Details
BOLYAI, Farkas (1775-1856) & Janos BOLYAI (1802-1860). Tentamen juventutem studiosam in elementa matheseos purae, elementaris ac sublimioris, methodo intuitiva, evidentiaque huic propria, introducendi, cum appendic triplici [appendix scientiam spatii absolute veram exhibens]. Maros Vasarhelyini: typis Collegii Reformatorum et Simon Kali, 1832-3.
2 volumes, 8° (205 x 125mm). Large folding table and 14 double-page diagrammatic tables (3 with overslips). Original half cloth.
Vol. I: [iv], lxxviii, 502 pp., appendix: [ii], 26, [2 errata], xxvi pp., one large folding plate printed both sides, 4 double-page plates, [plate III with 6 overslips]. (Lacking leaves 2x4 - 4x4, i.e. pp. lxxix-xcvii and V4 i.e. pp. 185-192; however, these leaves seem never to have been inserted in this copy; tear repaired in list of subscribers without loss, inkblot on p. 133). Vol. II: [vi], 16, 402 pp., 10 double-page plates [plate 7 with 10 overslips, plate 8 with 1 slip only, plate 9 with 3 slips, plate 10 with 5 slips], (Horblit calls for one slip on plate 6 but it is not present and may not be required; and 3 slips on plate 8).
Provenance: Topler Sàndorè (contemporary signature on title); George Bruce Halsted (signature on flyleaf of vol.I); ASSOCIATION COPY: Halsted translated Janos's Appendix to his father's work into English in 1891.
FIRST EDITION. OF THE VERY GREATEST RARITY. The list of subscribers lists 70 names, subscribing 128 copies, and it is doubtful if many more were printed. The National Union Catalogue records only a copy of the Appendix of the original edition at Yale, although there is in fact a copy at the Burndy Library (which was loaned to the Grolier exhibition). There is no copy in the Bibliothèque Nationale, nor in the British Library. The only complete copy ever sold at auction was sold in our rooms, 9 December 1987, lot 135. In spite of its defects the present copy is in excellent condition and the Appendix by Janos Bolyai is quite complete.
Grolier/Horblit, One hundred books famous in science 69B describes the work as an 'Independent early essay on non-Euclidean geometry, termed by Halsted (the translator into English) "the most extraordinary two dozen pages in the history of thought"'.
Dibner in Heralds of Science 116 details the mathematical significance of the work: "In the 26-page appendix to the mathematic work of his father, the young Bolyai established a generalised system of geometry free of Euclidian premises of the parallel-axiom, attempted earlier but neglected by Gauss. In this geometry of 'absolute space' an infinite number of lines can be drawn in a plane thru a point, yet none of these will cut a given line in the same plane, thereby proving Euclid's eleventh axiom unnecessary. Thus three bodies of geometrical doctrine, elliptic, parabolic (Euclidian) and hyperbolic are formed, involving a new theory of surfaces."
Farkas Bolyai spent his life in close correspondence with Gauss, reconsidering the foundations of mathematics and proving Euclidean axioms. He published at his own expense at the press of the College where he taught in Transylvania the Tentamen (An attempt to introduce studious youth into the elements of pure mathematics by an intuitive method and appropriate evidence, with a threefold appendix). This work is a most remarkable witness to the sharpness of his mind and to his perseverance. In many respects he can be taken as a precursor of Gottlob Frege, Pasch and Georg Cantor, but as with many pioneers, he did not enjoy the credit that accrued to those that followed. As an appendix to his work he published the short essay written by his son Janos Bolyai, which was recognized by Gauss and Lobachevski as one of the great original contributions to mathematics. The 'Appendix explaining the absolute true science of space', the classic study of 24 pages containing Janos's system of non-Euclidian geometry was the only work he published in his lifetime. It was first published in English in 1891 (often since reprinted). For full details of these mathematicians see the article by D.J. Struik in Dictionary of Scientific Biography, pp. 268-271.
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2 volumes, 8° (205 x 125mm). Large folding table and 14 double-page diagrammatic tables (3 with overslips). Original half cloth.
Vol. I: [iv], lxxviii, 502 pp., appendix: [ii], 26, [2 errata], xxvi pp., one large folding plate printed both sides, 4 double-page plates, [plate III with 6 overslips]. (Lacking leaves 2x4 - 4x4, i.e. pp. lxxix-xcvii and V4 i.e. pp. 185-192; however, these leaves seem never to have been inserted in this copy; tear repaired in list of subscribers without loss, inkblot on p. 133). Vol. II: [vi], 16, 402 pp., 10 double-page plates [plate 7 with 10 overslips, plate 8 with 1 slip only, plate 9 with 3 slips, plate 10 with 5 slips], (Horblit calls for one slip on plate 6 but it is not present and may not be required; and 3 slips on plate 8).
Provenance: Topler Sàndorè (contemporary signature on title); George Bruce Halsted (signature on flyleaf of vol.I); ASSOCIATION COPY: Halsted translated Janos's Appendix to his father's work into English in 1891.
FIRST EDITION. OF THE VERY GREATEST RARITY. The list of subscribers lists 70 names, subscribing 128 copies, and it is doubtful if many more were printed. The National Union Catalogue records only a copy of the Appendix of the original edition at Yale, although there is in fact a copy at the Burndy Library (which was loaned to the Grolier exhibition). There is no copy in the Bibliothèque Nationale, nor in the British Library. The only complete copy ever sold at auction was sold in our rooms, 9 December 1987, lot 135. In spite of its defects the present copy is in excellent condition and the Appendix by Janos Bolyai is quite complete.
Grolier/Horblit, One hundred books famous in science 69B describes the work as an 'Independent early essay on non-Euclidean geometry, termed by Halsted (the translator into English) "the most extraordinary two dozen pages in the history of thought"'.
Dibner in Heralds of Science 116 details the mathematical significance of the work: "In the 26-page appendix to the mathematic work of his father, the young Bolyai established a generalised system of geometry free of Euclidian premises of the parallel-axiom, attempted earlier but neglected by Gauss. In this geometry of 'absolute space' an infinite number of lines can be drawn in a plane thru a point, yet none of these will cut a given line in the same plane, thereby proving Euclid's eleventh axiom unnecessary. Thus three bodies of geometrical doctrine, elliptic, parabolic (Euclidian) and hyperbolic are formed, involving a new theory of surfaces."
Farkas Bolyai spent his life in close correspondence with Gauss, reconsidering the foundations of mathematics and proving Euclidean axioms. He published at his own expense at the press of the College where he taught in Transylvania the Tentamen (An attempt to introduce studious youth into the elements of pure mathematics by an intuitive method and appropriate evidence, with a threefold appendix). This work is a most remarkable witness to the sharpness of his mind and to his perseverance. In many respects he can be taken as a precursor of Gottlob Frege, Pasch and Georg Cantor, but as with many pioneers, he did not enjoy the credit that accrued to those that followed. As an appendix to his work he published the short essay written by his son Janos Bolyai, which was recognized by Gauss and Lobachevski as one of the great original contributions to mathematics. The 'Appendix explaining the absolute true science of space', the classic study of 24 pages containing Janos's system of non-Euclidian geometry was the only work he published in his lifetime. It was first published in English in 1891 (often since reprinted). For full details of these mathematicians see the article by D.J. Struik in Dictionary of Scientific Biography, pp. 268-271.
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