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Gottfried w. leibniz
Gottfried w. leibniz
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Gottfried Wilhelm Leibniz is an important figure in the history of philosophy and mathematics. Although his work was not fully appreciated during his day, he did much to advance the "thinking" on a variety of subjects. His fame was scarred by the infamous controversy with Isaac Newton on the subject of the discoverer of calculus. Leibniz's work encompassed a wide scope, ranging from philosopy to politics to mechanics and mathematics, but his most noteworthy accomplishment was the discovery of differential calculus and its highly efficient notation. Leibniz was born July 1, 1646 in Leipzig, Germany into a family of renowned scholars. His father, Friedrich Leibniz, was a professor of philosophy at the University of Leipzig. By the age of seven, Leibniz was self-taught in Greek and Latin and "was something of a prodigy" (Meyer 2). During this time, he was taught Aristotle's logic and sought to improve it. These ideas became the foundation of his mathematical proofs. "In later life Leibniz recalled that at this time he was trying to find orderings on logical truths which?were the ideas behind rigorous mathematical proofs" (O'Connor and Robertson). At the age of 15, Leibniz attended the University of Leipzig, and at 17, he left to Jena to study law over the summer. He submitted a legal thesis for a doctor's degree at age 20 to the University of Leipzig but was rejected (Broad 1). Leibniz was quite accomplished in many fields other than philosophy and mathematics. He was greatly interested in poems. "Although Leibniz's interests were clearly developing in a scientific direction, he still hankered after a literary career. All his life he prided himself on his poetry ?, and boasted t... ... middle of paper ... ...s itemque Tangentibus printed in his journal: Acta Eruditorium. Leibniz interpreted as the area under a curve. When this was published, Jacob Bernoulli was the first to refer to this as "Integral Calculus." Lastly, Leibniz formulated his own fundamental theorem. It states that "one can find a curve z such that by using the equation: (Carr 62). Clearly, Leibniz's form of calculus paved the way to modern calculus. During his waning years, Leibniz was quickly forgotten. On November 14, 1716, Leibniz passed away in Hannover, Germany. Sadly, only one person was recorded that attended his funeral: his secretary. While Newton, a world-renown scientist, was knighted by the Queen, Leibniz did not achieve the fame that he deserved. He was best known as a philosopher, but he also advanced the world's knowledge significantly in the form of calculus.
Before students can judge others ideologies they must understand the philosopher first. Rene Descartes, the father of modern western philosophy, was born in 1596 to French parents. Rene Descartes excelled in mathematics. By 1616 Descartes received his baccalaureate and became a licensed lawyer. In 1618 Descartes joined the army of Prince Maurice of Nassau. During his service Descartes never saw combat, but while in the service he was able to travel and explore the world. During his time in Germany Descartes began to inquire about life’s hardest questions regarding logic, reasoning, arithmetic, God and knowledge. By the early 1830’s Descartes continued his conquest of knowledge; he secluded himself from all temptations and began to write. Descartes
Question #1: Compare the Ways that Descartes, Leibniz, and Berkeley each deal with the problem of evil and human error in a world created by an omnipotent and perfectly good God/creator.
...use many of his concepts and ideas today, such as the law of conservation of matter and the calculus concept of dy/dx. Leibniz sought after knowledge and gave the world many new and innovative ways to think. Through his advancements in mathematics, many other fields of study took root and thrived. Leibniz died November 14, 1716. His contributions to society brought about a new way of thinking and challenged what the world knew.
mathematical formula can prove”. Leibniz ignored the problems and flaws in society that were so clearly in front of him because his logic rendered them impossible. This is where the conflict first began to arise between Leibniz and Voltaire. Voltai...
Descartes was born in 1596 in Touraine, France. His education consisted of attendance to a Jesuit school of La Fleche. He studied a liberal arts program that emphasized philosophy, the humanities, science, and math. He then went on to the University of Poitiers where he graduated in 1616 with a law degree. Descartes also served as a volunteer in several different armies to broaden his horizons.
