688:
3025:
40:
4355:
4341:
2456:, was considerably enlarged. This algebra is noteworthy as containing the first systematic use of formulae. A given magnitude is here represented by the numerical ratio which it bears to the unit of the same kind of magnitude: thus, when Wallis wants to compare two lengths he regards each as containing so many units of length. This perhaps will be made clearer by noting that the relation between the space described in any time by a particle moving with a uniform velocity is denoted by Wallis by the formula
4939:
4744:
408:
2528:
552:; that was said to have been the first occasion in Europe on which this theory was publicly maintained in a disputation. His interests, however, centred on mathematics. He received his Bachelor of Arts degree in 1637 and a Master's in 1640, afterwards entering the priesthood. From 1643 to 1649, he served as a nonvoting scribe at the
2971:. The book was based on his father's thoughts and presented one of the earliest arguments for a non-Euclidean hypothesis equivalent to the parallel postulate. After reading this, Wallis then wrote about his ideas as he developed his own thoughts about the postulate, trying to prove it also with similar triangles.
2987:
Another aspect of Wallis's mathematical skills was his ability to do mental calculations. He slept badly and often did mental calculations as he lay awake in his bed. One night he calculated in his head the square root of a number with 53 digits. In the morning he dictated the 27-digit square root of
2978:
is equivalent to the one currently named "Wallis postulate" after him. This postulate states that "On a given finite straight line it is always possible to construct a triangle similar to a given triangle". This result was encompassed in a trend trying to deduce Euclid's fifth from the other four
2210:
563:
Throughout this time, Wallis had been close to the
Parliamentarian party, perhaps as a result of his exposure to Holbeach at Felsted School. He rendered them great practical assistance in deciphering Royalist dispatches. The quality of cryptography at that time was mixed; despite the individual
3153:
Wallis' correspondence also shows details of the way he stood up for himself, when he thought he was under-appreciated, financially or otherwise. He lobbied enthusiastically, both on his own behalf, and that of his relatives, as witnessed by letters to Lord
Nottingham, Richard Hampden and the
3098:
from 1689 also employed Wallis as a cryptographer, sometimes almost on a daily basis. Couriers would bring him letters to be decrypted and waited in front of his study for the product. The king took a personal interest in Wallis' work and well-being as witnessed by a letter he sent to Dutch
2656:
Yet is not that
Supposition (of Negative Quantities) either Unuseful or Absurd; when rightly understood. And though, as to the bare Algebraick Notation, it import a Quantity less than nothing: Yet, when it comes to a Physical Application, it denotes as Real a Quantity as if the Sign were
576:. Wallis realised that the latter were far more secure – even describing them as "unbreakable", though he was not confident enough in this assertion to encourage revealing cryptographic algorithms. He was also concerned about the use of ciphers by foreign powers, refusing, for example,
516:. Wallis was first exposed to mathematics in 1631, at Felsted School (then known as Martin Holbeach's school in Felsted); he enjoyed maths, but his study was erratic, since "mathematics, at that time with us, were scarce looked on as academical studies, but rather mechanical" (
3181:
as it developed over time, played a role in the development of cryptology as a science. Wallis' development of a model of
English grammar, independent of earlier models based on Latin grammar, is a case in point of the way other sciences helped develop cryptology in his view.
3165:
Wallis bitterly complains that a courtier of the
Prussian Elector, by the name of Smetteau, had done him wrong in the matter of just compensation for services rendered to the Elector. In the letter he gives details of what he had done and gives advice on a simple
603:
in a few weeks in 1647. He soon began to write his own treatises, dealing with a wide range of topics, which he continued for the rest of his life. Wallis wrote the first survey about mathematical concepts in
England where he discussed the Hindu-Arabic system.
654:
had earlier taught a deaf man, Alexander Popham, to speak "plainly and distinctly, and with a good and graceful tone". Wallis later claimed credit for this, leading Holder to accuse Wallis of "rifling his
Neighbours, and adorning himself with their spoyls".
3869:
Dr. Wallis (1685) "Two extracts of the
Journal of the Phil. Soc. of Oxford; one containing a paper, communicated March 31, 1685, by the Reverend Dr. Wallis, president of that society, concerning the strength of memory when applied with due attention; … ",
2391:
is impossible since it requires the quadrature of the hyperbola. The solutions given by Neile and Wallis are somewhat similar to that given by van Heuraët, though no general rule is enunciated, and the analysis is clumsy. A third method was suggested by
1896:
675:, who despite his appointment to two professorships never published any mathematical works); while Wallis was perhaps the nation's leading cryptographer and was part of an informal group of scientists that would later become the
3135:
that king
William in 1689 used to cause a crisis in French-Polish diplomatic relations. He was quite open about it and Wallis was rewarded for his role. But Wallis became nervous that the French might take action against him.
