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Third edition of the first published work on the subject of calculus, in the 1684 volume of the German scientific journal Acta eruditorum, here included as part of a run of the first eight years of the journal in a uniform contemporary binding, and unusual in commerce in such state. The journal was issued in monthly parts. Recent scholarship by Samuel V. Lemley has determined there were three editions of the October monthly part including Leibniz's paper. The first edition was printed in 1684, the second in 1686. This is the third edition, incorporating Leibniz's revisions, printed in 1692 or 1693. The plate accompanying the paper is in the first state. It is apparent that individual parts were reprinted to allow subscribers to fill out incomplete sets, and that these reprintings were authorized, rather than piracies. The paper, just seven pages long, "was the first attempt to set out the rules governing infinitesimal procedures. The rules are introduced geometrically, translated into algebraic terms, and then redescribed in terms of differentials. This enables Leibniz to provide basic rules of addition, subtraction, multiplication, and division. Specifying rules for the manipulation of signs, depending on whether the ordinates increase or decrease, he moves to the behaviour of curves, leading him to introduce second-order differentials, and by these means he offers procedures for finding powers and taking roots... Nevertheless, it should be said that the Third edition of the first published work on the subject of calculus, in the 1684 volume of the German scientific journal Acta eruditorum, here included as part of a run of the first eight years of the journal in a uniform contemporary binding, and unusual in commerce in such state. The journal was issued in monthly parts. Recent scholarship by Samuel V. Lemley has determined there were three editions of the October monthly part including Leibniz's paper. The first edition was printed in 1684, the second in 1686. This is the third edition, incorporating Leibniz's revisions, printed in 1692 or 1693. The plate accompanying the paper is in the first state. It is apparent that individual parts were reprinted to allow subscribers to fill out incomplete sets, and that these reprintings were authorized, rather than piracies. The paper, just seven pages long, "was the first attempt to set out the rules governing infinitesimal procedures. The rules are introduced geometrically, translated into algebraic terms, and then redescribed in terms of differentials. This enables Leibniz to provide basic rules of addition, subtraction, multiplication, and division. Specifying rules for the manipulation of signs, depending on whether the ordinates increase or decrease, he moves to the behaviour of curves, leading him to introduce second-order differentials, and by these means he offers procedures for finding powers and taking roots... Through its adoption and elaboration by these and other contemporaries, calculus was soon firmly established in western mathematics. Leibniz's paper famously preceded Newton's publication of his own discovery of calculus, and the question of whether Leibniz plagiarized Newton's unpublished work caused a lengthy furore in the scientific world; it is now recognized that both men discovered calculus independently. "The infinitesimal calculus originated in the seventeenth century with the researches of Kepler, Cavalieri, Torricelli, Fermat and Barrow, but the two independent inventors of the subject, as we understand it today, were Newton and Leibniz. The subsequent controversy in the early part of the eighteenth century as to the priority of their discoveries - one of the most notorious disputes in the history of science - led to an unfortunate divorce of English from Continental mathematics that lasted until the end of the first quarter of the nineteenth century. Although both Newton and Leibniz developed similar ideas, Leibniz devised a superior symbolism and his notation is now an essential feature in all presentations of the subject" (PMM). The Acta Eruditorum was established in 1682, in imitation of the Journal des Savans, and ran till 1731. Published under the auspices of the Collegium Gellianum, with support from the Duke of Saxony, it covered a wide range of topics, including medicine, mathematics, physics, law, history, geography, and theology. The journal soon became the most well-known German publication of its kind. Contributors included Boyle, Leeuwenhoek, Bernoulli, Pascal, Huygens, Halley, and Descartes, alongside Leibniz. READ MORE Eight volumes, quarto (207 x 152 mm). Contemporary calf, twin red and brown calf labels, gilt in spine compartments, effaced early shelf labels at foot of spines, triple gilt rule to covers, marbled endpapers, red edges. With 117 plates, many folding. Bound without plate 14 in 1684 volume, and a few minor defects in other volumes. Slight peripheral wear, a few joints a little split at ends but all firm, bindings in generally fresh condition, browning to contents as usual, a few folding plates cropped into neatline, slight staining at edges of 1682, 1683, and 1685 volumes. A very good set. Dibner 109; Grolier/Horblit 66a; Norman 1326; PMM 160. Desmond M. Clarke & ‎Catherine Wilson, The Oxford Handbook of Philosophy in Early Modern Europe, 2013.

Gottfried Wilhelm von Leibniz's "Nova Methodus pro Maximis et Minimis," published in the "Acta Eruditorum" in 1684, stands as a cornerstone in the development of infinitesimal calculus. This seminal work, spanning pages 467 to 473 in the journal for that year, represents Leibniz's first published account of his differential calculus, a mathematical achievement that would fundamentally transform the understanding and application of mathematics. The essay presented here aims to explore the context, content, significance, and enduring legacy of Leibniz's contribution to mathematics and the broader scientific community. The late 17th century was a period of intense intellectual ferment and discovery, particularly in the fields of mathematics and physics. The foundations of modern science, laid by figures such as Galileo and Descartes, were rapidly evolving. It was within this milieu of scientific revolution that Leibniz, a polymath and philosopher, sought to address one of the age-old challenges in mathematics: finding precise methods to determine maxima and minima, tangents, and the area under curves. Leibniz's "Nova Methodus pro Maximis et Minimis" introduced the differential calculus, a method for analyzing variable quantities. His work provided a systematic approach to calculating the rates at which quantities change, a concept that is foundational to understanding motion, growth, and a myriad of natural phenomena. Leibniz's notation, particularly the use of the integral sign (∫) and the d for differentials, remains in use to this day, a testament to its elegance and utility. The paper outlined the method of finding maxima and minima of functions, calculating tangents, and determining areas under curves—problems of significant interest not only to mathematicians but also to physicists and engineers. Leibniz's work demonstrated how these problems, seemingly disparate, could be addressed through a unified approach that considered quantities in their infinitely small (infinitesimal) changes. Leibniz's contributions, as presented in the "Nova Methodus," were revolutionary for several reasons. First, they offered a new tool for mathematicians, one that expanded the realm of what was solvable. Second, the differential calculus, together with the integral calculus (which Leibniz also developed), formed the core of what is today known as calculus, a branch of mathematics essential to modern science and engineering. Leibniz's calculus was developed independently of Sir Isaac Newton's work in England, leading to a contentious debate over priority that overshadowed much of Leibniz's later life and the subsequent history of mathematics. Despite this controversy, Leibniz's notation and approach to calculus were widely adopted, particularly on the European continent, facilitating advances in a broad range of scientific fields. The legacy of Leibniz's "Nova Methodus" extends far beyond the realm of mathematics. By providing a tool to model and understand change and motion, calculus has played a critical role in the development of physics, engineering, economics, and other disciplines. Leibniz's vision of a universal science, reflected in his work on calculus, also anticipated later developments in logic, computation, and the philosophy of science. Moreover, Leibniz's contributions to the "Acta Eruditorum" underscore the importance of scientific communication and collaboration. His engagement with the broader intellectual community of his time through publications and correspondence facilitated the dissemination of his ideas, illustrating the vital role of academic discourse in the progress of science. new avenues of inquiry, laying the groundwork for the continued exploration of the natural world.