‎Mathematics‎

‎MANNA, ZOHAR.‎

‎Mathematical Theory of Computation.‎

‎Tokyo, McGraw-Hill Kogakusha, (1974). 8vo. Orig. printed wrappers. X,448 pp.‎

‎First edition. Published in 'McGraw-Hill Computer Science Series'.‎

Bookseller reference : 32767

‎GRZEGORCZYK, ANDRZEJ.‎

‎Fonctions récursives.‎

‎Paris, Gauthier-Villars, 1961. 8vo. Orig. printed wrappers, uncut. 100 pp.‎

‎First edition. Published in the series 'Collection de Logique Mathématique', Serie A.‎

Bookseller reference : 32777

‎KOBRINSKII, N. E. & B. A. TRAKHTENBROT.‎

‎Introduction to the Theory of Finite Automata. Translated from the Russian. Translation edited by J. C. Shepherdson.‎

‎Amsterdam, North-Holland Publ. Comp., 1965. 8vo. Orig. full cloth in orig. dust jacket. X,337 pp.‎

‎First English edition. Published in the series 'Studies in Logic and the Foundations of Mathematics', edited by L. E. J. Brouwer, A. Heyting, A. Robinson and P. Suppes.‎

Bookseller reference : 32841

‎"EUCLID (EUKLID) OF ALEXANDRIA.‎

‎Euclidis Megarensis mathematici clarissimi Elementorum geometricorum libri XV. Cum expositione Theonis in priores XIII à Bartholomæo Zamberto Veneto (= Zamberti) latinitate donata, Campani in omnes, & Hypsiclis Alexandrini in duos postremos. His addie...‎

‎Basel, Johannem Hervagium & Bernhardum Brand, 1558. Folio. (30,5x21,5). Bound in 19th century brown hmorocco with 5 raised bands. Light wear to back and corners a bit bumped. (2),587 pp.Numerous wood-cut diagrams and initials throughout. First ab. 20 leaves with different degrees of yellowing and occasional with marginal faint dampstaining. 3 leaves with upper right corners repaired without loss of text. The ""privilege"" at verso of title partly unreadable as a piece of paper is pasted on, some of these letters are faint, just as some letters in ""Basiliae"" on title are weak. Last leaf with colophon and printers large woodcut-device on verso is mounted, but not hiding the wood-cut. The word ""Basiliae"" on last leaf recto, is weak or nearly gone. Overall a large good copy as usually without the foreword by Melanchton. A small rubber-stamp on title: ""Duplum Bibliothecæ V.E."" and in old hand: ""Bibliothecæ Conventij Romani S. Andrea de Fratrij (?)""‎

‎Scarce third printing of the so-called Zambert-Campanus Edition of the Elements, all printed by Johann Herwagen in Basel - this edition printed together with his son-in-law Bernhard Brand. The first of the Herwagen prints was the famous Editio Princeps in Greek from 1533, and in 1537 he published a Latin version, which became the first Euclid-editon to contain also Euclids smaller tracts as ""Phenomena""(Spherical geometry), ""Katroptik"" (Mirror-reflexion), ""Optik"" und ""Data""(Geometrical excersises). The 1537- edition was reprinted 1546 and in 1558 (the present).""The most famous source of Greek geometry is the monumental work of Euclid of Alexandria, called the ""Elements"" (around 300 B.C.). No other book of science had a comparable influence on the intellectual development of mankind. It was a treatise of geometry in thirteen books which included all the fundamental results of scientific geometry up to his time. Euclid did not claim for himself any particular discovery, he was merely a compiler. Yet, in view of the systematic arrangement of the subject matter and the exact logical procedure followed, we cannot doubt that he himself provided a large body of specific formulations and specific auxiliary theorems in his deductions. It is no longer possible to pass judgement on the authorship of much of this material"" his book was meant as a textbook of geometry which paid attention to the material, while questions of priority did not enter the discussion."" (Cornelius Lanzos in ""Space through the Ages"").Max Steck III:57 - Thomas-Stanford: 15 - Riccardi 1558/3 - Adams E:976.‎

