fluxions

Gottfried Wilhelm von Leibniz (also Leibnitz) (July 1 (June 21 Old Style) 1646, Leipzig – November 14, 1716, Hanover) was a German polymath, deemed a genius in his lifetime and since, and the last true polyhistor. Trained as a lawyer and active as a diplomat and librarian, he wrote on philosophy, science, mathematics, theology, history, and comparative philology, even writing verse. Through his service to two major German noble houses, he played a major role in the European ...

Including:

• Gottfried Leibniz - Life
• Gottfried Leibniz - Early life and education
• Gottfried Leibniz - Career
• Gottfried Leibniz - Writings
• Gottfried Leibniz - Posthumous reputation
• Gottfried Leibniz - Philosopher
• Gottfried Leibniz - Metaphysics
• Gottfried Leibniz - Theodicy and optimism
• Gottfried Leibniz - Symbolic thought
• Gottfried Leibniz - Characteristica Universalis Universal characteristic and Calculus Ratiocinator
• Gottfried Leibniz - Formal logic
• Gottfried Leibniz - Mathematician
• Gottfried Leibniz - Topology
• Gottfried Leibniz - The dispute over who first invented the calculus
• Gottfried Leibniz - Science and technology
• Gottfried Leibniz - The vis viva
• Gottfried Leibniz - Information technology
• Gottfried Leibniz - Philology
• Gottfried Leibniz - The Sinophile
• Gottfried Leibniz - Works
• Gottfried Leibniz - Secondary literature
• Gottfried Leibniz - Quotes

Read more here: » Gottfried Leibniz: Encyclopedia - Gottfried Leibniz

The Analytical Society was a group of individuals in early-19th century Britain whose aim was to promote the use of Leibnizian or analytical calculus as opposed to Newtonian calculus. The latter system came into being in the 18th century as an invention of Sir Isaac Newton, and was in use throughout Great Britain for political rather than practical reasons. The Newtonian system of fluxions and fluents proved cumbersome to use, and less flexible and usable than L ...

Including:

• Analytical Society - External link

Read more here: » Analytical Society: Encyclopedia - Analytical Society

Leonhard Euler was born near Basel, Switzerland, the son of Paul Euler, a Lutheran minister. Although in his childhood he exhibited great mathematical talents, his father wanted him to study theology and become a minister. In 1720 Euler began his studies at the University of Basel. There Euler met Daniel and Nikolaus Bernoulli, who noticed Euler's skills in mathematics. Paul Euler had attended Jakob Bernoulli's mathematical lectures and respected his family. When Daniel and Nikolaus Bernoulli asked him to allow his son to study mathematics he finally ...

See also:

Leonhard Euler, Leonhard Euler - Biography, Leonhard Euler - Discoveries, Leonhard Euler - Honours, Leonhard Euler - Quotes

Read more here: » Leonhard Euler: Encyclopedia II - Leonhard Euler - Biography

Many of the results of Newton and Leibniz were known to mathematicians in Kerala, India almost 300 years previously. In 1835, Charles Whish published an article in the Transactions of the Royal Asiatic Society of Great Britain and Ireland, in which he claimed that the work of the Kerala school "laid the foundation for a complete system of fluxions." It was not until the 1940s however, that historians of mathematics verified Whish's claims, but their work is still underplayed in modern accounts of history ...

See also:

History of calculus, History of calculus - Invention of Calculus, History of calculus - Controversy Newton Leibnitz... or Madhava?, History of calculus - Rigorous foundations, History of calculus - Integrals, History of calculus - Symbolic methods, History of calculus - Calculus of variations, History of calculus - Applications

Read more here: » History of calculus: Encyclopedia II - History of calculus - Invention of Calculus

Although the mathematical notion of function was implicit in trigonometric and logarithmic tables, which existed in his day, Leibniz was the first, in 1692 and 1694, to employ it explicitly, to denote any of several geometric concepts derived from a curve, such as abscissa, ordinate, tangent, chord, and the perpendicular (Struik 1969: 367). Only later did "function" lose these geometrical associations. Leibniz was the first to see that the coefficients of a system of linear equations could be arranged into arrays, now called determina ...

See also:

Gottfried Leibniz, Gottfried Leibniz - Life, Gottfried Leibniz - Early life and education, Gottfried Leibniz - Career, Gottfried Leibniz - Writings, Gottfried Leibniz - Posthumous reputation, Gottfried Leibniz - Philosopher, Gottfried Leibniz - Metaphysics, Gottfried Leibniz - Theodicy and optimism, Gottfried Leibniz - Symbolic thought, Gottfried Leibniz - Characteristica Universalis Universal characteristic and Calculus Ratiocinator, Gottfried Leibniz - Formal logic, Gottfried Leibniz - Mathematician, Gottfried Leibniz - Topology, Gottfried Leibniz - The dispute over who first invented the calculus, Gottfried Leibniz - Science and technology, Gottfried Leibniz - The vis viva, Gottfried Leibniz - Information technology, Gottfried Leibniz - Philologist, Gottfried Leibniz - The Sinophile, Gottfried Leibniz - Works, Gottfried Leibniz - Secondary literature, Gottfried Leibniz - Quotes

