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FIRST EDITION of the first announcement of differential calculus. "The controversy with Newton on priority of invention of the calculus does not detract from the superiority of Leibniz' method of notation, one retained in modern use. He applied his new method to the solution of the cubic parabola and the inverse methods of tangents and many problems left unsolved by Descartes. Fifteen years after Newton's first work in fluxions and nine after his own independent discovery, Leibniz published [Nova Methodus], his first announcement of the differential calculus" (Dibner 109). "Leibniz was an almost universal genius whose place in the history of mathematics depends on his being an independent inventor of the infinitesimal calculus and on his contributions to combinatorial analysis which foreshadowed the development of modern mathematical analysis... The Acta Eruditorum was established in imitation of the French Journal des Scavans in Berlin in 1682 and Leibniz was a frequent contributor. Another German mathematician (E.W. Tschirnhausen) having published in it his paper on quadratures, based on researches that Liebniz had communicated to him, Leibniz at last decided in 1684 to present to the world the more abstruse parts of his own work on the calculus. His epoch-making papers give rules of calculation without proof for rates of variation of functions and for drawing tangents to curves... "The infinitesimal calculus originated in the 17th century with the researches of Kepler, Cavalieri, Torrecelli, Fermat and Barrow, but the two independant inventors of the subject, as we understand it today, were Newton and Leibniz... Although both Newton and Leibniz developed similar ideas, Leibniz devised a superior symbolism and his notation is now an essential feature in all presentation of the sibject.... With the calculus a new era began in mathematics, and the development of mathematical physics since the 17th century would not have been possible without the aid of this powerful technique" (PMM 160).IN: Acta Eruditorum, 1684-1685, pp. 467-73. The full volume offered, with volume title, index, and addenda. Thick quarto, contemporary half-calf with elaborately gilt-decorated spine; edges dyed red. Corners on binding bumped and worn. Text generally very clean with only ocassional light browning.

FIRST PUBLISHED EDITION of one of the rarest and most important papers of modern science: Oersted's discovery of the connection between electricity and magnetism. Preceded only by the legendarily rare privately-printed pamphlet (of which only a few copies are known to exist, only one in private hands), the first journal printing is exceedingly scarce.  Text in the original Latin."The 'Experimenta...' opened a new epoch in the history of physics. From it followed the creation of electrodynamics by Ampere and Faraday's 'Experimental Researches in Electricity" (DSB)."It was after lecturing to students in his own rooms in the Noerragade, Copenhagen, in 1819 or 1820 that [Oersted] invited a few of them to stay on to witness an experiment- the possible deflection of a compass -needle by an adjacent electric current. The experiment was successful; but only just; and Oersted repeated it many times before venturing on 21 July to proclaim the identity of magnetism and electricity in this four-page paper entitled 'Experiments relative to"The 'Experimenta...' opened a new epoch in the history of physics. From it followed the creation of electrodynamics by Ampere and Faraday's 'Experimental Researches in Electricity" (DSB). the Effect of the Contiguity of Electricity to a Magnetic Needle'."The results were as important as they were widespread. Oersted's paper was within the year reprinted in England, France, Germany, Italy and Denmark. In 1823 Ronalds and in 1833 Gauss and Weber constructed the first practical electric telegraphs. Faraday's momentous experiments with the sequels by Clerk Maxwell, Hertz and others bore further witness to its significance" (Printing and the Mind of Man, 282).Printed in the July, 1820 issue of Schweigger's Journal für Chemie und Physik. Less than a year later, "in 1821, volume 31 of the prestigious Journal für Chemie und Physik opened with an editorial announcing a change in format 'in part because a new epoch in chemistry and physics appears to have begun with Ørsted's important discoveries on the connection between magnetism and electricity.' A contributor wrote: 'Orsted's experiments regarding magnetism are the most interesting ones performed in more than a thousand years'" (Physics in Denmark, nobelprize.org).WITH: Neuere electro-magnetische Versuche, Oersted's succeeding paper on the interactions between an electric current and a magnetic field. In: Journal für Chemie und Physik. Hrsg. v. Schweigger u. Meinecke, Vol. 29, pp. 275-281 (Oersted in July issue);  Neuere electro-magnetische Versuche, pp. 364-369. Nuremberg: Schrag, 1820. The whole volume offered. Octavo, contemporary three-quarter green morocco, marbled boards. Some wear to edges of binding, text clean.  Provenance: with library and de-accession stamps on series title from the prestigious Gmelin Institute (after 1996, part of the Max Planck Institute). SCARCE.

FIRST EDITION. The Cologne Chronicle is famous for a lengthy passage, on leaf 311 (verso), that provides the first printed account of the development of printing. "There are few ancient books which have been so frequently quoted, yet so rarely seen, as the present Chronicle. The possession of it is, indeed, essential to a Library like the one under description; since there is an important passage in it, relating to the invention of the Art of Printing with Metal Types, which merits very particular attention; and which has been referred to, or quoted, by bibliographers for nearly the two last centuries...  The rarity of this Chronicle is sufficiently attested by bibliographers, even without noticing that Hartz and Buder... who wrote expressly upon German affairs, had no knowledge whatever of it; and Naudaus doubted its existence. I am disposed to think there are not three copies of it in this country..."–Dibdin Folio. Contemporary tooled half-leather over oak boards. 354 (of 368) leaves. This copy lacking first 12 leaves, containing the first title and the register (index). Second title toned and laid down. Some toning and staining. Woodcut illustrations throughout. A sound copy. VERY RARE.