2107:
3532:
757:
of
Cavalieri) to be made up of an infinite number of parallel lines, or as I would prefer, of an infinite number of parallelograms of the same altitude; (let the altitude of each one of these be an infinitely small part
2269:
and was the first curved line (other than the circle) whose length was determined, but the extension by Neile and Wallis to an algebraic curve was novel. The cycloid was the next curve rectified; this was done by
2050:
2960:(AD 901), an Arab mathematician, had produced a generalisation of the Pythagorean theorem applicable to all triangles six centuries earlier. It is a reasonable conjecture that Wallis was aware of Thabit's work.
2652:"for negative quantities" and "for operational purposes." This is based on a passage in his 1685 treatise on algebra in which he introduced a number line to illustrate the legitimacy of negative quantities:
671:
of Geometry and Astronomy. In 1649 Wallis was appointed as Savilian Professor of Geometry. Wallis seems to have been chosen largely on political grounds (as perhaps had been his Royalist predecessor
4388:
A Treatise of Algebra, both Historical and Practical. Shewing the Original, Progress, and Advancement thereof, from time to time, and by what Steps it hath attained to the Heighth at which it now is
919:
2101:
ought to be chosen so as to obey the law of this series. This, by an elaborate method that is not described here in detail, leads to a value for the interpolated term which is equivalent to taking
4263:
Wallis, J. (1691). A seventh letter, concerning the sacred Trinity occasioned by a second letter from W.J. / by John Wallis ... (Early English books online). London: Printed for Tho. Parkhurst ...
2475:
is the number representing the ratio of the space described to the unit of length; while the previous writers would have denoted the same relation by stating what is equivalent to the proposition
2452:, preceded by a historical account of the development of the subject, which contains a great deal of valuable information. The second edition, issued in 1693 and forming the second volume of his
1731:
1028:
2912:
3748:
3173:
Wallis' contributions to the art of cryptography were not only of a "technological" character. De Leeuw points out that even the "purely scientific" contributions of Wallis to the science of
2767:
It has been noted that, in an earlier work, Wallis came to the conclusion that the ratio of a positive number to a negative one is greater than infinity. The argument involves the quotient
777:
were systematised and extended, but some ideas were open to criticism. He began, after a short tract on conic sections, by developing the standard notation for powers, extending them from
5021:
679:, he had no particular reputation as a mathematician. Nonetheless, Wallis' appointment proved richly justified by his subsequent work during the 54 years he served as Savilian Professor.
3143:
was cordial. But Leibniz also had cryptographic interests and tried to get Wallis to divulge some of his trade secrets, which Wallis declined to do as a matter of patriotic principle.
1440:
1982:
3132:
1137:
863:
1259:
1763:
1563:
1509:
965:
1079:
2794:
2099:
1948:
1671:
1619:
2979:
postulates which today is known to be impossible. Unlike other authors, he realised that the unbounded growth of a triangle was not guaranteed by the four first postulates.
5036:
2261:
and hyperbola had been (necessarily) ineffectual, it had been supposed that no curves could be rectified, as indeed Descartes had definitely asserted to be the case. The
819:
1771:
508:. He was the third of five children of Revd. John Wallis and Joanna Chapman. He was initially educated at a school in Ashford but moved to James Movat's school in
2938:
2840:
2741:
2698:
2619:
2576:
2814:
2761:
2718:
2675:
2639:
2596:
2549:
2070:
1919:
387:(26 December 1650 – 14 March 1717), MP for Wallingford 1690–1695, married Elizabeth Harris (d. 1693) on 1 February 1682, with issue: one son and two daughters
3409:
2205:{\displaystyle {\frac {\pi }{2}}={\frac {2}{1}}\cdot {\frac {2}{3}}\cdot {\frac {4}{3}}\cdot {\frac {4}{5}}\cdot {\frac {6}{5}}\cdot {\frac {6}{7}}\cdots }
1210:= −1. In the latter case, his interpretation of the result is incorrect. He then showed that similar results may be written down for any curve of the form
3094:
and frequently employed to decipher encrypted intercepted correspondence, though he thought that he was not always adequately rewarded for his work. King
3059:
which he managed to decipher within two hours. This started his career as a cryptographer. He was a moderate supporter of the Parliamentarian side in the
2245:
could be used for the rectification of algebraic curves and gave a solution of the problem to rectify (i.e., find the length of) the semicubical parabola
2992:, the Secretary of the Royal Society, sent a colleague to investigate how Wallis did it. It was considered important enough to merit discussion in the
5031:
619:
28 October] 1703. In 1650, Wallis was ordained as a minister. After, he spent two years with Sir Richard Darley and Lady Vere as a private
4778:
4207:
5061:
4976:
4156:
3063:
and therefore worked as a decipherer of intercepted correspondence for the Parliamentarian leaders. For his services he was rewarded with the
5066:
4440:
734:
in which they were defined analytically. This was the earliest book in which these curves are considered and defined as curves of the second
4971:
3754:
3150:
of 3 August 1689. In it he gives a detailed account of his work on a particular letter and the parts he had encountered difficulties with.
