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Démonstration de l'intégrabilité des équations différentielles ordinaires. - [THE PROOF OF THE EXISTENCE THEOREM - INTRODUCING THE AXIOM OF CHOICE]
Leipzig, B.G. Teubner, 1890. Orig. printed wrappers, no backstrip. A small offsetting to upper left corner of frontwrapper. A small tear to endwrapper repaired. In ""Mathematische Annalen. Gegenwärtig hrsg. von Felix Klein, Walter Dyck, Adolph Mayer, 36. Band, 2. Heft."" Pp. (153-)320. The whole issue (Heft 2) with orig.wrappers. Peano's paper: pp. 182-288.
First edition and the first appearance of this fundamental paper in which Peano gives the proof of the so-called ""Peano-Existence-Theorem"" and at the same time contains the first explicit statement of ""The axiom of choice"".The Peano-Existence-Theorem, or ""Cauchy-Peano-Theorem"" guarantees the existence of solutions to certain initial value problems. He first published the theorem in 1886 in ""Sull'integrabilita della equazioni differenziali del primo ordine"" in Atti Accad. Sci. Torino, 21, with an incorrect proof. The new correct proof appeared in this paper, as offered.""Peano's work in analysis began in 1883 with an article on the integrability of functions. The article of 1890 (the paper offered) contains notions of integrals and areas. Peano wasthe first to show that the first-order differential equation y' = f(x,y) is solvable on the sole assumption that f is continuous. His first proof dates from 1886, but its rigor leaves something to be desired. In 1890 this result was generalized to systems of differential equations using a different method of proof. This work is also notable for containing the first explicit statement of the axiom of choice. Peano rejected the axiom of choice as being outside the ordinary logic used in mathematical proofs."" (Hubert T Kennedy in DSB).
Sur une courbe, qui remplit toute une aire plane. - [SPACE-FILLING CURVE - ANTICIPATING THE HILBERT CURVE]
Leipzig, B. G. Teubner, 1890. 8vo. Bound in recent full black cloth with gilt lettering to spine. In ""Mathematische Annalen"", Volume 36., 1890. Entire volume offered. Library label pasted on to pasted down front free end-paper. Small library stamp to lower part of title title page and verso of title page. Very fine and clean. Pp. 157160. [Entire volume: IV, 602 pp.].
First printing of Peano's seminal paper in which he for the very first time discovered a space-filling curve in a 2-dimensional plane, it is often referred to as Peano curves. Peano's ground-breaking paper contained no illustrations of his construction, which is defined in terms of ternary expansions and a mirroring operator. But the graphical construction was perfectly clear to him-he made an ornamental tiling showing a picture of the curve in his home in Turin. Peano's paper also ends by observing that the technique can be obviously extended to other odd bases besides base 3. His choice to avoid any appeal to graphical visualization was no doubt motivated by a desire for a well-founded, completely rigorous proof owing nothing to pictures. At that time (the beginning of the foundation of general topology), graphical arguments were still included in proofs, yet were becoming a hindrance to understanding often counter-intuitive results.Peano' purpose was to construct a continuous mapping from the unit interval onto the unit square. Peano was inspired by Georg Cantor's earlier counterintuitive result that the infinite number of points in a unit interval is the same cardinality as the infinite number of points in any finite-dimensional manifold, such as the unit square. The problem Peano solved was whether such a mapping could be continuous" i.e., a curve that fills a space.
Demonstration de l’intégrabilité des équations différentielles ordinaires. - [PEANO EXISTENCE THEOREM]
Leipzig, B.G. Teubner, 1890. 8vo. Bound in recent full black cloth with gilt lettering to spine. In ""Mathematische Annalen"", Volume 37, 1890. Entire volume offered. Library label pasted on to pasted down front free end-paper. Small library stamp to lower part of title title page and verso of title page. Fine and clean. Pp. 182-228. [Entire volume: IV, 604 pp.].
First printing of Peano's correct and complete Existence Theorem. Peano first published the theorem in 1886 with an incorrect proof. In 1890 he published a new correct proof using successive approximations. The theorem is also known as Peano existence theorem, Peano theorem or Cauchy-Peano theorem.
Studii di logica matematica. (Studies in Mathematical Logic).
Torino, Carlo Clausen, 1897. In: Atti della R. Accademia delle Scienze di Torino, Vol. XXXII, Disp. 11a, 1896-97, pp. 565-83. Royal8vo. Original printed wrappers. Some small tears. Wrappers loosening. Paper label pasted to front wrapper. Internally fine and clean. Uncut and unopened.
First edition.'In this work he is concerned with reducing the number of undefined terms to a minimum ... It was in this article that he introduced the symbol (left-facing E) for existence ... This paper also contains remarks on Frege's mathematical logic ...' (Kennedy, Life and works of Giuseppe Peano, p.68-69.) Frege and Peano worked independently on many of the same subjects in mathematical logic using each their own symbolism. Frege used a cumbrous two-dimensional system. It was Peano's notation which survived and was used in the 'Principia Mathematica'.Kennedy, No. 91.
