); with the addition, in the case of its falsity, of the geometric squaring of the circle."

János Bolyai's work, appearing as part of his father, Bolyai Farkas's extensive two-volume work, the Tentamen, as an appendix. The Tentamen (Marosvásárhely, 1832, 1833) summarizes his contemporary mathematical knowledge and includes some remarks regarding the Appendix. The Appendix was first published in the initial volume in 1832 but separately as a pamphlet in 1831.

In the Appendix, János Bolyai succinctly, rigorously, and elegantly presents his groundbreaking discovery in Latin. He constructs a new, axiomatic geometric system (absolute geometry) independent of Euclid's parallelism postulate (the 11th axiom), and, by negating the parallelism axiom, he develops non-Euclidean hyperbolic geometry. The text consists of 43 sections (§ 1-43) and is divided into two main parts: the discussion of absolute geometry and hyperbolic geometry.

Depicts the 10th geometric figure from the "Tabula Appendicis." Surrounding it, you'll find the name of the country (Hungarian Republic), while below, the mint mark (BP), denomination, and year of issue are clearly visible.

Absolute geometry, coined by János Bolyai in 1832, is a geometric system that operates without the parallel postulate or its alternatives from Euclidean geometry. Traditionally, it relies solely on the initial four postulates formulated by Euclid. Occasionally termed neutral geometry due to its neutrality towards the parallel postulate, it diverges from reliance solely on Euclid's first four postulates, now deemed inadequate for Euclidean geometry. Consequently, alternative systems, such as Hilbert's axioms excluding the parallel axiom, have replaced them.