1987:
568:, the principles underlying cipher design and analysis were very poorly understood. Most ciphers were ad hoc methods relying on a secret
3357:
1460:
Wallis showed considerable ingenuity in reducing the equations of curves to the forms given above, but, as he was unacquainted with the
5071:
4986:
5006:
2227:
219:
5081:
3189:
the tricks of the trade. With William he was so successful that he could persuade the government to allow the grandson to get the
3113:
reign directly obtaining foreign intercepted letters was a problem for the English, as they did not have the resources of foreign
4313:
5056:
4334:
611:, by which he incurred the lasting hostility of the Independents. In spite of their opposition he was appointed in 1649 to the
2289:
in 1659. Van Heuraët's method is as follows. He supposes the curve to be referred to rectangular axes; if this is so, and if (
3855:
3811:
3779:
2940:, followed by reasoning similar to Wallis's (he resolved the paradox by distinguishing different kinds of negative numbers).
869:
762:
of the whole altitude, and let the symbol ∞ denote Infinity) and the altitude of all to make up the altitude of the figure."
3830:
4771:
3091:
1353: = 1. He shows that the areas are, respectively, 1, 1/6, 1/30, 1/140, etc. He next considered curves of the form
3719:"How Much Mathematics Is "Hardwired," If Any at All: Biological Evolution, Development, and the Essential Role of Culture"
1676:
971:
472:
3447:
3162:
2849:
773:, the most important of Wallis's works, was published in 1656. In this treatise the methods of analysis of Descartes and
444:
5076:
4652:
4256:
Stedall, Jacqueline A. (2001) "Of Our Own Nation: John Wallis's Account of Mathematical Learning in Medieval England",
1170:, and he proved that the ratio of this area to that of the parallelogram on the same base and of the same height is 1/(
664:
4433:
4350:
3902:
3123:
without their own Black Chambers occasionally made gifts of such intercepted correspondence, like the letter of king
1175:
491:
136:
3472:
5016:
4364:
4294:
451:
295:
4288:
2375:) can be found, the first curve can be rectified. In this way van Heuraët effected the rectification of the curve
5011:
4981:
4764:
4487:
4465:
4457:
4718:
4606:
3879:
1385:
668:
612:
429:
4087:"The Black Chamber in the Dutch Republic during the War of the Spanish Succession and it Aftermath, 1707-1715"
4077:
1953:
5051:
4505:
3146:
Smith gives an example of the painstaking work that Wallis performed, as described by himself in a letter to
616:
557:
458:
276:
272:
191:
75:
51:
1085:
687:
5086:
5041:
5026:
4829:
4670:
4622:
4616:
4475:
4426:
4128:
Leeuw, K. de (2000). "The use of codes and ciphers in the Dutch Republic, mainly during the 18th century".
825:
672:
425:
20:
1216:
667:, that began in 1647, removed many senior academics from their positions, including in November 1648, the
4942:
4747:
3897:, Routledge Library Editions: History & Philosophy of Science, vol. 15, Routledge, p. 157,
1736:
1525:
1471:
925:
541:
113:
1034:
440:
5001:
4805:
3894:
The Common Scientist of the Seventeenth Century: A Study of the Dublin Philosophical Society, 1683–1708
3055:
While employed as lady Vere's chaplain in 1642 Wallis was given an enciphered letter about the fall of
4346:
4273:
4871:
4756:
4700:
3140:
2770:
2075:
1924:
1624:
1572:
2233:
A few years later, in 1659, Wallis published a tract containing the solution of the problems on the
4919:
4676:
4369:
4318:
3226:
2421:
1465:
549:
3628:
1371: = 1 is equal to the area of the rectangle on the same base and of the same altitude as
4996:
4865:
4853:
4553:
4547:
4129:
4086:
3072:
3060:
658:
418:
4308:
4787:
4682:
3193:
of the annual pension of £100 Wallis had received in compensation for his cryptographic work.