Bookseller reference : 32859

‎TARSKI, ALFRED.‎

‎Logic, Semantics, Metamathematics. Papers from 1923 to 1938. Translated by J.H. Woodger.‎

‎Oxford, Clarendon Press, 1956. 8vo. Original publisher's cloth with dust jacket fine condition. Owner's signature (Samuel Skulsky) on front free endpaper. A very fine copy. XIV,471,(1) pp.‎

‎First English edition of 17 papers by Tarski including 'The Concept of Truth in Formalized Languages'. The papers have been revised by Tarki himself, bibliographical and historical notes have been added.‎

Bookseller reference : 33473

‎CHURCH, ALONZO.‎

‎Introduction to Mathematical Logic. Part 1 (All published). (Annals of Mathematics Studies Number 13).‎

‎Princeton, Princeton University Press, 1944. 8vo. Original stiff wrappers. IV,118,(2) pp. A fine copy.‎

‎First edition. The forerunner to Church's classic text book 'Introduction to Mathematical Logic, 1956'.‎

Bookseller reference : 33478

‎PEANO, GIUSEPPE.‎

‎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.‎

Bookseller reference : 33644

‎ONICESCO, OCTAVE. & GEORGES MIHOC.‎

‎La dépendance Statistique: Chaines et Familles de Chaines discontinues. (Exposés d´analyse générale, vol. 7, Maurice Fréchet).‎

‎Paris, Hermann & Cie, 1937. 8vo. One issue of 'Actualités Scientifiques et Industrielles', no. 503. Original printed wrappers. Fine condition. 46,(2) pp.‎

‎First edition.‎

Bookseller reference : 33792

‎BÔCHER, M.‎

‎Einführung in die höhere Algebra.‎

‎Leipzig & Berlin, B.G. Teubner, 1910. 8vo. Publishers full cloth. XII,348,(4) pp. A fine copy.‎

‎First German edition.‎

Bookseller reference : 33801

‎BORENIUS, GUSTAF.‎

‎Hit Probability in Salvos and Series.‎

‎Stockholm, Almqvist & Wiksell, 1963. 8vo. Original printed wrappers. 164 pp.‎

Bookseller reference : 33804

‎"EUCLID (EUKLID) OF ALEXANDRIA. - TARTAGLIA'S TRANSLATION.‎

‎Euclide Megarense Philosopho, solo Introduttore delle Scientie Mathematice. Diligentementee Rassettato, et alla integrità ridotto, per il degno professore di tal Scientie Nicolo Tartalea Brisciano (Nicolo Tartaglia). Secondo le due Tradottioni. Con un...‎

‎Venetia, Curtio Trojano, 1565. 4to. Bound in a very nice recent hcalf in old style. Raised bands and richly gilt back. 315,(1) leaves (=632 pp). Profusely illustrated with gemetrical diagramss in the text. Printers woodcut-device at end. Small part of lower right corner of title gone, no loss of text. Light browning to first and last leaf. 6 last leaves with a faint dampstain. Very light browning to outher margins. Otherwise a fine clean copy.‎

‎Scarce second edition of Tartaglia's very influential translation of all Euclid's 15 Books, as this Italian translation of Euclid was the first translation at all into the vernacular. The translation by Tartaglia was first published 1543 and was founded on the latin edition of Campanus and Zambetti.Niccolo Fontana of Brescia has a great name in the history of mathematics. A cut in the face from a French soldier caused him to stammer and as a consequence of this he was called 'Tartaglia'. He is famous for his solution of third-degree equations which occasioned a long polemic with Cardano about priority. He is also known for ""Tartaglia's Triangle"", later known as ""Pascal's Triangle"", and he is well-known for his Archimedes-edition of 1543 and 1551 with his commentaries.""The most famous source of Greek geometry is the monumental work of Euclid of Alexandria, called the ""Elements"" (around 300 B.C.). No other book of science had a comparable influence on the intellectual development of mankind. It was a treatise of geometry in thirteen books which included all the fundamental results of scientific geometry up to his time. Euclid did not claim for himself any particular discovery, he was merely a compiler. Yet, in view of the systematic arrangement of the subject matter and the exact logical procedure followed, we cannot doubt that he himself provided a large body of specific formulations and specific auxiliary theorems in his deductions. It is no longer possible to pass judgement on the authorship of much of this material"" his book was meant as a textbook of geometry which paid attention to the material, while questions of priority did not enter the discussion."" (Cornelius Lanzos in ""Space through the Ages"").Max Steck III:72 - Thomas-Stanford: 39 - Riccardi Euclideana V:1 - Adams E:993. - Brunet II:1090.‎

Bookseller reference : 34674

‎"EULER, LEONHARD.‎

‎Recherches sur les plus Grand et plus Petits qui se trouvent dans les Actions des Forces.‎

‎(Berlin, Haude et Spener, 1750). 4to. No wrappers, as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome IV, pp. 149-188 and 2 folded engraved plates..‎

‎First edition. Euler shows that any discrete system obeys the Maupertois principle" from this result, he derives the general equation for the balance of moments in a plane elastica, which includes the general catenary as a special case. He also proves that Daniel Bernoulli's principle for the elastica that is free of distributed loads is also a special case of this general equation. - Enestrom No. 145.‎

Bookseller reference : 34682

‎"ARCHIMEDES OF SYRACUSE.‎

‎Des Unvergleichlichen Archimedis Kunst=Bücher Oder Heutigs Tags befindliche Schrifften, Aus dem Griechischen in das Hoch-Deutsche übersetzt, und mit nothwendigen Anmerkungen durch und durch erläutert von Johanne Christophoro Sturmio. (und) Des Unvergl... - [FIRST GERMAN ARCHIMEDES]‎

‎Nürnberg, Paulus Fürsten, 1670 (Sand=Rechnung: 1667). Folio. Cont. full calf, rebacked in old style with 5 raised bands. Corners neatly repaired. Extremities slightly rubbed. Engraved frontispiece with globes, world-systems and archimedean figures. Title in red a. black. (18),427,(1) pp. and (8),32 pp. Numerous diagrams in the text. Occasional light browning, a few brownspots. Some leaves in the ""Sand-Rechnung"" with a dampstain. In general fine, printed on good paper.‎

‎First German edition of Archimedes' main mathematical works. The translation was made on the basis of David Rivault's latin-greek edition of 1615 and it has commentaries by the editor J.C. Sturm. It comprises, in first German translation, these main works of Archimedes: 1. Sphere & Cylinder (2 Books) - 2. Measurement of the Circle. - 3. Equilibrium of planes. - 4. Quadrature of the parabola. 5. Conoids & spheroids. 6. Spirals. - 7. Sand reckoner (Psammites, Arenarius) here with its own titlepage dated 1667.The famous Sand reckoner introduced an extremely large number in arithmetics, ""How many grains of sand could the whole universe hold"" ?, and this work also contained the first printed statement of the heliostatic world-picture, a theory first put forward by ARISTARCHUS in a lost work and here referred by Archimedes: ""Dann er fetzet (Aristarchus) die Fix-oder Haft-Sterne, samt der Sonne als unbeweglich in einem Kreiss umb die Sonne, welche das Mittel solches Kreises besitze. Der Fix-oder Haft-Sternen aber ihren umb der Sonnen Mittelpunct ausgespannten, Himmel beschreibet er in solcher Grösse, dass der Erden Lauffkreiss, auf welchem sie umb die Sonne bewegt werden solle, gegen derer Haft-Sternen fernen Entlegenheit, sich nicht anderst verhalte, als einer Kugel Mittel-punct gegen deroselben Umbkreiss."" (pp. 2 -3 in Sand=Rechnung"").Archimedes was called ""the God of Mathematics"" by Plinius, and he is without doubt the greatest mathematician, physicist and engineer of ancient times and one of the greatest geniuses of all times. ""There is no one individual whose work epitomizes the character of the Alexandrian age so well as Archimedes (287-212 B.C.), the greatest mathematician in antiquity."" (Morris Kline). ""He gave birth to the calculus of the infinite conceived and brought to perfection successively by Kepler, Cavalieri, Fermat, Leibnitz and Newton."" (Chasles) - Poggendorff II:1043. -‎