Read more here: » Gottfried Leibniz: Encyclopedia II - Gottfried Leibniz - Mathematician

Leibniz is credited along with Isaac Newton with inventing the infinitesimal calculus in the 1670s. According to Leibniz's notebooks, a critical breakthrough occurred on November 11, 1675, when he employed integral calculus for the first time to find the area under the function y = x. He introduced several notations used to this day, for instance the integral sign ∫ representing an elongated S, from the Latin word summa and the See also:

Newton v. Leibniz calculus controversy, Newton v. Leibniz calculus controversy - The quarrel, Newton v. Leibniz calculus controversy - Sources

Read more here: » Newton v. Leibniz calculus controversy: Encyclopedia II - Newton v. Leibniz calculus controversy - The quarrel

Leibniz's writingss are currently discussed seriously in a number of fields at the forefront of science, not only as anticipations and possible discoveries not yet recognized, but as ways of advancing present knowledge. Until the discovery of subatomic particles and the quantum mechanics governing them, many of Leibniz's speculative ideas made no sense. Leibniz devised a new theory of motion (dynamics) based on kinetic and potential energy. He anticipated Einstein by arguing, against Newton, that space, time and motion are relative, not abso ...

See also:

Gottfried Leibniz, Gottfried Leibniz - Life, Gottfried Leibniz - Early life and education, Gottfried Leibniz - Career, Gottfried Leibniz - Writings, Gottfried Leibniz - Posthumous reputation, Gottfried Leibniz - Philosopher, Gottfried Leibniz - Metaphysics, Gottfried Leibniz - Theodicy and optimism, Gottfried Leibniz - Symbolic thought, Gottfried Leibniz - Characteristica Universalis Universal characteristic and Calculus Ratiocinator, Gottfried Leibniz - Formal logic, Gottfried Leibniz - Mathematician, Gottfried Leibniz - Topology, Gottfried Leibniz - The dispute over who first invented the calculus, Gottfried Leibniz - Science and technology, Gottfried Leibniz - The vis viva, Gottfried Leibniz - Information technology, Gottfried Leibniz - Philologist, Gottfried Leibniz - The Sinophile, Gottfried Leibniz - Works, Gottfried Leibniz - Secondary literature, Gottfried Leibniz - Quotes

Read more here: » Gottfried Leibniz: Encyclopedia II - Gottfried Leibniz - Science and technology

Madhava of Sangamagrama and the Kerala school were the first to come up with the important ideas of calculus in the 14th century and some [3] propose these ideas may have been transmitted to Europe by the 17th century. There is no evidence by way of relevant manuscripts but the evidence of methodological similarities, communication routes and a suitable chronology for transmission is hard to dismiss. In the controversy between Newton and Leibniz, suggestions were made that the work of Leibniz was not independent, as he claimed, but in ...

See also:

History of calculus, History of calculus - Invention of Calculus, History of calculus - Controversy Newton Leibnitz... or Madhava?, History of calculus - Rigorous foundations, History of calculus - Integrals, History of calculus - Symbolic methods, History of calculus - Calculus of variations, History of calculus - Applications

Read more here: » History of calculus: Encyclopedia II - History of calculus - Controversy Newton Leibnitz... or Madhava?

Niels Henrik Abel seems to have been the first to consider in a general way the question as to what differential expressions can be integrated in a finite form by the aid of ordinary functions, an investigation extended by Liouville. Cauchy early undertook the general theory of determining definite integrals, and the subject has been prominent during the 19th century. Frullani's theorem (1821), Bierens de Haan's work on the theory (1862) and his elaborate tables (1867), Dirichlet's lectures (1858) embodied in Meyer's treatise (1871), and num ...

See also:

History of calculus, History of calculus - Invention of Calculus, History of calculus - Controversy Newton Leibnitz... or Madhava?, History of calculus - Rigorous foundations, History of calculus - Integrals, History of calculus - Symbolic methods, History of calculus - Calculus of variations, History of calculus - Applications

Read more here: » History of calculus: Encyclopedia II - History of calculus - Integrals

It is very difficult to grasp Leibniz's philosophical thinking, because his philosophical writings consist mainly of a multitude of short pieces: journal articles, manuscripts published long after his death, and many letters to many correspondents. He only wrote two philosophical treatises, and the only one he published in his lifetime, the Théodicée of 1710, is as much theological as philosophical. Leibniz dated his beginning as a philosopher to his Discourse on Metaphysics, which he composed in 1686 as a commentary on an on ...

