**John Playfair** worked on geology, physics and geometry and studied at the University of St Andrews. His best-known contribution to mathematics is his form of Euclid's parallelism axiom.

- Playfair was awarded a scholarship to the University in 1762, and there his aptitude and keenness to study gained him both the respect and friendship of his professors.
- Playfair graduated from the University of St Andrews with an M.A. in 1765.
- In 1766, while still only eighteen, Playfair entered a contest for the Chair of Mathematics at Marischal College in Aberdeen.
- Playfair was unsuccessful, however, finishing third out of the six candidates, behind the Reverend Dr Trail, who was appointed to the Chair, and Dr Hamilton, who succeeded him in the Chair.
- However Playfair, at a very young age, had proved his extraordinary talent combined with his comprehensive knowledge of mathematics.
- Going on to study divinity at the University of St Andrews, Playfair undertook his theological studies at St Mary's College, St Andrews.
- During the period between 1769 and 1773, Playfair had twice attempted to obtain an academic post.
- In 1772 Playfair applied for the Chair of Natural Philosophy in the University of St Andrews, which was left vacant after the death of his friend Wilkie but again another candidate was appointed.
- The case went before the Court of Session and, in August 1773, Playfair received confirmation by a resolution of the General Assembly of the Church.
- During this period Playfair did not neglect his own academic studies, and beside making occasional visits to Edinburgh, he made an excursion in 1774 to Schiehallion, Perthshire, to conduct experiments with Neville Maskelyne, the Astronomer Royal.
- He persuaded Playfair to submit his first successful paper on mathematics to the Royal Society of London and this was published in the Philosophical Transactions in 1779.
- Playfair became Moderator of the Synod but soon after this he received, in 1782, a lucrative offer to resign his church position and to become the tutor to the two sons of Ferguson of Raith.
- Playfair became involved in the establishment of the Royal Society of Edinburgh in 1783 and was one of the original Fellows of that Society.
- In 1785 Playfair was appointed Joint Professor of Mathematics in the University of Edinburgh, a position which he was to hold for twenty years.
- From 1787 Playfair published on various topics in the Transactions of the Royal Society of Edinburgh and also contributed to the Edinburgh Review.
- In the following year, he adopted James's eldest son, William Henry Playfair, then only six years of age.
- In 1795 Playfair published an edition of the Elements which he intended for use by his students.
- The main innovation was Playfair's use of algebraic notation to abbreviate the proofs which he taught in his class.
- It is curious that Playfair's name should be associated with this axiom, particularly since he clearly points out that he derived the axiom from Proclus.
- "Given a line and a point not on the line, it is possible to draw exactly one line through the given point parallel to the line." is what is usually known as Playfair's Axiom.
- To these books, which specifically deal with plane geometry, Playfair added three more books intended to supplement the preceding six; On the Quadrature of the Circle and the Geometry of Solids, Elements of Plane and Spherical Trigonometry and The Arithmetic of Sines.
- The fact that it ran to six editions shows the popularity of Playfair's edition of Euclid.
- The death of his friend, James Hutton, moved Playfair to compose a biographical memoir, which gradually became a reply to the critics of Hutton's theories of geology.
- This in turn gave rise to Playfair's geological work Illustrations of the Huttonian Theory of the Earth.
- Playfair presented Hutton's theories in a different style from Hutton's original presentation.
- Playfair's simple and eloquent style consisted of a series of chapters clearly stating the Huttonian theory, giving the facts to support it, and the arguments given against it.
- The success of Playfair's presentation can be judged by the fame and credit which have since been given to Hutton, who is now regarded as the first great British geologist.
- Playfair spent almost five years, from 1797 to 1802, writing the Illustrations.
- Playfair had hoped to extend his researches to the Continent, but he was prevented in doing so by the war in Europe.
- In 1803 Playfair published his biographical sketch of Hutton in the Transactions of the Royal Society of Edinburgh.
- Playfair was a successful teacher in his position as Professor of Mathematics at the University of Edinburgh, lecturing with a verve for the subject, doing his utmost to inspire his students with an enthusiasm for mathematical investigation, and rewarding those who succeeded by praising them in front of the class.
- Playfair was among the first in Britain to teach modern analysis.
- To express their gratitude, class members presented Playfair with a precious astronomical circle, which was placed in the Observatory of the Astronomical Institution.
- However, despite his success as a mathematician, Playfair exchanged the Chair of Mathematics for the Chair of Natural Philosophy in 1805.
- Playfair was its first president.
- The New Observatory on Calton Hill was built largely through Playfair's efforts in support of the project.
- In 1812 Playfair published the first of the volumes of his Outlines of Natural Philosophy, again intended primarily for the use of his students.
- In 1815 Playfair succeeded his friend and colleague, Professor Robison, as the Secretary of the Royal Society of Edinburgh.
- Playfair published many papers in the Transactions of the Society including a set of meteorological tables constructed from his own observations.
- Later in 1815 peace in Europe followed the defeat of Napoleon and Playfair began a 17 month, 4000 mile geological study of the Continent to gather material for the second edition of the Illustrations of the Huttonian Theory of the Earth.
- Although 68 years of age, Playfair set out on an arduous and extensive journey through France and Switzerland, continuing to the southern tip of Italy, examining the geological structure of the parts of the world he visited.
- He was accompanied for part of the time by his eldest nephew, James George Playfair, who assisted him by recording the details of their journeys.
- It was Playfair's aim to base the principles of geology on unquestionable assumptions and arguments.
- It would conclude with Playfair's model of geology and its applications.
- However, this plan was interrupted when Playfair received a request he write an essay entitled Dissertation on the Progress of the Mathematical and Physical Science since the Revival of Letters in Europe for the supplement to Encyclopaedia Britannica.
- Soon after completing the Dissertation Playfair suffered a severe attack of a disease of the bladder which prevented him from continuing his planned second edition of the Illustrations and interrupted his lectures.
- In June 1819 the bladder disease recurred with increased severity and Playfair returned to Burntisland.
- After an illness lasting a month Playfair died.
- Playfair earned for himself a high reputation in at least three branches of pure science, not primarily as a discoverer but rather as an expounder of theories.
- Playfair's character made him a popular personality.

Born 10 March 1748, Benvie (near Dundee), Scotland. Died 20 July 1819, Burntisland, Fife, Scotland.

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Astronomy, Geometry, Origin Scotland

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive