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John Playfair | |
---|---|
Born | Benvie, Forfarshire, Scotland, UK | 10 March 1748^{[ citation needed ]}
Died | 20 July 1819 71) Burntisland, Fife, Scotland | (aged
Resting place | Old Calton Burial Ground |
Nationality | Scottish |
Alma mater | University of St Andrews University of Edinburgh |
Known for | Playfair's axiom Playfair (lunar crater) Playfair (Martian crater) playfairite |
Scientific career | |
Fields | Mathematics, natural philosophy, geology |
Institutions | University of Edinburgh |
Influences | James Hutton |
John Playfair FRSE, FRS (10^{[ citation needed ]} March 1748 – 20 July 1819) was a Church of Scotland minister, remembered as a scientist and mathematician, and a professor of natural philosophy at the University of Edinburgh. He is best known for his book Illustrations of the Huttonian Theory of the Earth (1802), which summarised the work of James Hutton.^{ [1] } It was through this book that Hutton's principle of uniformitarianism, later taken up by Charles Lyell, first reached a wide audience. Playfair's textbook Elements of Geometry made a brief expression of Euclid's parallel postulate known now as Playfair's axiom.
In 1783 he was a co-founder of the Royal Society of Edinburgh. He served as General Secretary to the society 1798–1819.^{ [2] }
Born at Benvie, slightly west of Dundee to Margaret Young (1719/20 – 1805) and Reverend James Playfair (died 1772), the kirk minister of Liff and Benvie.^{ [3] }^{ [4] }
Playfair was educated at home until the age of 14, when he entered the University of St Andrews to study divinity. He also did further studies at Edinburgh University. In 1766, when only 18, he was a candidate for the chair of mathematics in Marischal College (now part of the University of Aberdeen), and, although he was unsuccessful, his claims were admitted to be high.
Six years later (1772) he applied for the chair of natural philosophy (physics) at St Andrews University, but again without success. In 1773 he was licensed to preach by the Church of Scotland and was offered the united parishes of Liff and his home parish of Benvie (made vacant by the death of his father). However, Playfair chose to continue his studies in mathematics and physics, and in 1782 he resigned his charge to become the tutor of Adam Ferguson. By this arrangement Playfair regularly visited Edinburgh and went on to cultivate the literary and scientific society for which the city was at that time specially distinguished. In particular, he attended the natural history course of John Walker. Through Nevil Maskelyne, whose acquaintance he had first made in the course of the celebrated Schiehallion experiments in 1774, he also gained access to the scientific circles of London. In 1785 when Dugald Stewart succeeded Ferguson in the University of Edinburgh Chair of Moral Philosophy, Playfair succeeded the former to become the chair of mathematics.
In 1795 Playfair published an alternative, more stringent formulation of Euclid's parallel postulate, which is now called Playfair's axiom. Although the axiom bears Playfair's name, he did not create it, but credited others, in particular William Ludlam with its prior use.^{ [5] }
In 1802 Playfair published his celebrated volume entitled Illustrations of the Huttonian Theory of the Earth. The influence exerted by James Hutton on the development of geology is thought to be largely due to its publication. In 1805 Playfair exchanged the Chair of Mathematics for that of natural philosophy in succession to John Robison, whom also he succeeded as general secretary to the Royal Society of Edinburgh. He took a prominent part, on the liberal side, in the ecclesiastical controversy that arose in connection with Sir John Leslie's appointment to the post he had vacated, and published a satirical letter (1806).
He moved from 6 Buccleuch Place to a new house at 2 Albany Street (then called Albany Row) in 1807.^{ [6] }^{ [7] }
Playfair was an opponent of Gottfried Leibniz's vis viva principle, an early version of the conservation of energy. In 1808, he launched an attack^{ [8] } on John Smeaton and William Hyde Wollaston's work championing the theory. In 1808 he also published a review of Laplace's Traité de Mécanique Celeste.^{ [9] }
He died at 2 Albany Street on 20 July 1819. He is buried nearby in Old Calton Burial Ground (a secular burial ground).^{ [10] }
Playfair's brothers were architect James Playfair, solicitor Robert Playfair and engineer William Playfair. His nephew, William Henry Playfair (1790–1857) was an eminent architect in Scotland.
