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Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations.
Gottfried Wilhelm Leibniz was a German polymath active as a mathematician, philosopher, scientist and diplomat who invented calculus in addition to many other branches of mathematics and statistics. Leibniz has been called the "last universal genius" due to his knowledge and skills in different fields and because such people became less common during the Industrial Revolution and spread of specialized labor after his lifetime. He is a prominent figure in both the history of philosophy and the history of mathematics. He wrote works on philosophy, theology, ethics, politics, law, history, philology, games, music, and other studies. Leibniz also made major contributions to physics and technology, and anticipated notions that surfaced much later in probability theory, biology, medicine, geology, psychology, linguistics and computer science. In addition, he contributed to the field of library science by devising a cataloguing system whilst working at the Herzog August Library in Wolfenbüttel, Germany, that would have served as a guide for many of Europe's largest libraries. Leibniz's contributions to a wide range of subjects were scattered in various learned journals, in tens of thousands of letters and in unpublished manuscripts. He wrote in several languages, primarily in Latin, French and German.
In philosophy, rationalism is the epistemological view that "regards reason as the chief source and test of knowledge" or "any view appealing to reason as a source of knowledge or justification", often in contrast to other possible sources of knowledge such as faith, tradition, or sensory experience. More formally, rationalism is defined as a methodology or a theory "in which the criterion of truth is not sensory but intellectual and deductive".
Method of Fluxions is a mathematical treatise by Sir Isaac Newton which served as the earliest written formulation of modern calculus. The book was completed in 1671 and posthumously published in 1736.
Leibniz University Hannover, also known as the University of Hannover, is a public research university located in Hanover, Germany. Founded on 2 May 1831 as Higher Vocational School, the university has undergone six periods of renaming, its most recent in 2006.
Calculus, originally called infinitesimal calculus, is a mathematical discipline focused on limits, continuity, derivatives, integrals, and infinite series. Many elements of calculus appeared in ancient Greece, then in China and the Middle East, and still later again in medieval Europe and in India. Infinitesimal calculus was developed in the late 17th century by Isaac Newton and Gottfried Wilhelm Leibniz independently of each other. An argument over priority led to the Leibniz–Newton calculus controversy which continued until the death of Leibniz in 1716. The development of calculus and its uses within the sciences have continued to the present.
In the philosophy of mind, innatism is the view that the mind is born with already-formed ideas, knowledge, and beliefs. The opposing doctrine, that the mind is a tabula rasa at birth and all knowledge is gained from experience and the senses, is called empiricism.
Essais de Théodicée sur la bonté de Dieu, la liberté de l'homme et l'origine du mal, more simply known as Théodicée, is a book of philosophy by the German polymath Gottfried Leibniz. The book, published in 1710, introduced the term theodicy, and its optimistic approach to the problem of evil is thought to have inspired Voltaire's Candide. Much of the work consists of a response to the ideas of the French philosopher Pierre Bayle, with whom Leibniz carried on a debate for many years.
The integral symbol:
The Latin term characteristica universalis, commonly interpreted as universal characteristic, or universal character in English, is a universal and formal language imagined by Gottfried Leibniz able to express mathematical, scientific, and metaphysical concepts. Leibniz thus hoped to create a language usable within the framework of a universal logical calculation or calculus ratiocinator.
In the history of calculus, the calculus controversy was an argument between the mathematicians Isaac Newton and Gottfried Wilhelm Leibniz over who had first invented calculus. The question was a major intellectual controversy, which began simmering in 1699 and broke out in full force in 1711. Leibniz had published his work first, but Newton's supporters accused Leibniz of plagiarizing Newton's unpublished ideas. Leibniz died in 1716, shortly after the Royal Society, of which Newton was a member, found in Newton's favor. The modern consensus is that the two men developed their ideas independently.
Natura non facit saltus has been an important principle of natural philosophy. It appears as an axiom in the works of Gottfried Leibniz, one of the inventors of the infinitesimal calculus. It is also an essential element of Charles Darwin's treatment of natural selection in his Origin of Species. The Latin translation comes from Linnaeus' Philosophia Botanica.
The law of continuity is a heuristic principle introduced by Gottfried Leibniz based on earlier work by Nicholas of Cusa and Johannes Kepler. It is the principle that "whatever succeeds for the finite, also succeeds for the infinite". Kepler used the law of continuity to calculate the area of the circle by representing it as an infinite-sided polygon with infinitesimal sides, and adding the areas of infinitely many triangles with infinitesimal bases. Leibniz used the principle to extend concepts such as arithmetic operations from ordinary numbers to infinitesimals, laying the groundwork for infinitesimal calculus. The transfer principle provides a mathematical implementation of the law of continuity in the context of the hyperreal numbers.
New Essays on Human Understanding is a chapter-by-chapter rebuttal by Gottfried Leibniz of John Locke's major work An Essay Concerning Human Understanding (1689). It is one of only two full-length works by Leibniz. It was finished in 1704, but Locke's death was the cause alleged by Leibniz to withhold its publication. The book was published in 1765, some 60 years following its completion. Leibniz had died in 1716, and never saw its published form.
Joseph Ehrenfried Hofmann was a German historian of mathematics, known for his research on Gottfried Wilhelm Leibniz.
Eberhard Knobloch is a German historian of science and mathematics.
"Nova Methodus pro Maximis et Minimis" is the first published work on the subject of calculus. It was published by Gottfried Leibniz in the Acta Eruditorum in October 1684. It is considered to be the birth of infinitesimal calculus.
Bernhard Wilhelm Roth is a German experimental physicist.
The following outline is provided as an overview of and topical guide to Gottfried Wilhelm Leibniz:
References
- ↑ de:Gottfried Wilhelm Leibniz Bibliothek – Niedersächsische Landesbibliothek
- ↑ "Home". gwlb.de.
- ↑ "Leibniz-Bibliographie - 1.95".
- ↑ New Essays on Human Understanding Langley translation 1896.
- ↑ Leibniz's New Essays Concerning the Human Understanding – A Critical Exposition, Dewey 1888
- ↑ De Arte Combinatoria, original Latin-language text
- ↑ Discourse on Metaphysics . translated by G. R. Montgomery.
- ↑ Strickland Translation
- ↑ "Mathematical Treasure: Leibniz's Papers on Calculus - Differential Calculus | Mathematical Association of America".
- ↑ A New Method for Finding Maxima and Minima