3120:
3095:
3082:
Because of his Parliamentarian sympathies Wallis was not employed as a cryptographer after the
2266:
735:
284:
4287:
4024:
3892:
3658:
753:, Wallis popularised the symbol ∞ for infinity. He wrote, "I suppose any plane (following the
607:
Wallis joined the moderate Presbyterians in signing the remonstrance against the execution of
4571:
4330:
4236:
3769:
3024:
1891:{\displaystyle \int _{0}^{1}(1-x^{2})^{0}\,dx\ {\text{ and }}\int _{0}^{1}(1-x^{2})^{1}\,dx,}
1297:
1142:
Leaving the numerous algebraic applications of this discovery, he next proceeded to find, by
791:
774:
646:
and philosophy, and he was involved in devising a system for teaching a deaf boy to speak at
581:
4277:
3674:
3351:
4966:
4961:
4664:
4541:
4257:
4194:
3714:
3670:
3327:
3231:
3155:
3068:
3008:
and Bryennius, and Porphyrius's commentary on Ptolemy. He also published three letters to
2964:
608:
588:
553:
196:
3047:, that remained in print well into the eighteenth century. He also published on theology.
2988:
the number, still entirely from memory. It was a feat that was considered remarkable, and
8:
4895:
4883:
4565:
4304:
3220:
3167:
3124:
3087:
3056:
2949:
2917:
2819:
2644:... And each designs (at least in the same Infinite Line) one Single Point: And but one."
2437:
2429:
2405:
2364:
565:
465:
39:
4354:
4340:
2963:
Wallis was also inspired by the works of Islamic mathematician Sadr al-Tusi, the son of
2723:
2680:
2601:
2558:
4859:
4847:
4376:
4324:
4224:
4164:
4150:
4109:
3696:
3514:
3381:
3297:
3083:
2975:
2968:
2799:
2746:
2703:
2660:
2624:
2581:
2534:
2417:
2262:
2223:
2055:
1904:
719:
573:
3718:
5046:
4991:
4938:
4889:
4877:
4743:
4658:
4583:
4559:
4535:
4386:
4228:
4113:
3898:
3851:
3807:
3775:
3726:
Minnesota Symposium on Child Psychology: Culture and Developmental Systems, Volume 38
3700:
3555:
3215:
3190:
3128:
3103:
3013:
2953:
2425:
2334:
743:
577:
378:
4406:
4246:
Guicciardini, Niccolò (2012) "John Wallis as editor of Newton's Mathematical Work",
4185:
4168:
3318:
3301:
1449:= 2. He stated, but did not prove, the corresponding result for a curve of the form
739:
4835:
4817:
4577:
4493:
4392:
4216:
4202:
4180:
4101:
4073:
3729:
3686:
3678:
3506:
3414:
3313:
3209:
3186:
3178:
3100:
2957:
2413:
2393:
2271:
1461:
778:
647:
628:
596:
237:
209:
3433:
591:
in 1643 – Wallis joined the group of scientists that was later to evolve into the
4907:
4640:
4190:
3834:
3827:
3323:
3197:
3158:
3147:
3044:
3009:
2989:
2424:; but, while Wren and Huygens confined their theory to perfectly elastic bodies (
782:
711:
643:
537:
529:
3581:
3196:
William Blencowe eventually succeeded Wallis as official Cryptographer to Queen
1272:, its area can be determined: thus he says that if the equation of the curve is
393:(1658–1703), married William Benson (1649–1691) of Towcester, died with no issue
4730:
4706:
4529:
4499:
3418:
3185:
Wallis tried to teach his own son John, and his grandson by his daughter Anne,
2843:
2216:
1566:
651:
533:
521:
513:
264:
124:
108:
4360:
4105:
3733:
3682:
3401:
2278:
1363:
and established the theorem that the area bounded by this curve and the lines
1178:. He apparently assumed that the same result would be true also for the curve
659:
Wallis' appointment as Savilian Professor of Geometry at the Oxford University
4955:
4841:
4724:
4688:
4634:
4595:
4523:
4066:
3346:
2440:: these provide a convenient synopsis of what was then known on the subject.