Bookseller reference : 34702

‎ZORETTI, LUDOVIC.‎

‎Lecons sur le Prolongement Analytique.‎

‎Paris, Gauthier-Villars, 1911. Royal8vo. Uncut in orig. printed wrappers. Backstrip a little torn at top and bottom. VI,114,(4) pp.‎

‎First edition.‎

Bookseller reference : 34706

‎"VON NEUMANN, JOHN.‎

‎Die Einführung analytischer Parameter in topologischen Gruppen.‎

‎Princeton & Hamburg, 1933. Offprint from 'Annals of Mathematics' volume 34, pp. 170-190. Royal8vo. Original printed wrappers. Small tear to back wrapper. Corners a little bumped and frayed. Internally fine and clean. In all a good copy.‎

‎First edition offprint issue. ""One of the highlights of Von Neumann's career... solving Hilbert's fifth problem for compact groups."" (DSB).‎

Bookseller reference : 34733

‎"CARNAP, RUDOLF.‎

‎Der Raum. Ein Beitrag zur Wissenschaftslehre. - [SPACE - CARNAP'S FIRST PUBLICATION]‎

‎Berlin, Reuther & Reichard, 1922. 8vo. Original grey printed wrappers w. very minor loss to capitals. Printing on spine nearly fully intact. Internally near mint. A very good, nice and clean copy of a publication, which in itself is quite fragile. 87 pp.‎

‎First edition of Carnap's first publication, his doctoral dissertation. Printed in Kant-Studien, Ergänzungshefte, Nr. 56. Issued by H. Vaihinger, M. Frischeisen-Kähler and A Liebert. Rudolf Carnap (born 1891 in Ronsdorf, Germany, died 1970 in Santa Monica, California) was an immensely influential analytic philosopher, who has contributed decisively to the fields of logic, epistemology, semantics, philosophy of science, and philosophy of language. He was one of the leading figures of the Vienna Circle, and a prominent logical positivist. He studied philosophy, physics and mathematics at the universities of Berlin and Freiburg, and worked at the universities of Jena, Vienna and Prague until 1935, when he, due to the war, emigrated to the U.S., where he became an American citizen in 1941. In America he became professor of the University of Chicago. In Jena he was appointed Professor of Mathematics, though his main interest at that time was in physics. By 1913 he planned to write his dissertation on thermionic emission, but this was interrupted by World War I, where he served at the front until 1917. Afterwards he studied the theory of relativity under Einstein in Berlin, and he developed the theory for a new dissertation, namely on an axiomatic system for the physical theory of space and time. He thus ended up writing the important dissertation under the direction of Bouch on the theory of space (Raum) from a philosophical point of view. The dissertation was submitted in 1921, and, due to the clear influence from Kantian philosophy, it was published the following year in this supplement to the ""Kant-Studien"". After the publication of his first work, Carnap's involvement with the Vienna Circle began to develop. He met Reichenbach in 1923 and was introduced to Moritz Schlick in Vienna, where he then moved to become assistant professor at the university. He soon became one of the leading members of the Vienna Circle, and in 1929 he, Neurath, and Hahn wrote the manifest of the Circle.As the title indicates, ""Der Raum"" deals with the philosophy of space. Partly influenced by Husserl, under whom he studied at Freiburg, Carnap poses the question weather our knowledge of space is analytic, synthetic a priori or empirical. His answer is that it depends on what is meant by ""space"", and thus differentiates between three kinds of theories of space: Formal (which is analytic [a priori]), intuitive (which is synthetic a priori), and physical (which is empirical [or synthetic aposteriori]). He compares this division of space with that of geometry into: projective, metric and topological. This, of course, anticipates much of his later philosophy, and some of his theories developed in this paper became the official position of logical empiricism on the philosophy of space. In this work he also develops a formal system for space-time topology, which became quite influential.‎