Operazioni sulle grandezze.
Torino, Fratelli Bocca, 1922. Royal8vo. Uncut, unopened in the original blue printed wrappers. In ""Atti della R. Accademia delle Scienze di Torino"", Vol. LVII, Disp. 8a e 9a, 1921-1922. Small paper label pasted on to lower left part of front wrapper. A few nicks to front wrapper. A very fine and clean copy. Pp. 310-331. [Entire issue: Pp. 305-347].
First appearance of Peano's important paper operations of variables. The famous Italian mathematician, logical philosopher, pioneer of symbolic logic, and a founder of mathematical logic and set theory, Giuseppe Peano (1858 -1932) studied mathematics at the University of Turin, where he was employed just after graduating (1880), and where he stayed almost all of his life, devoting this to mathematics. After having graduated with honours, he was employed to assist first Enrico D'Ovidio, and then the renowned Angelo Genocchi, who possessed the chair of Infinitesimal calculus. In 1890 Peano became extraordinary professor, and in 1895 ordinary professor, of infinitesimal calculus at the Unversity of Turin. hIS ""Principles of Arithmetics"" (the present work) constitutes his groundbreaking main work.
Generalizzazione della formola di Simpson.
Torino, Fratelli Bocca, 1891-1892. Royal8vo. Uncut, unopened in the original blue printed wrappers. In ""Atti della R. Accademia delle Scienze di Torino"", Vol. XXVII, Disp. 10a, 1891-92. Small paper label pasted on to lower left part of front wrapper. A very fine and clean copy. Pp. 608-612. [Entire issue: Pp. 597-655].
First appearance of Peano's first work on the quadrature formulas.The famous Italian mathematician, logical philosopher, pioneer of symbolic logic, and a founder of mathematical logic and set theory, Giuseppe Peano (1858 -1932) studied mathematics at the University of Turin, where he was employed just after graduating (1880), and where he stayed almost all of his life, devoting this to mathematics. After having graduated with honours, he was employed to assist first Enrico D'Ovidio, and then the renowned Angelo Genocchi, who possessed the chair of Infinitesimal calculus. In 1890 Peano became extraordinary professor, and in 1895 ordinary professor, of infinitesimal calculus at the Unversity of Turin. hIS ""Principles of Arithmetics"" (the present work) constitutes his groundbreaking main work.
La numerazione binaria applicata alla stenografia.
Torino, Carlo Clausen, 1898. Royal8vo. Uncut, unopened in the original blue printed wrappers. In ""Atti della R. Accademia delle Scienze di Torino"", Vol. XXXIV, Disp. 1a, 1894-95. Small paper label pasted on to lower left part of front wrapper. Wrappers with nicks and lacking lower right corner of front wrapper. Internally with occassional brown spots. Fine. Pp. 20-41. [Entire issue: 78 pp].
First appearance of Peano's important paper in which he presented his ""shorthand machine"" which worked on the basis of the binary system. Peano was to a very large extend inspired by Leibnitz on this subject.
Sulla formola di Taylor.
Torino, Carlo Clausen, 1891-1892. Royal8vo. Uncut, unopened in the original blue printed wrappers. In ""Atti della R. Accademia delle Scienze di Torino"", Vol. XXVII, Disp. 1a, 1891-92. Small paper label pasted on to lower left part of front wrapper. A very fine and clean copy. Pp. 40-46. [Entire issue: 154 pp].
First appearance of Peano's paper on the conditions for expressing a function of several variables with Taylor’s formula.
La Geometria basata sulle idee di punto e distanza.
Torino, Carlo Clausen, 1903. Royal8vo. Uncut, unopened in the original blue printed wrappers. In ""Atti della R. Accademia delle Scienze di Torino"", Vol. XXXVIII, Disp. 1a e 2a, 1902-1903. Small paper label pasted on to lower left part of front wrapper and stamp to top of front wrapper and title page. Wrappers with nicks, miscolouring and traces after having been bended. Title page with a browning. Internally fine. Pp. 6-10. [Entire issue: 53 pp].
First appearance of Peano's paper on his theory of geometry based on the ideas of point and distance.
Calcolo differenziale e principii di calcolo integrale, pubbicato con aggiunte dal Dr. Giuseppe Peano. - [A FOUNDATIONAL WORK OF THE SCIENCE OF INFINITESIMAL CALCULUS]
Torino, Fratelli Bocca, 1884. 8vo. Cont. full green cloth w. gilt title and ornamentation to spine. Minor occasional browning. A very nice and clean copy. XXXII, 333, (5, -index and errata) pp.