2409:
2277:
Early in 1658 a similar discovery, independent of that of Neile, was made by
2254:
2238:
1673:, it might be supposed that, as an approximation, the area of the semicircle
1516:
731:
676:
615:
at Oxford University, where he lived until his death on 8 November [
592:
505:
373:
311:
291:
280:
161:
57:
3826:
The Mathematics of Egypt, Mesopotamia, China, India, and Islam:A Sourcebook
3361:. Vol. 28 (11th ed.). Cambridge University Press. p. 284–285.
2420:
sent correct and similar solutions, all depending on what is now called the
4913:
4901:
4823:
4646:
4511:
4481:
4414:(Subscription ed.). Canterbury: Cross & Jackman. pp. 139–140.
4220:
3691:
3510:
3114:
2282:
1984:
or 3.26... as the value of π. But, Wallis argued, we have in fact a series
699:
624:
315:
3282:
4925:
4799:
4694:
4589:
3174:
2649:
2301:
is the length of the normal, and if another point whose coordinates are (
319:
178:
87:
4396:
4251:
3385:
3250:
Smith quotes his sometimes acrimonious letters to Nottingham and others.
2241:. In this he incidentally explained how the principles laid down in his
738:. It helped to remove some of the perceived difficulty and obscurity of
432: in this section. Unsourced material may be challenged and removed.
345:
Cambridge University, Emmanuel College, 1632–40; B.A., 1637; M.A., 1640.
4712:
4517:
3518:
3110:
2226:
are also discussed, the subject having been brought into prominence by
1194:
any number positive or negative, but he discussed only the case of the
595:. He was finally able to indulge his mathematical interests, mastering
4786:
4418:
3724:. In Sera, Maria D.; Carlson, Stephanie M.; Maratsos, Michael (eds.).
4281:
2045:{\displaystyle 1,{\tfrac {1}{6}},{\tfrac {1}{30}},{\tfrac {1}{140}},}
1203:
569:
509:
4025:"Original Letter of dr. Wallis with Some Particulars of his Pension"
407:
3350:
3064:
1195:
1143:
707:
703:
635:
620:
540:. As it was intended he should be a doctor, he was sent in 1632 to
303:
141:
128:
318:
and one of the greatest intellectuals of the early renaissance of
3399:
Joan Thirsk (2005). "Blencowe, Anne, Lady Blencowe (1656–1718)".
3005:
2433:
2258:
2234:
759:
307:
298:
and, later, the royal court. He is credited with introducing the
275:
23 November] 1616 – 8 November [
4405:
3559:
3161:
that Smith quotes. In a letter to the English envoy to Prussia,
2846:
came to the same conclusion by considering the geometric series
3918:
Music Theory from Zarlino to Schenker: A Bibliography and Guide
3602:
W. Holder, W. (1668). "Of an Experiment, Concerning Deafness".
3076:
2842:
from the positive side. Wallis was not alone in this thinking:
2333:
is the element of the length of the required curve, we have by
1520:
299:
83:
3642:
The Mathematical Work of John Wallis, D.D., F.R.S. (1616–1703)
639:
560:
in 1644, from which he had to resign following his marriage.
525:
3771:
Negative Math: How Mathematical Rules Can Be Positively Bent
5022:
English Presbyterian ministers of the Interregnum (England)
3804:
The Crest of the Peacock: Non-European Roots of Mathematics
1147:
2527:
246:
3872:
Philosophical Transactions of the Royal Society of London
3448:"WALLIS, John (1650-1717), of Soundness, Nettlebed, Oxon"
3372:
Kearns, D. A. (1958). "John Wallis and complex numbers".
2412:
in 1668 for the consideration of mathematicians. Wallis,
252:
4235:
Stedall, Jacqueline, 2005, "Arithmetica Infinitorum" in
2967:, particularly by al-Tusi's book written in 1298 on the
1765:
might be taken as the geometrical mean of the values of
279:
28 October] 1703) was an English clergyman and
3223:– former ChristChurch school in Ashford renamed in 2010
914:{\displaystyle x^{-n}={\frac {1}{x^{n}}}{\text{ etc.}}}
2854:
2775:
2428:), Wallis considered also imperfectly elastic bodies (
2080:
2028:
2013:
1998:
1962:
1929:
1741:
3740:
2920:
2852:
2822:
2802:
2773:
2749:
2726:
2706:
2683:
2663:
2627:
2604:
2584:
2561:
2537:
2110:
2078:
2058:
1990:
1956:
1927:
1907:
1774:
1739:
1679:
1627:
1575:
1528:
1474:
1388:
1219:
1088:
1037:
974:
928:
872:
828:
794:
283:, who is given partial credit for the development of
255:
243:
4205:(1970). "The autobiography of John Wallis, F.R.S.".
4065:
The initial text of this article was taken from the
3767:
3750:
A treatise of algebra, both historical and practical
1726:{\displaystyle \int _{0}^{1}\!{\sqrt {1-x^{2}}}\,dx}
1023:{\displaystyle x^{2/3}={\sqrt{x^{2}}}{\text{ etc.}}}
342:
School of Martin Holbeach at Felsted, Essex, 1631–2.
249:
5037:
Keepers of the Archives of the University of Oxford
4163:
3497:Yule, G. Udny (1939). "John Wallis, D.D., F.R.S.".
3296:
2907:{\displaystyle {\tfrac {1}{1-x}}=1+x+x^{2}+\cdots }
1445:He illustrated this by the parabola, in which case
587:Returning to London – he had been made chaplain at
381:(30 November 1642 – 6 May 1726) in 1675, with issue
240:
3400:
3139:Wallis relationship with the German mathematician
2932:
2906:
2834:
2808:
2788:
2755:
2735:
2712:
2692:
2669:
2648:Wallis has been credited as the originator of the
2633:
2613:
2590:
2570:
2543:
2204:
2093:
2064:
2044:
1976:
1942:
1913:
1890:
1757:
1725:
1665:
1613:
1557:
1511:, since he was unable to expand this in powers of
1503:
1434:
1253:
1131:
1073:
1022:
959:
913:
857:
813:
4302:
2531:Referring to advancing and retreating from point
2383:but added that the rectification of the parabola
2253:, which had been discovered in 1657 by his pupil
1695:
1379: + 1. This is equivalent to computing
4953:
4248:Notes and Records of the Royal Society of London
4208:Notes and Records of the Royal Society of London
4072:
3937:
3935:
3920:(Stytvesant, NY: Pendragon Press, 1990), p. 374.
3728:. John Wiley & Sons, Inc. pp. 83–124 .
3499:Notes and Records of the Royal Society of London
3271:The mathematical work of John Wallis (1616-1703)
2052:... and therefore the term interpolated between
4131:Cryptology and statecraft in the Dutch Republic
4078:"A Short Account of the History of Mathematics"
3659:"Historical Objections Against the Number Line"
3617:Philosophical Transactions of the Royal Society
3604:Philosophical Transactions of the Royal Society
2677:; but to be interpreted in a contrary sense...
682:
4047:
3652:
3650:
3644:. Chelsea Publishing Co., New York, NY. p. 18.
2297:) are the coordinates of any point on it, and
4772:
4434:
4173:Bulletin of the American Mathematical Society
3962:
3932:
3916:David Damschoder and David Russell Williams,
3552:The Codebreakers: The Story of Secret Writing
3306:Bulletin of the American Mathematical Society
2948:He is usually credited with the proof of the
2222:In this work the formation and properties of
1296:/3 + ... . He then applied this to the
4127:
4084:
3878: : 1269-1271. Available on-line at:
3848:The History of Mathematics / An Introduction
3761:
3413:(online ed.). Oxford University Press.
3016:, which was being used in England's organs.
2436:(centres of gravity), and in 1670 by one on
2396:in 1660, but it is inelegant and laborious.
572:, as opposed to systems based on a variable
4331:"Archival material relating to John Wallis"
4298:. London: Smith, Elder & Co. 1885–1900.
4007:
3647:
3398:
3039:, published in 1687, was very popular. The
634:Besides his mathematical works he wrote on
368:– 16 March 1687). They had three children:
339:Grammar School at Tenterden, Kent, 1625–31.
4779:
4765:
4441:
4427:
4403:
4353:
4339:
4155:: CS1 maint: location missing publisher (
3998:
3989:
3980:
3971:
3944:
3850:(7th ed.), McGraw-Hill, p. 566,
3774:. Princeton University Press. p. 22.
3565:
3050:
2432:). This was followed in 1669 by a work on
1515:. He laid down, however, the principle of
528:. By this time, he also was proficient in
38:
4184:
3828:Victor J. Katz Princeton University Press
3690:
3631:, maths.ox.ac.uk. Accessed 19 April 2024.
