leibniz, bernoulli and the logarithms of negative numbers

... chapter entitled, “The Exponential and Logarithmic Concepts.” We take the deep connection between these two ideas for granted. Hence, one may be surprised to learn that this connection was not explicitly stated until the mid-eighteenth century, more than one hundred thirty years after the introducti ...

... chapter entitled, “The Exponential and Logarithmic Concepts.” We take the deep connection between these two ideas for granted. Hence, one may be surprised to learn that this connection was not explicitly stated until the mid-eighteenth century, more than one hundred thirty years after the introducti ...

METAPHORS IN LEIBNIZ`S PHILOSOPHY

... ornamental or ‘eloquence’ devices. Yet, in his less-known work on natural languages, Leibniz considers tropes also as an essential instrument of linguistic creativity. Unlike formal languages, natural languages evolve (Leibniz was one of the first to point out the close links between cultural and li ...

... ornamental or ‘eloquence’ devices. Yet, in his less-known work on natural languages, Leibniz considers tropes also as an essential instrument of linguistic creativity. Unlike formal languages, natural languages evolve (Leibniz was one of the first to point out the close links between cultural and li ...

Developing the Calculus

... Observe that, using purely geometric methods, Barrow was able to arrive at this conclusion. He did not actually use the functional notation, nor did he realize the importance of the calculations that he was making. Therefore, it is not proper to say that Barrow invented Calculus. He merely stumbled ...

... Observe that, using purely geometric methods, Barrow was able to arrive at this conclusion. He did not actually use the functional notation, nor did he realize the importance of the calculations that he was making. Therefore, it is not proper to say that Barrow invented Calculus. He merely stumbled ...

Leibniz`s Harmonic Triangle Paper

... He obtained his bachelors degree at the age of seventeen, and his doctorate in Law from the University of Altdorf, Nuremburg, at the age of twenty. Leibniz taught himself mathematics, by reading papers and journals, and meeting many mathematicians in his early career as counsel and legal advisor to ...

... He obtained his bachelors degree at the age of seventeen, and his doctorate in Law from the University of Altdorf, Nuremburg, at the age of twenty. Leibniz taught himself mathematics, by reading papers and journals, and meeting many mathematicians in his early career as counsel and legal advisor to ...

Newton and Leibniz: the Calculus Controversy

... height, but not how they reached this conclusion. The Babylonians were able to devise a formula for the value of a square root of any rational number to as many decimal places as was desired. The Babylonians did not realize that this was an infinite process. ...

... height, but not how they reached this conclusion. The Babylonians were able to devise a formula for the value of a square root of any rational number to as many decimal places as was desired. The Babylonians did not realize that this was an infinite process. ...

PDF

... This triangle can be used to obtain examples for the Erdős-Straus conjecture when 4|n. ∗ hLeibnizHarmonicTrianglei created: h2013-03-21i by: hPrimeFani version: h39022i Privacy setting: h1i hDefinitioni h05A10i † This text is available under the Creative Commons Attribution/Share-Alike License 3.0. ...

... This triangle can be used to obtain examples for the Erdős-Straus conjecture when 4|n. ∗ hLeibnizHarmonicTrianglei created: h2013-03-21i by: hPrimeFani version: h39022i Privacy setting: h1i hDefinitioni h05A10i † This text is available under the Creative Commons Attribution/Share-Alike License 3.0. ...

Gottfried Wilhelm von Leibniz (also Godefroi Guillaume Leibnitz, /ˈlaɪbnɪts/; German: [ˈɡɔtfʁiːt ˈvɪlhɛlm fɔn ˈlaɪbnɪts] or [ˈlaɪpnɪts]; July 1, 1646 – November 14, 1716) was a German polymath and philosopher, and to this day he occupies a prominent place in the history of mathematics and the history of philosophy. Most scholars believe Leibniz developed calculus independently of Isaac Newton, and Leibniz's notation has been widely used ever since it was published. It was only in the 20th century that his Law of Continuity and Transcendental Law of Homogeneity found mathematical implementation (by means of non-standard analysis). He became one of the most prolific inventors in the field of mechanical calculators. While working on adding automatic multiplication and division to Pascal's calculator, he was the first to describe a pinwheel calculator in 1685 and invented the Leibniz wheel, used in the arithmometer, the first mass-produced mechanical calculator. He also refined the binary number system, which is the foundation of virtually all digital computers.In philosophy, Leibniz is most noted for his optimism, i.e., his conclusion that our Universe is, in a restricted sense, the best possible one that God could have created, an idea that was often lampooned by others such as Voltaire. Leibniz, along with René Descartes and Baruch Spinoza, was one of the three great 17th century advocates of rationalism. The work of Leibniz anticipated modern logic and analytic philosophy, but his philosophy also looks back to the scholastic tradition, in which conclusions are produced by applying reason of first principles or prior definitions rather than to empirical evidence.Leibniz made major contributions to physics and technology, and anticipated notions that surfaced much later in philosophy, probability theory, biology, medicine, geology, psychology, linguistics, and computer science. He wrote works on philosophy, politics, law, ethics, theology, history, and philology. Leibniz's contributions to this vast array of subjects were scattered in various learned journals, in tens of thousands of letters, and in unpublished manuscripts. He wrote in several languages, but primarily in Latin, French, and German. There is no complete gathering of the writings of Leibniz.