The scarce first edition of Peano's first major publication, his first book, the work that brought him international fame, and one of the most important calculus texts since the time of Euler and Cauchy.The present book, which has a somewhat strange history, contributing to its scarcity, is considered a constitutional work of the science of infinitesimal calculus. In 1899 it was translated into German, and in 1903 into Russian.The famous Italian mathematician, logical philosopher, pioneer of symbolic logic, and a founder of mathematical logic and set theory, Giuseppe Peano (1858 -1932), studied mathematics at the University of Turin, where he was employed just after graduating (1880), and where he stayed almost all of his life, devoting his life to mathematics. After having graduated with honours, he was employed to assist first Enrico D'Ovidio, and then the renowned Angelo Genocchi, who possessed the chair of Infinitesimal calculus. At this time, Genocchi's health was declining, and the teaching of the infinitesimal calculus course was handed over to Peano already in 1882. In 1880 Peano had published his first paper, and the following year he published another three" in 1884 he published his first book, the foundational ""Calculus and Principles of Integral Calculus"", which constitutes one of ""the most important works on the development of the general theory of functions since the work of the French mathematician Augustin-Louis Cauchy (1789-1857)"". (Encycl. Britt.)As is evident from the title-page, the work was based on Genocchi's lectures on calculus"" however, the book turned out to be much more than, and in fact something completely different from, that. Peano stands as the editor of the work, but in fact most of the book is written by Peano himself. Apparently, Genocchi had given his approval to the publication of an edited version of his lectures, but when he saw the final result, he regretted the fact that it had appeared under his name. Genocchi stated in a letter that ""... the volume contains important additions, some modifications, and various annotations, which are placed first. So that nothing will be attributed to me which is not mine, I must declare that I have had no part in the compilation of the aforementioned book and that everything is due to that outstanding young man Dr Giuseppe Peano ..."".Peano assumed full responsibility for the work and also recognised it as his own. He later saw the importance that this book has had on the development of the science of infinitesimal calculus. ""In 1915 he (Peano) printed a list of his writings, adding: ""My works refer especially to infinitesimal calculus, and they have not been entirely useless, seeing that, in the judgment of competent persons, they contributed to the constitution of this science as we have it today."" This ""judgment of competent persons"" refers in part to the ""Encyclopädie der mathematischen Wissenschaften"", in which Alfred Pringsheim lists two of Peano's books among nineteen important calculus texts since the time of Euler and Cauchy. The first of these books was Peano's first major publication and is something of an oddity in the history of mathematics, since the title page gives the author as Angelo Genocchi, not Peano: ""Angelo Genocchi, Calcolo differenziale e principia de calcolo integrale, publicato con aggiunte dal Dr. Guiseppe Peano."" The origin of the book is that Bocca Brothers wished to publish a calculus text based on Genocchi's lectures. Genocchi did not wish to write such a text but gave Peano permission to do so. After its publication Genocchi, thinking Peano lacked regard for him, publicly disclaimed all credit for the book, for which Peano then assumed full responsibility."" (D.S.B. X:441).Later the same year, after the publication of this his first major work, Peano became professor at the university of Turin. His first work now stands, not only as one of the founding texts of modern infinitesimal calculus, but also as a prime example of Peano's excellent style, which perfectly mixes simplicity and rigour. ""Beginning with a strict definition of real number, essentially that of Dedekind, he develops the calculus systematically, formulating every theorem with the greatest possible accuracy and precision, and strictly avoiding in the proofs any illegitimate appeal to intuitive properties of curves. When the customary enunciations of theorems are too loose, or conditions that need to be satisfied are not as a rule clearly stated, Peano often constructs counter-examples to show that assertions made in standard textbooks are incomplete or erroneous...."" (Kneebone, Mathematical Logic and Foundations of Mathematics, p. 142). Cellerino nr. 1. ""Prima edizione del primo libro di Peano che venne tradotto nel 1899 in tedesco e nel 1903 in russo. Pubblicato sotto il nome di Genocchi di cui Peano era assistente, il volume è in realtà interamente opera sua tanto che Genocchi lo disconobbe publicamente dando origine ad una breve polemice. Questa è l'opera che diede a Peano notorietà internazionale."" (Cellerino, Guiseppe Piano e la sua scuola. Catalogo monografico. Milano, 2004).
Differentialrechnung und Grundzüge der Integralrechnung. Herausgegeben von Giuseppe Peano. Autorisierte Deutsche Übersetzung von G. Bohlmann und A. Schepp. Mit einem Vorwort von A. Mayer.
Leipzig, B.G. Teubner, 1899. Wrappers blank. Old owners name on titlepage. VII,308 pp.
First German edition of Peano's first major publication, his first book, the work that brought him international fame, and one of the most important calculus texts since the time of Euler and Cauchy.The present book, which has a somewhat strange history, is considered a constitutional work of the science of infinitesimal calculus.