3582:"Find could end 350-year science dispute"
3477:Early Modern Letters Online : Person
3317:
1878:
1819:
1716:
1435:{\displaystyle \int _{0}^{1}x^{1/m}\,dx.}
1422:
698:Wallis made significant contributions to
492:Learn how and when to remove this message
330:
290:Between 1643 and 1689 he served as chief
4241:Landmark Writings in Western Mathematics
4022:
3345:
3341:
3339:
3337:
3023:
2526:
1977:{\displaystyle 4{\sqrt {\tfrac {2}{3}}}}
1268:of a curve can be expanded in powers of
730:In 1655, Wallis published a treatise on
686:
524:, Wallis learned how to speak and write
19:For other people named John Wallis, see
4448:
4314:MacTutor History of Mathematics Archive
3953:
3923:
3656:
3531:
3410:Oxford Dictionary of National Biography
3403:Oxford Dictionary of National Biography
4954:
4381:
4201:
3890:
3845:
3801:
3753:. London: Richard Davis. p. 265.
3746:
3371:
3212:, an asteroid that was named after him
3004:Wallis translated into Latin works of
2816:approaches and then crosses the point
2399:
1132:{\displaystyle x^{p/q}={\sqrt{x^{p}}}}
377:(4 June 1656 – 5 April 1718), married
5062:Original fellows of the Royal Society
5032:Fellows of Queens' College, Cambridge
4977:Alumni of Emmanuel College, Cambridge
4760:
4422:
3713:
3334:
3177:in the field of the "rationality" of
858:{\displaystyle x^{-1}={\frac {1}{x}}}
5067:Participants in the Savoy Conference
3806:(2 ed.). Penguin. p. 337.
3554:, New York: Macmillan, p. 169,
3549:
3496:
2257:. Since all attempts to rectify the
1254:{\displaystyle y=\sum _{m}^{}ax^{m}}
765:
725:
564:successes of mathematicians such as
556:. He was elected to a fellowship at
430:adding citations to reliable sources
401:
314:. John Wallis was a contemporary of
4972:17th-century English mathematicians
3657:Heeffer, Albrecht (10 March 2011).
3273:, Taylor and Francis, 1938, p. 109.
1758:{\displaystyle {\tfrac {1}{4}}\pi }
1558:{\displaystyle y={\sqrt {1-x^{2}}}}
1504:{\displaystyle y={\sqrt {1-x^{2}}}}
960:{\displaystyle x^{1/2}={\sqrt {x}}}
13:
3012:concerning tuning. He approved of
1074:{\displaystyle x^{1/n}={\sqrt{x}}}
665:Parliamentary visitation of Oxford
14:
5098:
5072:People educated at Felsted School
4987:British historians of mathematics
4351:National Portrait Gallery, London
4267:
3490:
3170:for the use of Johnston himself.
2999:
1345:, etc., taken between the limits
718:I (1695) he introduced the term "
512:in 1625 following an outbreak of
16:English mathematician (1616–1703)
5007:English male non-fiction writers
4937:
4742:
4365:Post-Reformation Digital Library
4295:Dictionary of National Biography
4289:"Wallis, John (1616-1703)"
4169:"John Wallis As a Cryptographer"
3302:"John Wallis As a Cryptographer"
2796:and considering what happens as
1264:and hence that, if the ordinate
623:. In 1661, he was one of twelve
406:
236:
5082:Savilian Professors of Geometry
4186:10.1090/s0002-9904-1917-03015-7
4016:
3910:
3884:
3863:
3839:
3820:
3795:
3707:
3634:
3622:
3609:
3596:
3574:
3543:
3525:
3319:10.1090/s0002-9904-1917-03015-7
3244:
2789:{\displaystyle {\tfrac {1}{x}}}
2578:doth as truly design the Point
2094:{\displaystyle {\tfrac {1}{6}}}
1950:; this is equivalent to taking
1943:{\displaystyle {\tfrac {2}{3}}}
1666:{\displaystyle y=(1-x^{2})^{1}}
1614:{\displaystyle y=(1-x^{2})^{0}}
1569:of the ordinates of the curves
1519:. Thus, as the ordinate of the
517:
417:needs additional citations for
3465:
3440:
3392:
3365:
3290:
3276:
3263:
3019:
2996:of the Royal Society of 1685.
2522:
2285:in his edition of Descartes's
1869:
1849:
1810:
1790:
1654:
1634:
1602:
1582:
1176:Cavalieri's quadrature formula
751:Treatise on the Conic Sections
302:∞ to represent the concept of
137:Cavalieri's quadrature formula
1:
5057:Mathematics of infinitesimals
3768:Martínez, Alberto A. (2006).
3257:
3200:after Wallis' death in 1703.
3041:Grammatica linguae Anglicanae
2982:
584:students about cryptography.
362:
357:On 14 March 1645, he married
336:Cambridge, M.A., Oxford, D.D.