Bookseller reference : 34800

‎BOLYAI, JÁNOS.‎

‎Appendix. Scientiam Spatii Absolute Veram exhibens: a veritate aut falsitate Axiomatis XI Euclidei (a priori haud unquam decidenda) independentem: adjecta ad casum falsitatis, quadratura circuli geometrica. - [THE ABSOLUTELY TRUE SCIENCE OF SPACE]‎

‎Budapest, Hungarian Academy of Sciences, 1904. This is a reprint of the second volume the second edition of Farkas Bolyai's 'Tentamen', which conatined János Bolyai's discovery of non-Euclidean geoemtry as an appendix (pp.359-394 and 7 plates).‎

‎Unabridged reprint of János Boyai's famous appendix to his fathers treatise in which he first announced his discovery of non-Euclidean geometry.‎

Bookseller reference : 34850

‎"LAGRANGE, JOSEPH LOUIS.‎

‎Nouvelle Methode pour Résoudre les Équations littérales par les moyen des Séries.‎

‎(Berlin, Haude et Spener, 1770). 4to. No wrappers as issued in ""Mémoires de l'Academie Royale des Sciences et Belles-Lettres"", tome XXIV, pp. 251-326. Clean and fine.‎

‎First edition of an importent paper in algebraic analysis. The method used by Lagrange was probably suggested to him by Lambert, and both Euler, Lexell, d'Alembert and Condorcet all became highly intereste in this discovery as soon as they heard about it. ""Laplace later presented a better proof. Lagrange's formula occupied numerous other mathematicians, including Arbogast, Parceval, Servois, Hindenburg and Bürgman...."" and virtually every analyst of the nineteenth century considered the problem."" (Jean Itard in DSB). - Poggendorff I:1344.‎

Bookseller reference : 34947

‎"HILBERT, DAVID.‎

‎The Foundations of Geometry. Authorized translation by E.J. Townsend.‎

‎Chicago, Open Court, 1902. Small 8vo. Orig. full red cloth, gilt. A rather faint dampstain along first hinge on frontcover, otherwise fine. VII,143 pp.‎

‎First English edition of Hilbert's ""Grundlagen der Geometrie"" from 1899, one of the most influential publications in 2oth Century mathematics.Throughout the 19th century geometry was developed far beyond our intuitive conception of space" hyperbolic geometry was discovered by Gauss, Bolyai, and Lobachevsky and elliptic geometry by Riemann. However, Euclidean and non-Euclidean geometry still involved an intuitive idea about the concepts 'point', 'line', 'lies on', 'between', etc. In his 'Grundlagen' Hilbert set out to give a strictly formal formulation of geometry were points, lines, planes are nothing more than abstract symbols and concepts as 'lies on' are simply algebraic relations between these symbols. Through his method Hilbert could analyse independence and completeness of the axioms for geometry and he presented a new smaller set of axioms for Euclidean geometry. It can not be said that the 'Grundlagen' contains new and surprising discoveries, its importance lies in the great influence which Hilbert's method had on all fields of mathematics, and even other sciences as physics, chemistry, and biology. The 'Grundlagen' initiated a whole new paradigm shift and eventually evolved mathematics, throughout the 20th century, into a network of axiomatic formal systems.‎

