BOLZANO, Bernard Der binomische Lehrsatz, und als Folgerung aus ihm der polynomische, und die Reihen, die zur Berechnung der Logarithmen und Exponentialgršssen dienen, genauer als bisher erweisen. Prague, C.W. Enders, 1816
8vo (204 x 116 mm), pp xvi 144 [4]; some occasional light browning and/or spotting, a very good copy in contemporary half calf and boards, worn. £4850
First edition, exceptionally rare, of BolzanoÕs work on the foundation of analysis, in which the modern definition of a limit (for any there exists an index N so that ...) is given for the first time. This work passed unnoticed and CauchyÕs Cours dÕanalyse (1821) is often cited as the first.
ÔAround the turn of the nineteenth century, mathematicians in Europe were concerned with two major problems. The first was the status of EuclidÕs parallel postulate, and the second was the problem of providing a solid foundation for mathematical analysis, so as to remove the so-called scandal of the infinitesimals. Bolzano tried his hand at both problems, with varying success...
ÔIt should be emphasized that Bolzano was not the only one, or even the first, to be concerned with the problem of rigorous proofs in mathematics. A curious fact, however, is that although many of the mathematicians actively interested in the problem of the foundation of mathematical analysis surpassed him in mathematical skill, Bolzano overcame them decisively in the foundation of analysis...
ÔTo overcome the difficulties presented by infinitesimals, Lagrange proposed to base analysis on the existence of TaylorÕs expansion for functions, and this attitude was widely accepted for a time. Bolzano did not escape its influence, and made extensive studies on TaylorÕs theorem (see Der binomische Lehrsatz)Õ (DSB).
The rarity of this work is perhaps accounted for by the fact that Bolzano (1781-1848) held to the chair of religious philosophy at Prague but his Enlightenment views aroused suspicion. ÔIn the struggle between the Catholic restoration and the Enlightenment action against Bolzano was postponed until 1816, when a charge was brought against him at the court in Vienna... He was forbidden to publish and was put under police supervisionÕ (ibid). Bolzano was nicknamed the ÔBohemian LeibnizÕ.
no copies recorded in OCLC nor RLIN; KVK lists a copy at the National Library of Austria, and copies in Berlin, Erfurt, Freiburg, and Leipzig; Poggendorff I 229; Winter Bolzano 4
£4850
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