The Arenarius and Dimensio Circuli, with Eutocius' commentary on the latter, were edited by Wallis with Latin translation and notes in 1678 (Oxford), and the Arenarius was also published in English by George Anderson (London, 1784), with useful notes and illustrations.
Wallis Budge (1896, 2 vols., with English translation); the Syriac text of pseudo-Callisthenes by Budge (Cambridge, 1889); cp. K.
With the exception of Augustus de Morgan, Boole was probably the first English mathematician since the time of John Wallis who had also written upon logic. His novel views of logical method were due to the same profound confidence in symbolic reasoning to which he had successfully trusted in mathematical investigation.
In 1767 Samuel Wallis re-discovered it, and named it King George's Island.
All voyagers agree that for varied beauty of form and colour the Society Islands are unsurpassed in the Pacific. Innumerable rills gather in lovely streams, and, after heavy rains, torrents precipitate themselves in grand cascades from the mountain cliffs - a feature so striking as to have attracted the attention of all voyagers, from Wallis downwards.
The expedition, consisting of the " Dolphin " commanded by Wallis, and the " Swallow " under Captain Philip Carteret, sailed in September 1766, but the ships were separated on entering the Pacific from the Strait of Magellan.
Wallis discovered Tahiti on the 19th of June 1767, and he gave a detailed account of that island.
Wallis and Carteret were followed very closely by the French expedition of Bougainville, which sailed from Nantes in November 1766.
The next visit was that of Samuel Wallis in 1767, followed in 1773 by that of Captain Cook.
Another edition of his Poetical Works (1899) has a preface and bibliography by Alfred Wallis, and a complete edition of his poems by C. E.
Kepler's Problem, namely, that of finding the co-ordinates of a planet at a given time, which is equivalent - given the mean anomaly - to that of determining the true anomaly, was solved approximately by Kepler, and more completely by Wallis, Newton and others.
Although these conclusions were arrived at independently, and, as it would seem, several years previous to their publication, they were in great measure anticipated by the communications on the same subject of John Wallis and Christopher Wren, made respectively in November and December 1668.
John Wallis and Lord Brounker jointly obtained a tedious solution which was published in 1658, and afterwards in 1668 by John Pell in his Algebra.
Continued fractions, one of the earliest examples of which is Lord Brouncker's expression for the ratio of the circumference to the diameter of a circle (see Circle), were elaborately discussed by John Wallis and Leonhard Euler; the convergency of series treated by Newton, Euler and the Bernoullis; the binomial theorem, due originally to Newton and subsequently expanded by Euler and others, was used by Joseph Louis Lagrange as the basis of his Calcul des Fonctions.
See also John Wallis, Opera Mathematica (1693-1699), and Charles Hutton, Mathematical and Philosophical Dictionary (1815), article " Algebra."
Wallis Budge, to whom the present writer owes his information, was shown the stream in which their last christ had been baptized.
Of New Caledonia; the Huon Islands, a practically barren group; the Wallis Archipelago; and Futuna and Alofa, S.
Of the Wallis group.
Wallis Budge (British Museum, 1909); F.
Wallis Budge, The Egyptian Sudan (London, 1907); J.
"In the beginning of my mathematical studies, when I was perusing the works of the celebrated Dr Wallis, and considering the series by the interpolation of which he exhibits the area of the circle and hyperbola (for instance, in this series of curves whose common base 0 or axis is x, and the ordinates respectively (I -xx)l, (i (I &c), I perceived that if the areas of the alternate curves, which are x, x 3x 3, x &c., could be interpolated, we should obtain the areas of the intermediate ones, the first of which (I -xx) 1 is the area of the circle.
Local tradition connects the name with that of Wallis or Wallace, a Scottish buccaneer, who, in 1638, settled, with a party of logwood cutters, on St George's Cay, a small island off the town.
In the 18th century the names Wallis and Belize were used interchangeably for the town, the river and the whole country.
Pell's connexion with the problem simply consists of the publication of the solutions of John Wallis and Lord Brounker in his edition of Branker's Translation of Rhonius's Algebra 0.668).
Editio princeps by Wallis (1688); Fortia d'Urban (1810); Nizze (1856).
JOHN WALLIS (1616-1703), English mathematician, logician and grammarian, was born on the 23rd of November 1616 at Ashford, in Kent, of which parish his father, Rev. John Wallis (1567-1622), was incumbent.
When the Independents obtained the superiority Wallis adhered to the Solemn League and Covenant.