Bookseller reference : 35061

‎"LAGRANGE, JOSEPH LOUIS.‎

‎Nouvelle Méthode pour Résoudre les Problemes indéterminés en Nombre entiers.‎

‎(Berlin, Haude & Spener, 1770). 4to. No wrappers, as issued in ""Memoires de l'Academie Royale des Sciences et Belles-Lettres"", tome XXIV, pp. 181-250. Clean and fine.‎

‎First edition. An importent paper in the Theory of Numbers. The year before Lagrange gave a complete solution to the problem of giving all integral solutions of a special general equation (Sur la Solution des Problemes Indéterminés du Second Degré). In this paper he sets up a simpler proof of the same problem. - Cajori calls Lagrange ""One of the greatest mathematicians of all times"". - Poggendorff I:1344.‎

Bookseller reference : 35218

‎ZUBLER, LEONHARD.‎

‎Novum Instrumentum Geometricum: Das ist, Kurtzer und grundtlicher Bericht alle Weite, Breite, Höhe und Tieffe, mit sonderbarem Vortheil, kunstlichen und gewiss, auch von der Arithmetic unerfahrnen abzumessen: Mit XXII. schönen, kunstreichen und verstä... - [INSTRUMENT FOR SURVEYING AND GUNNERY]‎

‎Basel, Ludwig Königs, 1607. 4to. Sewn as issued in later blank wrappers. Engraved ornamental title showing 2 geometers with instruments, on verso large engraved coat of arms (Henry Prince of Wales). (8),65,(2) pp. With 20 large engravings in the text. Printed on good paper, fine and clean.‎

‎First edition, though a Latin translation appeared at the same time. Zubler was a prolific mathematician and instrument-maker in Zürich, and in this work he describes a triangulation instrument (depicted on a full-page engraving), invented by himself, and shows its use in different situations of practical surveying and military use in artistic settings. The triangulation instrument was able to provide measures for length, width, height and angles all at once, to be read on the scales on the baseline etc. The instrument has two arms and a baseline. By fixing the angle between the baseline and the pivoted arm, setting the sliding sight on the baseline arm to the scaled length of the baseline itself, and finally, from the second station, sighting across the two arms while moving the second sliding sight into alignment with the first sight and the target, the side of the triangle on the ground will be given with the position of the second sight, adjusted to the scale. The provision of a degree scale on a semicircular plate at the pivot permits other techniques involving angle measurements or setting the arms at right angles.Cockle: 947 (Latin ed.) - Poggendorff II:1420.‎

Bookseller reference : 35352

‎GÖDEL, KURT.‎

‎Über eine bisher noch nicht benützte Erweiterung des finiten Standpunktes. (In: Dialectica, volume 12, pp.280-87). - [GÖDEL'S FINAL PAPER]‎

‎Neuchâtel, Dialectica, 1958. 8vo. Original printed wrappers. The entire issue 47/48 offered here. Uncut and unopened.‎

‎First edition of Gödel's 'Dialectica-paper' in which he presented his consistency proof for arithmetic. In 1931 Gödel formulated and proved his second incompleetness theorem" that the consistency of Peano arithmetic cannot be proved using Peano arithmetic itself or any of its direct extensions. The title of Gödel's famous 1931 paper (Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I) states that it is the first part of several papers. Gödel mentions, in a footnote, that the second part of his paper will deal with the source of the incompleteness of formal systems using the theory of types. But no actual continuation of Gödel's 1931 paper ever appeared. However, in his 1958 ""Dialectica-paper"" (the offered item) Gödel showed how type theory can be used to give a consistency proof for arithmetic. In this paper Gödel furthermore discussed some of the philosophical implications of his results. Paul Bernays thought highly of this paper, and planned to publish an English translation, but during the revision of the paper Gödel became dissatisfied with the philosophical introduction and rewrote it completely. When the proof sheets of the revised paper arrived from the printer, Gödel once again became unpleased with the sections concerning his philosophical views. He never returned the proof sheets. The issue offered, which is a festschrift on the occasion of Paul Bernay's 70th birthday, furthermore contains original contributions by Ackermann, Carnap, Curry, Fraenkel, Robinson, Skolem.‎