See also:

Gottfried Leibniz, Gottfried Leibniz - Life, Gottfried Leibniz - Early life and education, Gottfried Leibniz - Career, Gottfried Leibniz - Writings, Gottfried Leibniz - Posthumous reputation, Gottfried Leibniz - Philosopher, Gottfried Leibniz - Metaphysics, Gottfried Leibniz - Theodicy and optimism, Gottfried Leibniz - Symbolic thought, Gottfried Leibniz - Characteristica Universalis Universal characteristic and Calculus Ratiocinator, Gottfried Leibniz - Formal logic, Gottfried Leibniz - Mathematician, Gottfried Leibniz - Topology, Gottfried Leibniz - The dispute over who first invented the calculus, Gottfried Leibniz - Science and technology, Gottfried Leibniz - The vis viva, Gottfried Leibniz - Information technology, Gottfried Leibniz - Philologist, Gottfried Leibniz - The Sinophile, Gottfried Leibniz - Works, Gottfried Leibniz - Secondary literature, Gottfried Leibniz - Quotes

Read more here: » Gottfried Leibniz: Encyclopedia II - Gottfried Leibniz - Philosopher

LL = Loemker (1969). W = Wiener (1951). The ongoing complete critical edition of Leibniz's writings is Sämtliche Schriften und Briefe. Selected works; major ones in bold. The year shown is usually the year in which the work was completed, not of its eventual publication. 1666. De Arte Combinatoria (On the Art of Combination). LL §1 (part). 1671. Hypothesis Physica Nova (New Physical Hypothesis). 1684. Nova methodus pro maximis et minimis (New Method for maximums and m ...

See also:

Gottfried Leibniz, Gottfried Leibniz - Life, Gottfried Leibniz - Early life and education, Gottfried Leibniz - Career, Gottfried Leibniz - Writings, Gottfried Leibniz - Posthumous reputation, Gottfried Leibniz - Philosopher, Gottfried Leibniz - Metaphysics, Gottfried Leibniz - Theodicy and optimism, Gottfried Leibniz - Symbolic thought, Gottfried Leibniz - Characteristica Universalis Universal characteristic and Calculus Ratiocinator, Gottfried Leibniz - Formal logic, Gottfried Leibniz - Mathematician, Gottfried Leibniz - Topology, Gottfried Leibniz - The dispute over who first invented the calculus, Gottfried Leibniz - Science and technology, Gottfried Leibniz - The vis viva, Gottfried Leibniz - Information technology, Gottfried Leibniz - Philologist, Gottfried Leibniz - The Sinophile, Gottfried Leibniz - Works, Gottfried Leibniz - Secondary literature, Gottfried Leibniz - Quotes

Read more here: » Gottfried Leibniz: Encyclopedia II - Gottfried Leibniz - Works

Euler, with Daniel Bernoulli, established the law that the torque on a thin elastic beam is proportional to a measure of the elasticity of the material and the second moment of area of a cross section, about an axis through the center of mass and perpendicular to the plane of the moment, see Euler-Bernoulli beam equation. He also deduced the Euler equations, a set of laws of motion in fluid dynamics, directly from Newton's laws of motion. These equations are formally identical to the Navier-Stokes equations with zero viscosity. They are interesting ch ...

See also:

Leonhard Euler, Leonhard Euler - Biography, Leonhard Euler - Discoveries, Leonhard Euler - Honours, Leonhard Euler - Quotes

Read more here: » Leonhard Euler: Encyclopedia II - Leonhard Euler - Discoveries

The only biography in English is Aiton (1986). Also see MacDonald Ross (1984: chpt. 1), Mates (1986: 14-35), Jolley (2005: chpt. 1 & references therein), and the excerpt from Rouse Ball (1908) bearing on Leibniz. Gottfried Leibniz - Early life and education. Leibniz's parents were Friedrich Leibniz and Catharina Schmuck. His father, a Professor of Moral Philosophy at the University of Leipzig, died in Leibniz's sixth year. From age 8 on, Leibniz was granted free access to his late father's library. By ...

See also:

Gottfried Leibniz, Gottfried Leibniz - Life, Gottfried Leibniz - Early life and education, Gottfried Leibniz - Career, Gottfried Leibniz - Writings, Gottfried Leibniz - Posthumous reputation, Gottfried Leibniz - Philosopher, Gottfried Leibniz - Metaphysics, Gottfried Leibniz - Theodicy and optimism, Gottfried Leibniz - Symbolic thought, Gottfried Leibniz - Characteristica Universalis Universal characteristic and Calculus Ratiocinator, Gottfried Leibniz - Formal logic, Gottfried Leibniz - Mathematician, Gottfried Leibniz - Topology, Gottfried Leibniz - The dispute over who first invented the calculus, Gottfried Leibniz - Science and technology, Gottfried Leibniz - The vis viva, Gottfried Leibniz - Information technology, Gottfried Leibniz - Philologist, Gottfried Leibniz - The Sinophile, Gottfried Leibniz - Works, Gottfried Leibniz - Secondary literature, Gottfried Leibniz - Quotes

Read more here: » Gottfried Leibniz: Encyclopedia II - Gottfried Leibniz - Life