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Swiss mathematician and physicist (1707–1783) who founded the studies of graph theory and topology and made pioneering and influential discoveries in many other branches of mathematics; he introduced much of modern mathematical terminology and notation. Autograph manuscript signed in Latin as the author, "Auct. Leonhardo Euler," four pages on two adjoining sheets, 7.5 x 9.25, no date but likely circa 1730s. Untranslated handwritten manuscript entitled "De Resolutione Aquationis Differentialis axndx = dy+y2dx [On the Resolution of the Differential Equation axndx = dy+y2dx]." Euler pens the mathematical manuscript in his typically neat Latin, carefully written for interpretation by a typesetter. In very good to fine condition, with overall light creasing and minor fold splits, soiling to the first page, and wear to the edges which does not affect any of the handwriting.
Euler was a prolific author of research papers and mathematical monographs. When Swedish mathematician Gustaf Eneström completed a comprehensive survey of Euler's works in the early 20th century, he counted and enumerated 866 distinct works; most historical scholars today refer to the works of Euler by their number in the Eneström index. While this paper does not appear to have been indexed by Eneström, a longer one upon the same subject—"Constructio aequationis differentialis axndx = dy+y2dx [Solution to differential equations of the form axndx = dy+y2dx]," written in 1733 and published in 1738—was recorded as Enestrom Number 31. In 1755, Euler would publish Institutiones Calculi Differentialis (Foundations of Differential Calculus), laying the groundwork for differential calculus.
Leonhard Euler's legacy endures as one of the most prolific and influential mathematicians in history, with contributions spanning calculus, number theory, and graph theory. His development of Euler’s formula and the concept of functions shaped modern mathematics and physics, bridging complex numbers with exponential functions and laying the foundation for modern analysis. Euler's vast contributions continue to influence fields from engineering to economics to music theory, underscoring his profound impact on both theoretical and applied mathematics.
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