John Pell and the Obelus

John Pell (1611 - 1685)

John Pell (1611 – 1685)

On March 1, 1611English mathematician John Pell was born. Pell introduced the division sign (obelus, ÷) into England. The obelus was first used by Johann Rahn (1622-1676) in 1659 in Teutsche Algebra. Rahn’s book was interpreted into English and published, with additions made by John Pell.

John Pell attended Trinity College, Cambridge and earned his bachelor’s degree in 1628. Two years later, Pell received his master’s degree and began teaching at Chichester Academy, set up by Samuel Hartlib. For a long time, Pell worked under the influence of Hartlib in the areas of pedagogy, encyclopedism and pansophy, combinatorics and the legacy of Trithemius. In mathematics, he concentrated on expanding the scope of algebra in the theory of equations, and on mathematical tables.

Pell became chair of mathematics in Amsterdam and moved to Breda on the invitation of Frederick Henry, Prince of Orange. John Pell taught at the university from 1646 to 1652. However, he then realized that war between the English and the Dutch was imminent and that he would be in an extremely difficult position in Breda. He returned to England before the outbreak of the First Anglo-Dutch War in July 1652. After his return, Pell was appointed by Oliver Cromwell to a post teaching mathematics in London.

During the 1650s, John Pell moved to Switzerland as Cromwell’s political agent in Zurich. The mathematician, Johann Heinrich Rahn (known as Rhonius) was also located in Switzerland. Rahn is credited with the invention of the division sign ÷ (obelus), however, it has also been attributed to Pell, who taught Rahn a three-column spreadsheet-style technique of tabulation of calculations, and acted as editor for Rahn’s 1659 book Teutsche Algebra in which it appeared. This book by Rahn also contained what would become known as the “Pell equation” ax2-1 =y2. This problem was in fact proposed by Pierre de Fermat [4] first to Bernard Frénicle de Bessy, and in 1657 to all mathematicians. Pell’s connection with the problem is through Rahn. It consisted of publication of the solutions of John Wallis and Lord Brouncker in his edition of Thomas Branker’s Translation of Rhonius’s Algebra (1668); added to his earlier editorial contributions, whatever they were, to the 1659 algebra book written by Rahn.

The term ‘obelus‘ originates in the Ancient Greek word for a sharpened stick, spit, or pointed pillar. Originally the sign was used in ancient manuscripts to mark passages that were suspected of being corrupted or spurious. Even though the symbol was previously used for subtraction, Rahn was the first to use it as a symbol for division. While today most countries use the slash or solidus (/) or the fraction bar as a symbol for division, some still use the obelus symbol, including some parts of Germany and Norway.

After his return to England Pell took orders and in 1661 became rector of Fobbing in Essex. In 1663 he was given an honorary D. D. (Lambeth degree) and was also elected a Fellow of the Royal Society. In 1673 Pell met Leibniz in London, and was able to inform him that some of his mathematical work had been anticipated by François Regnaud and Gabriel Mouton.[5] His devotion to mathematics seems to have interfered with his advancement in the Church and with his private life.

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