In later life he admired and proposed to the wealthy widow Jane Apreece. She turned him down and married Sir Humphry Davy.^{ [11] }
He died of strangury on 20 July 1819, and, although an eminent man, was buried in an unmarked grave in Old Calton Burial Ground, on Waterloo Place in Edinburgh. His, and his brother, James's graves were marked by a plaque unveiled in 2011 following a local campaign.^{ [12] } The monument to his memory by William Henry Playfair, on Calton Hill,^{ [13] } is visible from the spot.
A four-volume collected edition of Playfair's works, with a memoir by James G. Playfair, appeared at Edinburgh in 1822.^{ [16] }
His writings include a number of essays contributed to the Edinburgh Review from 1804 onwards, various papers in the Philosophical Transactions of the Royal Society (including his earliest publication, "On the Arithmetic of Impossible Quantities", 1779, and an "Account of the Lithological Survey of Schehallion", 1811) and in the Transactions of the Royal Society of Edinburgh ("On the Causes which Affect the Accuracy of Barometrical Measurements" and others), the articles "Aepinus" and "Physical Astronomy", and a "Dissertation on the Progress of Mathematical and Physical Science since the Revival of Learning in Europe" in the Encyclopædia Britannica (Supplement to fourth, fifth and sixth editions). He also took an interest in Indian astronomy and compared them with traditional and ancient astronomy from Egypt and Greece.^{ [17] } He also examined Indian concepts in trigonometry.^{ [18] }
His Elements of Geometry first appeared in 1795 and has passed through many editions; his Outlines of Natural Philosophy (2 vols., 1812–1816) consist of the propositions and formulae which were the basis of his class lectures. Playfair's contributions to pure mathematics were not considerable, his papers "On the Arithmetic of Impossible Quantities" and "On the Causes which Affect the Accuracy of Barometrical Measurements", and his Elements of Geometry, all already referred to, being the most important. His lives of Matthew Stewart, Hutton, and Robison, many of his reviews, and above all his "Dissertation" are of the utmost value.
An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word ἀξίωμα (axíōma), meaning 'that which is thought worthy or fit' or 'that which commends itself as evident'.
Euclid was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the Elements treatise, which established the foundations of geometry that largely dominated the field until the early 19th century. His system, now referred to as Euclidean geometry, involved new innovations in combination with a synthesis of theories from earlier Greek mathematicians, including Eudoxus of Cnidus, Hippocrates of Chios, Thales and Theaetetus. With Archimedes and Apollonius of Perga, Euclid is generally considered among the greatest mathematicians of antiquity, and one of the most influential in the history of mathematics.
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated earlier, Euclid was the first to organize these propositions into a logical system in which each result is proved from axioms and previously proved theorems.
James Hutton was a Scottish geologist, agriculturalist, chemical manufacturer, naturalist and physician. Often referred to as the father of modern geology, he played a key role in establishing geology as a modern science.
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises by either replacing the parallel postulate with an alternative, or relaxing the metric requirement. In the former case, one obtains hyperbolic geometry and elliptic geometry, the traditional non-Euclidean geometries. When the metric requirement is relaxed, then there are affine planes associated with the planar algebras, which give rise to kinematic geometries that have also been called non-Euclidean geometry.
Foundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics. In this latter sense, the distinction between foundations of mathematics and philosophy of mathematics turns out to be quite vague. Foundations of mathematics can be conceived as the study of the basic mathematical concepts and how they form hierarchies of more complex structures and concepts, especially the fundamentally important structures that form the language of mathematics also called metamathematical concepts, with an eye to the philosophical aspects and the unity of mathematics. The search for foundations of mathematics is a central question of the philosophy of mathematics; the abstract nature of mathematical objects presents special philosophical challenges.