Rene Descartes was one of the most influential thinkers in the history of the philosophy. Born in 1596, he lived to become a great mathematician, scientist, and philosopher. In fact, he became one of the central intellectual figures of the sixteen hundreds. He is believed by some to be the father of modern philosophy, although he was hampered by living in a time when other prominent scientists, such as Galileo, were persecuted for their discoveries and beliefs. Although this probably had an impact on his desire to publish controversial material, he went on to devise works such as the Meditations on First Philosophy and the Principles of Philosophy Aside from these accomplishments, his most important and lasting mathematical work was the invention of analytic geometry. It seems that the underlying point of Descartes’s philosophy is to specify exactly what it is that we are sure we know.
Although philosophy rarely alters its direction and mood with sudden swings, there are times when its new concerns and emphases clearly separate it from its immediate past. Such was the case with seventeenth-century Continental rationalism, whose founder was Rene Descartes and whose new program initiated what is called modern philosophy. In a sense, much of what the Continental rationalists set out to do had already been attempted by the medieval philosophers and by Bacon and Hobbes. But Descartes and Leibniz fashioned a new ideal for philosophy. Influenced by the progress and success of science and mathematics, their new program was an attempt to provide philosophy with the exactness of mathematics. They set out to formulate clear and rational principles that could be organized into a system of truths from which accurate information about the world could be deduced. Their emphasis was upon the rational ability of the human mind, which they now considered the source of truth both about man and about the world. Even though they did not reject the claims of religion, they did consider philosophical reasoning something different than supernatural revelation. They saw little value in feeling and enthusiasm as means for discovering truth, but they did believe that the mind of an individual is structured in such a way that simply by operating according to the appropriate method it can discover the nature of the universe. The rationalists assumed that what they could think clearly with their minds did in fact exist in the world outside their minds. Descartes and Leibniz even argued that certain ideas are innate in the human mind, that, given the proper occasion, experience would cause...
René Descartes (1596 – 1650) is one of the most widely known philosophers in history and he is frequently discussed as an inventor of the modern scientific method. Rene Descartes was born on March 31, 1596, in La Haye of Touraine. He came from a wealthy family, and thus did not have any real financial worries. At age ten, his father sent him to the College Henri IV at La Fleche. This was a newly established Jesuit school, which was considered one of the best in Europe in terms of academic quality. Although Descartes appreciated what he was taught in mathematics, he was nonetheless discontent with the scholastic teaching he received from that school (Cress, 1993).
The argument in this paper that even though the onus of the discovery of calculus lies with Isaac Newton, the credit goes to Leibniz for the simple fact that he was the one who published his works first. Appending to this is the fact that the calculus wars that ensue was merely and egotistic battle between humans succumbing to their bare primal instincts. To commence, a brief historical explanation must be given about both individuals prior to stating their cases.
...st important scientists in history. It is said that they both shaped the sciences and mathematics that we use and study today. Euclid’s postulates and Archimedes’ calculus are both important fundamentals and tools in mathematics, while discoveries, such Archimedes’ method of using water to measure the volume of an irregularly shaped object, helped shaped all of today’s physics and scientific principles. It is for these reasons that they are remembered for their contributions to the world of mathematics and sciences today, and will continue to be remembered for years to come.
Differential calculus is a subfield of Calculus that focuses on derivates, which are used to describe rates of change that are not constants. The term ‘differential’ comes from the process known as differentiation, which is the process of finding the derivative of a curve. Differential calculus is a major topic covered in calculus. According to Interactive Mathematics, “We use the derivative to determine the maximum and minimum values of particular functions (e.g. cost, strength, amount of material used in a building, profit, loss, etc.).” Not only are derivatives used to determine how to maximize or minimize functions, but they are also used in determining how two related variables are changing over time in relation to each other. Eight different differential rules were established in order to assist with finding the derivative of a function. Those rules include chain rule, the differentiation of the sum and difference of equations, the constant rule, the product rule, the quotient rule, and more. In addition to these differential rules, optimization is an application of differential calculus used today to effectively help with efficiency. Also, partial differentiation and implicit differentiation are subgroups of differential calculus that allow derivatives to be taken to more challenging and difficult formulas. The mean value theorem is applied in differential calculus. This rule basically states that there is at least one tangent line that produces the same slope as the slope made by the endpoints found on a closed interval. Differential calculus began to develop due to Sir Isaac Newton’s biggest problem: navigation at sea. Shipwrecks were frequent all due to the captain being unaware of how the Earth, planets, and stars mov...