Bookseller reference : 35481

‎ABEL, NIELS HENRIK.‎

‎Oeuvres Completes. Nouvelle Édition publiée aux frais de L'État Norvégien par L. Sylow et S. Lie. 2 vols.‎

‎Christiania, Grøndahl & Søn, 1881. 4to. Bound in one contemp. hcalf. Richly gilt. Top edge gilt. Spine loose. Block tight and fine. (4),VIII,621(4),338,(3) pp. Printed on good paper, internally clean and fine.‎

Bookseller reference : 35655

‎"MAHALANOBIS, P.C.‎

‎On Large-Scale Sample Surveys. (Offprint from: Philosophical Transactions of the Royal Society of London, Series B, Vol. 231, pp.329-451).‎

‎London, Cambridge University Press, 1944. Large 4to. Original printed wrappers. A fine copy. Owner's signature of statistician Anders Hald (the author of ""A History of Mathematical Statistics""). (123 pp.).‎

‎First edition, offprint issue of this important paper in the history of statistics. ""Mahalanobis's contributions to large scale sample surveys are among his most significant and lasting gifts to statistics. He started his work on sample surveys with estimation of area and yield of jute crop in Bengal in 1937. However, it was not easy for him to get these estimates"" controversy between him and the advocates of complete enumeration continued for over a decade. Ultimately he was able to demonstrate that estimates based on sample surveys were often more accurate than those based on complete enumeration, and that sample surveys could yield estimates with small margins of error within a short time and at a smaller cost than complete enumeration. He made many methodological contributions to survey sampling that included optimal choice of sampling design using variance and cost functions, and the technique of interpenetrating network of sub-samples for assessment and control of errors, especially non-sampling errors, in surveys. The concept of pilot surveys was a forerunner of sequential sampling developed by Abraham Wald, as acknowledged by Wald in his book. In addition to introducing these concepts, Mahalanobis raised important and difficult philosophical questions on randomness and representativeness of a sample, which remain relevant and challenging even today. He was elected Chairman of the United Nations Sub-Commission on Statistical Sampling in 1947, and held this post until 1951. His tireless advocacy of the usefulness of sample surveys resulted in the final recommendation of this Sub-Commission that sampling methods should be extended to all parts of the world. Mahalanobis received the Weldon Medal from Oxford University in 1944 and was elected Fellow of the Royal Society, London, in 1945, for his fundamental contributions to statistics, particularly in the area of large-scale sample surveys."" - Heyde: Statisticians of the Centuries, p.436.‎

Bookseller reference : 35747

‎"ROBINSON, ABRAHAM.‎

‎Non-Standard Analysis. - [THEORY OF INFINITESIMALS]‎

‎Amsterdam, North-Holland, 1966. 8vo. Publishers full cloth with dust jacket. Both in fine condition. Previous owners signature to front free end paper.Otherwise completely clean throughout. A fine copy.‎

‎First edition of this foundational work in mathematics. In this book Robinson gave the first rigorous formulation of Analysis using infinitesimals. Both Leibniz and Newton had used the notion of infinitesimals when they developed the Differentail and Integral Calculus in the 17th century. As Leibniz argued the theory of infinitesimals implies the introduction of ideal numbers which might be infinitely small or large compared to the real numbers. However, neither he nor his disciples and succesors were able to give a rational development leading up to a system of this sort. As a result, the theory of infinitesimals gradually fell into disrepute and was replaced by eventually by the classical theory of limits. Robinson was the first to show that Leibniz's ideas in fact can be fully vindicated and that they lead to a fruitful approach to classical Analysis. He coined his model ""Non-Standard Anlysis"".‎

Bookseller reference : 35775