FIRST EDITIONS. "To this task Gibbon brought a width of vision and a critical mastery of the available sources which have not been equalled to this day; and the result was clothed in an inimitable prose" (PMM, 222). Six volumes. Quarto. Contemporary tan calf rebacked with old red and green lettering-pieces laid down, gilt in compartments. Engraved portrait frontispiece in Vol. I, 2 folding maps in Vol. II, 1 folding map in Vol. III, without half-titles in Vols. II and III, others present. Frontispiece slightly foxed as usual, some offsetting, a few gatherings slightly foxed, a very good set. With portrait frontispiece of Gibbon (in vol. I), 1 folding map of Europe adjacent to Constantinople (in vol. II) 1 folding map of the Eastern Roman Empire and 1 folding map of the Western Roman Empire (in vol. III). The portrait of Gibbon "engraved by Joseph Hall from an original picture painted by Sir Joshua Reynolds" published by Strahan and Cadell in 1780 and issued with the second volume, has been moved by the binder to the appropriate place, at the beginning of vol. I. That volume is in the second of two variant states, without the cancels X4 and a4.

FIRST EDITION of the defining work of the Beat generation. ADVANCE COPY, with extremely rare additional printed white dust jacket announcing the publication over regular dust jacket: "This is a copy of the first edition of ON THE ROAD by Jack Kerouac. It will be published in September 1957 by The Viking Press and is certain to cause violently conflicting reactions among readers and critics. We believe that readers will find truth in the book; to some this truth may be beautiful, to others it may be ugly, but no one can fail to be impressed by what this books says and the way it says it." Octavo, original cloth, original dust jacket together with review copy white dust jacket; custom cloth box. Book fine, extremely vibrant original dust jacket with light edgewear including closed tear at top right corner of front panel. Exceedingly rare advance jacket with toning to spine, some soiling, and matching closed tear at top right corner.

FIRST EDITION of Bacon’s argument for and development of the scientific method. PMM 119.Bacon “insisted on experiment in determining truth in nature and the above book is a proposed method for the assessment of all knowledge. The accumulation of observation and fact must be the basis of a new philosophy and not the authority of Aristotle or anyone else... Bacon’s inspiration led directly to the formation of the Royal Society. The famous engraved title-page showing a ship boldly sailing beyond the Pillars of Hercules (the limits of the old world) is interpreted to represent the bold spirit of adventure and research of the new age of science” (Dibner 80). “Bacon conceived a massive plan for the reorganization of scientific method an gave purposeful thought to the relation of science to public and social life. His pronouncement ‘I have taken all knowledge to be my province’ it he motto of his work... The frontispiece to his magnum opus shows a ship in full sail passing through the Pillars of Hercules from the old to the new world. It symbolizes the vision of its author whose ambitious proposal was: ‘a total reconstruction of sciences, arts and all human knowledge... to extend the power and dominion of the human race... over the universe’” (PMM 119). Second issue (as usual) with “Billium” only (omitting Bill Norton) in colophon and added errata. With engraved title by Simon van de Passe. Folio, contemporary full calf rebacked with original spine laid-down; custom box. Some soiling to binding and repairs to corners. Title page with early signature and notation in top margin, a few scattered rust spots, tiny tear to corner of B2. Overall, text extremely clean and crisp with wide margins.

SCARCE FIRST EDITION of one of the most significant works in the prehistory of calculus. With the rare errata leaf present in two variant states."The task of writing a complete treatise on volumetric determination seems to have been suggested to Kepler by the prosaic problem of determining the best proportions for a wine cask. The result was the Nova stereometria, which appeared in 1615. This contains three parts, of which the first is on Archimedean stereometry, together with a supplement containing some ninety-two solids not treated by Archimedes. The second part is on the measurement of Austrian wine barrels, and the third on applications of the whole" (Boyer, The History of the Calculus).Kepler's basic method was to regard the circle as a polygon with an infinite number of sides and its area as being composed of an infinite number of infinitesimal triangles with vertex at the centre of the circle and base one of the sides of the polygon. Similarly, the volume of a sphere was made up of an infinite number of pyramids, the cone and cylinder of infinitely thin circular discs or of infinitesimal wedge-shaped segments radiating from the axis. "Kepler then extended his work to solids not considered by the ancients. The areas of the segments cut from a circle by a chord he rotated about this chord, obtaining solids which he designated characteristically as apple or citron-shaped, according as the generating segment was greater or less than a semi-circle... Kepler's Doliometha... exerted such a strong influence in the infinitesimal considerations which followed its appearance, and which culminated a half century later in the work of Newton, that it has been called [by Moritz Cantor] the source of inspiration for all later cubatures" (Boyer).Kepler's book on integration methods also contains the germ of the differential calculus. "The subject of the measurement of wine casks had led Kepler to the problem of determining the best proportions for these. This brought him to the consideration of a number of problems on maxima and minima ... he showed, among other things, that of all right parallelepipeds inscribed in a sphere and having square bases, the cube is the largest, and that of all right circular cylinders having the same diagonal, that one is greatest which has the diameter and altitude in the ratio of [square root of 2]:1. These results were obtained by making up tables in which were listed the volumes for given sets of values of the dimension ... He remarked that as the maximum volume was approached, the change in volume for a given change in the dimensions became smaller" (Boyer). Kepler had noted, in modern terms, that when a maximum occurs the rate of change becomes zero, a basic principle of the differential calculus that is usually credited to Fermat later in the century.Nova Stereometria doliorum vinariorum, in primis Austriaci, figurae omnium aptissimae; et usus in eo virgae cubicae compendiosossimus & plane singularis. Accessit Stereometriae Archimedae Supplememtum. Folio, contemporary calf sympathetically rebacked. With two errata leaves, woodcut on H3v shaved at foot as usual, ocassional foxing, small closed tears to final leaf; a very good crisp copy. RARE.