# Wallis sentence example

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.In 1764 Byron himself was sent on a voyage of discovery round the world, which led immediately after his return to the despatch of another to complete his work, under the command of Captain Samuel

**Wallis**.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.Advertisement**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.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.Advertisement**Wallis**Budge, to whom the present writer owes his information, was shown the stream in which their last christ had been baptized.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.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.AdvertisementThe 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.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).AdvertisementEssentially, 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.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.AdvertisementObtaining 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.**Wallis**'s Elenchus geometriae Hobbianae, published in 1655 about three months after the De corpore, contained also an elaborate criticism of Hobbes's whole attempt to relay the foundations of mathematical science in its place within the general body of reasoned knowledge - a criticism which, if it failed to allow for the merit of the conception, exposed only too effectually the utter inadequacy of the result.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.He was even unable, in dealing with the elementary conceptions of geometry, to work out with any consistency the few original thoughts he had, and thus became the easy sport of

**Wallis**.He did not scruple, in the ardour of conflict, even to maintain positions that he had resigned in the translation, and he was not afraid to assume the offensive by a counter criticism of three of

**Wallis**'s works then published.In this particular part of his task, it must be allowed, he succeeded very well; his criticism of

**Wallis**'s works, especially the great treatise Arithmetica infinitorum (1655), only showed how little able he was to enter into the meaning of the modern analysis.**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.One of

**Wallis**'s rough sallies in this kind suggested to Hobbes the title of the next rejoinder with which, in 1657, he sought to close the unseemly wrangle.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.He now attacked more in detail but not more happily than before

**Wallis**'s great work, while hardly attempting any further defence of his own positions; also he repelled with some force and dignity the insults that had been heaped upon him, and fought the verbal points, but could not leave the field without making political insinuations against his adversary, quite irrelevant in themselves and only noteworthy as evidence of his own resignation to Cromwell's rule.The thrusts were easily and nimbly parried by

**Wallis**in a reply (Hobbiani puncti dispunctio, 1657) occupied mainly with the verbal questions.**Wallis**having meanwhile published other works and especially a comprehensive treatise on the general principles of calculus (Mathesis universalis, 1657), he might take this occasion of exposing afresh the new-fangled methods of mathematical analysis and reasserting his own earlier positions.**Wallis**, however, would not take the bait.Next year, having solved, as he thought, another ancient crux, the duplication of the cube, he had his solution brought out anonymously at Paris in French, so as to put

**Wallis**and other critics off the scent and extort a judgment that might be withheld from a work of his.**Wallis**, who had deftly steered his course amid all the political changes of the previous years, managing ever to be on the side of the ruling power, was now apparently stung to fury by a wanton allusion in Hobbes's latest dialogue to a passage of his former life (his deciphering for the parliament the king's papers taken at Naseby), whereof he had once boasted but after the Restoration could not speak or hear too little.The propositions on the circle, forty-six in number (shattered by

**Wallis**in 1662), were omitted by Hobbes when he republished the Dialogues in 1668, in the collected edition of his Latin works from which Molesworth reprints.This earlier society had been continued also at Oxford after the year 1649, when

**Wallis**and others of its members received appointments there.But all the more eagerly did he take advantage of

**Wallis**'s loose calumny to strike where he felt himself safe.In this piece, which is of great biographical value, he told his own and

**Wallis**'s " little stories during the time of the late rebellion " with such effect that**Wallis**, like a wise man, attempted no further reply.**Wallis**replied shortly in the Philosophical Transactions (August 1666).**Wallis**, who had promised to leave him alone henceforward, refuted him again before the year was out.**Wallis**replied in the Transactions, and then finally held his hand.He even went the length of bestowing on Hobbes (but not always paying) a pension of £loo, and had his portrait hung up in the royal 4

**Wallis**'s pieces were excluded from the collected edition of his works (1693-1697), and have become extremely rare.His eagerness to defend himself against

**Wallis**'s imputation of disloyalty, and his apologetic dedication of the Problemata physica to the king, are evidence of the hostility with which he was being pressed as early as 1662; but it was not till 1666 that he felt himself seriously in danger.He was a great mathematician in an age which produced Descartes, Fermat, Huygens,

**Wallis**and Roberval.Solutions were furnished by

**Wallis**, Huygens, Wren and others; and Pascal published his own in the form of letters from Amos Dettonville (his assumed name as challenger) to Pierre de Carcavy.Dr John

**Wallis**, the keeper, allowed him free access to the university registers in 1660; "here he layd the foundation of that book which was fourteen years afterwards published, viz.During the last two decades of the 19th century the decrease has been from 30,000 to 17,500 in Tonga; from 11,500 to 8400 in the Cook group; from 8000 to 3600 in

**Wallis**;.John

**Wallis**utilized the intersections of this curve with a right line to solve cubic equations, and Edmund Halley solved sextic equations with the aid of a circle.John

**Wallis**seems to have been the first to push this idea further.Max Muller, Lectures on the Origin and Growth of Religion (Hibbert Lect., 1878), v., and the Vedic treatises of Ludwig, Bergaigne and

**Wallis**.John

**Wallis**, discussing this fraction in his Arithmetica finitorum (1656), gives many of the elementary properties of the convergents to the general continued fraction, including the rule for their formation.John

**Wallis**discussed both the history and properties of the curve in a tract De cycloide published at Oxford in 1659.Having established his priority, Pascal published his investigations, which occasioned a great sensation among his contemporaries, and

**Wallis**was enabled to correct his methods.In a small commonplace book, bearing on the seventh page the date of January 1663/1664, there are several articles on angular sections, and the squaring of curves and " crooked lines that may be squared," several calculations about musical notes, geometrical propositions from Francis Vieta and Frans van Schooten, annotations out of

**Wallis**'s Arithmetic of Infinities, together with observations on refraction, on the grinding of " spherical optic glasses," on the errors of lenses and the method of rectifying them, and on the extraction of all kinds of roots, particularly those " in affected powers."The Principia gives no information on the subject of the notation adopted in the new calculus, and it was not until 1693 that it was com municated to the scientific world in the second volume of Dr

**Wallis**'s works.Newton's admirers in Holland had informed Dr

**Wallis**that Newton's method of fluxions passed there under the name of Leibnitz's Calculus Di fferentialis.It was therefore thought necessary that an early opportunity should be taken of asserting Newton's claim to be the inventor of the method of fluxions, and this was the reason for this method first appearing in

**Wallis**'s works.Passing through the Straits of Magellan, he visited the Tuamotu archipelago, and Tahiti, where the English navigator

**Wallis**had touched eight months before.It was further investigated by John

**Wallis**, Christiaan Huygens (who determined the length of any arc in 1657), and Pierre de Fermat (who evaluated the area between the curve and its asymptote in 1661).Dr

**Wallis**Budge visited several of the far southern sites and made some tentative excavations, but no extensive explorations were undertaken until an unexpected event produced a sudden outburst of activity.**Wallis**Budge, The Egyptian Sudan (2 vols., 1907) and The Anglo-Egyptian Sudan (1095), edited by Count Gleichen.John

**Wallis**, in addition to translating the Conics of Apollonius, published in 1655 an original work entitled De sectionibus conicis nova methodo expositis, in which he treated the curves by the Cartesian method, and derived their properties from the definition in piano, completely ignoring the connexion between the conic sections and a cone.Other theorems were published in his Opera Varia, and in John

**Wallis**'s Commercium epistolicum (1658).The King abdicated the throne on 10 December 1936 for his love for

**Wallis**Simpson.The Duke of Windsor married a commoner,

**Wallis**Simpson.Its Mosquitoes were intended to be the carriers of a variation of the

**Wallis**bomb used by No.617 Squadron on the Ruhr dams.I remain, Sir, Your obedient servant, R.M.

**Wallis**.King of Great Britain in January 1936 he abdicated the throne on 10 December 1936 for his love for

**Wallis**Simpson.He had been given a typewriter by Louisa

**Wallis**, wife of the Hollywood producer Hal**Wallis**, who believed he had talent.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.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.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.He attempted the quadrature of the circle by interpolation, and arrived at the remarkable expression known as

**Wallis**'s Theorem (see Circle, Squaring Of).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.The only offices which Roman Catholics are not legally capable of holding now are the lord chancellorship of England and the lord lieutenancy of Ireland (see, however, Lilly and

**Wallis**, pp. 36-43).Aristarchus of Samos observed at Alexandria 280-264 B.C. His treatise on the magnitudes and distances of the sun and moon, edited by John

**Wallis**in 1688, describes a theoretically valid method for determining the relative distances of the sun and moon by measuring the angle between their centres when half the lunar disk is illuminated; but the time of dichotomy being widely indeterminate, no useful result was thus obtainable.Major Carr, Captains Saurin and Smith, Lieutenant

**Wallis**, two Quartermasters and twenty-eight troopers wounded as well as twenty-four horses.