# John Wallis

John Wallis , born the November 23rd 1616 with Ashford, and dead the October 28th 1703 with Oxford, is a Mathématicien English. Its work is precursory those of Newton. It is also precursory Phonétique, education of the deaf persons and Orthophonie.

## Biography

Wallis made its studies with Cambridge, with the Emmanuel College initially, then with the Queen' S college. Studying the Theology initially, it is ordered in 1640. It is reorientated then towards mathematics and shows a great talent for the Cryptographie during the civil war, by deciphering the messages of the Royalist are. It occupies then the Savilian flesh of geometry to the Université of Oxford, succeeding Peter Turner, returned because royalist. It was one of the founders of the Royal Society.

## Work

### In mathematics

Its work relates to mainly the differential and integral calculus. One owes him the symbol of the Infini ($\ infty \,$) that one uses nowadays.
It assisted the astronomer Jeremiah Horrocks for its calculations of éphéméride S, in particular at the time of the Transit of Venus of 1639.

It solved the problem of the vault quarrable (1692), posed by Vincenzo Viviani: to find a window in a hemispherical vault so that the remainder of the vault is quarrable, i.e. whose surface can be written C ², where C is a constructible number with the rule and the compass .

#### Product of Wallis

$\ frac \left\{\ pi\right\} \left\{2\right\} = \ frac \left\{2\right\} \left\{1\right\} \ times \ frac \left\{2\right\} \left\{3\right\} \ times \ frac \left\{4\right\} \left\{3\right\} \ times \ frac \left\{4\right\} \left\{5\right\} \ times \ frac \left\{6\right\} \left\{5\right\} \ times \ frac \left\{6\right\} \left\{7\right\} \ times \ frac \left\{8\right\} \left\{7\right\} \ times \ frac \left\{8\right\} \left\{9\right\} \ cdots \ frac \left\{2k\right\} \left\{2k-1\right\} \ times \ frac \left\{2k\right\} \left\{2k+1\right\} \ cdots$

$=2 \ times \ frac \left\{3^2-1\right\} \left\{3^2\right\} \ times \ frac \left\{5^2-1\right\} \left\{5^2\right\} \ times \ frac \left\{7^2-1\right\} \left\{7^2\right\} \ cdots=2 \ times \ left \left(1 \ frac \left\{1\right\} \left\{3^2\right\} \ right\right) \ left \left(1 \ frac \left\{1\right\} \left\{5^2\right\} \ right\right) \ left \left(1 \ frac \left\{1\right\} \left\{7^2\right\} \ right\right) \ cdots$

$=2 \ times \ prod_ \left\{k=1\right\} ^ \ infty \ left \left(1 - \ frac \left\{1\right\} \left\{\left(2k+1\right) ^2\right\} \ right\right)$

This formula made it possible William Brouncker to obtain a development in Fraction continues generalized of 4/π.

### In phonetics and education of the deaf-mute ones

Wallis is the author of the first treaty of Phonétique of the English language, in introduction to its Grammatica Linguae Anglicanae . It is also known like precursor of the education of the deaf-mute ones. It exposed its practice in two letters, published several times in addition to Manche. Its work influenced the abbot Charles-Michel of the Sword, which adapted to the French language its method of demutisation of the deaf-mute ones. Wallis also applied phonetics, from a clinical point of view, with the Dyslalies functional calculuses and the correction of the foreign accents. It had posterior epistolary exchanges on these questions with another precursor in phonetics and orthoepy: Johann Conrad Amman.

## Works

• Arithmetica Infinitorum , Oxford, 1655
• Opera , 1670 - 1671
• Treatise off Algebra , London, 1685
• Mathesis Universalis , Oxford, 1685
• Of sectionibus conicis
• Operum mathematicorum leave PRIMA , Oxford, 1657
• Tractatus Prœmialis. Of loquela, sive Literarum Formatione omnium & genuino Sound system , Oxford, Leon Lichfield, 1653. (Preliminary Treaty. Word or formation of all the letters and original sound.
• Grammatica Linguae Anglicanae, cui praefigitur of loquela sive of sonorum omnium loquelarum formatione tractatus grammatico physicus , Oxford, Leon Lichfield, 1653. (Grammar of the English language, which is preceded by a physico-grammatical treaty on the word or the formation of the sounds.
• the letter of Dr. John Wallis in Robert Boyle, Philosophical Transactions , 1670.
• the letter of Dr. John Wallis to Mr. Thomas Beverly, Philosophical Transactions , 1698.
• Three republications of the only phonetic part (1721, Königsberg, 1727 and 1740, Leiden), comprising in appendix the treaty of Johann Conrad Amman Surdus loquens , were also published.

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