Ever wonder how scientists figure out how long it takes for the radiation from a nuclear weapon to decay? This dilemma can be solved by calculus, which helps determine the rate of decay of the radioactive material. Calculus can aid people in many everyday situations, such as deciding how much fencing is needed to encompass a designated area. Finding how gravity affects certain objects is how calculus aids people who study Physics. Mechanics find calculus useful to determine rates of flow of fluids in a car. Numerous developments in mathematics by Ancient Greeks to Europeans led to the discovery of integral calculus, which is still expanding. The first mathematicians came from Egypt, where they discovered the rule for the volume of a pyramid and approximation of the area of a circle. Later, Greeks made tremendous discoveries. Archimedes extended the method of inscribed and circumscribed figures by means of heuristic, which are rules that are specific to a given problem and can therefore help guide the search. These arguments involved parallel slices of figures and the laws of the lever, the idea of a surface as made up of lines. Finding areas and volumes of figures by using conic section (a circle, point, hyperbola, etc.) and weighing infinitely thin slices of figures, an idea used in integral calculus today was also a discovery of Archimedes. One of Archimedes's major crucial discoveries for integral calculus was a limit that allows the "slices" of a figure to be infinitely thin. Another Greek, Euclid, developed ideas supporting the theory of calculus, but the logic basis was not sustained since infinity and continuity weren't established yet (Boyer 47). His one mistake in finding a definite integral was that it is not found by the sums of an infinite number of points, lines, or surfaces but by the limit of an infinite sequence (Boyer 47). These early discoveries aided Newton and Leibniz in the development of calculus. In the 17th century, people from all over Europe made numerous mathematics discoveries in the integral calculus field. Johannes Kepler "anticipat(ed) results found… in the integral calculus" (Boyer 109) with his summations. For instance, in his Astronomia nova, he formed a summation similar to integral calculus dealing with sine and cosine. F. B. Cavalieri expanded on Johannes Kepler's work on measuring volumes. Also, he "investigate[d] areas under the curve" ("Calculus (mathematics)") with what he called "indivisible magnitudes.
Born in the Netherlands, Daniel Bernoulli was one of the most well-known Bernoulli mathematicians. He contributed plenty to mathematics and advanced it, ahead of its time. His father, Johann, made him study medicine at first, as there was little money in mathematics, but eventually, Johann gave in and tutored Daniel in mathematics. Johann treated his son’s desire to lea...
...ocity. On the other hand, Leibniz had taken a geometrical approach, basing his discoveries on the work of previous thinkers like Fermat and Pascal. Though Newton had been the first to derive calculus as a mathematical approach, Leibniz was the first one to widely disseminate the concept throughout Europe. This was perhaps the most conclusive evidence that Newton and Leibniz were both independent developers of calculus. Newton’s timeline displays more evidence of inventing calculus because of his refusal to use theories or concepts to prove his answers, while Leibniz furthered other mathematician’s ideas to collaborate and bring together theorems for the application of calculus. The history of calculus developed as a result of sequential events, including many inventions and innovations, which led to forward thinking in the development of the mathematical system.
The 17th Century saw Napier, Briggs and others greatly extend the power of mathematics as a calculator science with his discovery of logarithms. Cavalieri made progress towards the calculus with his infinitesimal methods and Descartes added the power of algebraic methods to geometry. Euclid, who lived around 300 BC in Alexandria, first stated his five postulates in his book The Elements that forms the base for all of his later Abu Abd-Allah ibn Musa al’Khwarizmi, was born abo...