Dugald Stewart was a Scottish philosopher and mathematician. Today regarded as one of the most important figures of the later Scottish Enlightenment, he was renowned as a populariser of the work of Francis Hutcheson and Adam Smith. His lectures at the University of Edinburgh were widely disseminated by his many influential students. In 1783 he was a joint founder of the Royal Society of Edinburgh. In most contemporary documents he is referred to as Prof Dougal Stewart.
James Ivory, FRS FRSE KH LLD was a British mathematician. He was creator of Ivory's Theorem on confocal conic sections.
Robert Jameson FRS FRSE was a Scottish naturalist and mineralogist.
Nikolai Ivanovich Lobachevsky was a Russian mathematician and geometer, known primarily for his work on hyperbolic geometry, otherwise known as Lobachevskian geometry, and also for his fundamental study on Dirichlet integrals, known as the Lobachevsky integral formula.
Sir John Leslie, FRSE KH was a Scottish mathematician and physicist best remembered for his research into heat.
The City Observatory was an astronomical observatory on Calton Hill in Edinburgh, Scotland. It is also known as the Calton Hill Observatory.
Plutonism is the geologic theory that the igneous rocks forming the Earth originated from intrusive magmatic activity, with a continuing gradual process of weathering and erosion wearing away rocks, which were then deposited on the sea bed, re-formed into layers of sedimentary rock by heat and pressure, and raised again. It proposes that basalt is solidified molten magma. The theory lead to plutonic (intrinsic) rock classification, which includes intrinsic igneous rocks such as gabbro, diorite, granite and pegmatite. The name plutonism references Pluto, the classical ruler of the underworld and the Roman god of wealth. A main reason Pluto was incorporated into the classification was due to the plutonic rocks commonly being present in gold and silver ore deposits (veins).
William Wallace LLD was a Scottish mathematician and astronomer who invented the eidograph.
The Edinburgh Astronomical Institution was founded in 1811 and wound up in 1847. It was instrumental in the foundation of the Royal Observatory, Edinburgh in 1822. The Institution raised funds, mostly by member subscription, to create three departments: A scientific observatory with an observer was to be under the control of the professors of mathematics, philosophy and astronomy of the University of Edinburgh, a popular observatory was to provide general instruction and amusement and a "physical cabinet" would comprise books, globes, meteorological and other instruments.
Foundations of geometry is the study of geometries as axiomatic systems. There are several sets of axioms which give rise to Euclidean geometry or to non-Euclidean geometries. These are fundamental to the study and of historical importance, but there are a great many modern geometries that are not Euclidean which can be studied from this viewpoint. The term axiomatic geometry can be applied to any geometry that is developed from an axiom system, but is often used to mean Euclidean geometry studied from this point of view. The completeness and independence of general axiomatic systems are important mathematical considerations, but there are also issues to do with the teaching of geometry which come into play.
In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's Elements, is a distinctive axiom in Euclidean geometry. It states that, in two-dimensional geometry:
If a line segment intersects two straight lines forming two interior angles on the same side that are less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.
In geometry, Playfair's axiom is an axiom that can be used instead of the fifth postulate of Euclid :
In a plane, given a line and a point not on it, at most one line parallel to the given line can be drawn through the point.
Theory of the Earth was a publication by James Hutton which laid the foundations for geology. In it he showed that the Earth is the product of natural forces. What could be seen happening today, over long periods of time, could produce what we see in the rocks. It also hypothesized that the age of the Earth was much older than what biblical literalists claim. This idea, uniformitarianism, was used by Charles Lyell in his work, and Lyell's textbook was an important influence on Charles Darwin. The work was first published in 1788 by the Royal Society of Edinburgh, and later in 1795 as two book volumes.
Events from the year 1802 in Scotland.
This article incorporates text from a publication now in the public domain : Chisholm, Hugh, ed. (1911). "Playfair, John". Encyclopædia Britannica . Vol. 21 (11th ed.). Cambridge University Press. p. 831.