While complying with the terms of the Act of Uniformity, Wallis seems always to have retained moderate and rational notions of ecclesiastical polity.
The works of Wallis are numerous, and relate to a multiplicity of subjects.
In the same work Wallis obtained an expression for the length of the element of a curve, which reduced the problem of rectification to that of quadrature.
For the prolonged conflict between Hobbes and Wallis, see Hobbes, Thomas.
Uvea Wallis Archipelago >>
In 1767 Samuel Wallis worked through the central part of the Paumotus, and visited Tahiti and the Marianas, while his companion Philip Carteret discovered Pitcairn, and visited Santa Cruz, the Solomons and New Pomerania.
The remaining fragments were, under the directions of the Royal Society, reduced by Dr Wallis to a compact form, with the heading Astronomia Kepleriana defensa et promota, and published with numerous extracts from the letters of Horrocks to Crabtree, and a sketch of the author's life, in a volume entitled Jeremiae Horroccii opera posthuma (London, 1672).
Essentially, therefore, Descartes's process is that known later as the process of isoperimeters, and often attributed wholly to Schwab.2 In 16J5 appeared the Arithmetica Infinitorum of John Wallis, where numerous problems of quadrature are dealt with, the curves being now represented in Cartesian co-ordinates, and algebra playing an important part.
The work of Wallis had evidently an important influence on the next notable personality in the history of the subject, James Gregory, who lived during the period when the higher algebraic analysis was coming into power, and whose genius helped materially to develop it.
(2) Pappi alexandrini secundi libri mathematicae collectionis fragmentum e codice MS. edidit latinum fecit notisque illustravit Johannes Wallis (Oxonii, 1688).
(b) Wallis showed that such bodies reduce one another to a joint mass with a common velocity equal to their joint momentum divided by their joint weights or masses.
He made experiments, simultaneously with Wallis and Wren, on the collision of hard spherical bodies, and his statement of the results (1669) included a clear enunciation of the conservation of linear momentum, as demonstrated for these cases of collision, and apparently correct in certain other cases, mass being estimated by weight.
War went on for four years; the successes gained by Russia were outweighed by Austria's various reverses, terminating by the defeat of Wallis at Krotzka, and the peace concluded at Belgrade was a triumph for Turkish diplomacy.
Ward's colleague, the more famous John Wallis, Savilian professor of geometry from 1649, had been privy to the challenge thrown out in 1654, and it was arranged that they should critically dispose of the De corpore between them.
Wallis was to confine himself to the mathematical chapters, and set to work at once with characteristic energy.
Obtaining also a copy of the work as it had been printed before Hobbes had any doubt of the validity of his solutions, Wallis was able to track his whole course front the time of Ward's provocation - his passage from exultation to doubt, from doubt to confessed impotence, yet still without abandoning the old assumption of confident strength; and all his turnings and windings were now laid bare in one of the most trenchant pieces of controversial writing ever penned.
The consequence was that, when not spending himself in vain attempts to solve the impossible problems that have always waylaid the fancy of self-sufficient beginners, he took an interest only in the elements of geometry, and never had any notion of the full scope of mathematical science, undergoing as it then was (and not least at the hands of Wallis) the extraordinary development which made it before the end of the century the potent instrument of physical discovery which it became in the hands of Newton.
I.) to appear in 1656, take care to remove some of the worst mistakes exposed by Wallis, and, while leaving out all the references to Vindex, now profess to make, in altered form, a series of mere " attempts " at quadrature; but he was far from yielding the ground to the enemy.
Wallis, on his side, was not less ready to keep up the game in English than he had been to begin it in Latin.
Wallis having been betrayed originally by his fatal cleverness into the pettiest carping at words, Hobbes had retorted in kind, and then it became a high duty in the other to defend his Latin with great parade of learning and give fresh provocation.
Arguing in the Lessons that a mathematical point must have quantity, though this were not reckoned, he had explained the Greek word UTCy v, used for a point, to mean a visible mark made with a hot iron;; whereupon he was charged by Wallis with gross ignorance for confounding artypii and o - y,ua.
Hence the title of his new piece: Ertl/mat eyewperpias, aypoudas, avruroXcreias, apaBeias, or Marks of the Absurd Geometry, Rural Language, Scottish Church Politics, and Barbarisms of John Wallis, Professor of Geometry and Doctor of Divinity (E.
The thrusts were easily and nimbly parried by Wallis in a reply (Hobbiani puncti dispunctio, 1657) occupied mainly with the verbal questions.