3891:Hoppen, K. Theodore (2013),
3452:History of Parliament Online
3434:UK public library membership
3119:as yet, but allies like the
2363:. Hence, if the area of the
2281:, and this was published by
1174: + 1), extending
683:Contributions to mathematics
580:'s request of 1697 to teach
325:
21:John Wallis (disambiguation)
7:
4943:University of Oxford portal
4790:of the University of Oxford
4748:University of Oxford portal
3537:A Cambridge Alumni Database
3203:
3109:In these early days of the
2943:
2237:which had been proposed by
2230:'s use of these fractions.
2215:(which is now known as the
1150:enclosed between the curve
542:Emmanuel College, Cambridge
114:Emmanuel College, Cambridge
10:
5103:
4412:Men of Kent and Kentishmen
4137:. Amsterdam. pp. 6–51
4059:
3539:. University of Cambridge.
2994:Philosophical Transactions
2443:
1464:, he could not effect the
613:Savilian Chair of Geometry
558:Queens' College, Cambridge
544:. While there, he kept an
192:Queens' College, Cambridge
54:23 November] 1616
18:
5077:People from Ashford, Kent
4935:
4795:
4740:
4701:Edward Charles Titchmarsh
4605:
4464:
4454:
4404:Hutchinson, John (1892).
4391:. Oxford: Richard Davis.
4106:10.1017/S0018246X98008292
3846:Burton, David M. (2011),
3734:10.1002/9781119301981.ch3
3683:10.1007/s11191-011-9349-0
3141:Gottfried Wilhelm Leibniz
2448:In 1685 Wallis published
1288:+ ..., its area would be
352:
225:
215:
205:
184:
174:
167:
156:
152:Susanna Glynde (m. 1645)
148:
120:
104:
96:
65:
46:
37:
30:
4677:Henry John Stephen Smith
4347:Portraits of John Wallis
4319:University of St Andrews
4029:The Gentleman's Magazine
3533:"Wallys, John (WLS632J)"
3269:Joseph Frederick Scott,
3237:
2976:Euclid's fifth postulate
2422:conservation of momentum
2329:is a constant; then, if
1466:quadrature of the circle
1162:-axis, and any ordinate
755:Geometry of Indivisibles
550:circulation of the blood
504:John Wallis was born in
5017:English music theorists
3968:De Leeuw (1999), p. 139
3941:De Leeuw (1999), p. 138
3880:Royal Society of London
3675:2011Sc&Ed..20..863H
3663:Science & Education
3374:The Mathematics Teacher
3358:Encyclopædia Britannica
3284:Random House Dictionary
3061:First English Civil War
3051:Wallis as cryptographer
2243:Arithmetica Infinitorum
814:{\displaystyle x^{0}=1}
771:Arithmetica Infinitorum
627:representatives at the
548:on the doctrine of the
397:
271:; 3 December [
5012:English mathematicians
4982:British cryptographers
4788:Keeper of the Archives
4683:James Joseph Sylvester
4456:Chairs established by
4221:10.1098/rsnr.1970.0003
4094:The Historical Journal
4053:De Leeuw (1999), p.143
4023:Cave, E., ed. (1788).
3833:1 October 2016 at the
3629:John Wallis: Time-line
3511:10.1098/rsnr.1939.0012
3419:10.1093/ref:odnb/41326
3121:Elector of Brandenburg
3032:
2934:
2908:
2836:
2810:
2790:
2765:
2757:
2737:
2714:
2694:
2671:
2645:
2635:
2615:
2592:
2572:
2545:
2408:was propounded by the
2267:Evangelista Torricelli
2265:had been rectified by
2206:
2095:
2066:
2046:
1978:
1944:
1915:
1892:
1759:
1727:
1667:
1615:
1559:
1505:
1436:
1255:
1237:
1133:
1075:
1024:
961:
915:
859:
815:
710:, and the analysis of
695:
348:D.D. at Oxford in 1654
331:Educational background
285:infinitesimal calculus
268:
4375:- digital facsimile,
4372:A treatise of algebra
4237:Ivor Grattan-Guinness
4085:Leeuw, K. de (1999).
4013:De Leeuw (2000), p. 9
3802:Joseph, G.G. (2000).
3747:Wallis, John (1685).
3227:Wallis's conical edge
3090:he was sought out by
3027:
2935:
2909:
2837:
2811:
2791:
2758:
2738:
2715:
2695:
2672:
2654:
2636:
2616:
2593:
2573:
2553:A treatise of algebra
2546:
2530:
2309:) is taken such that
2207:
2096:
2067:
2047:
1979:
1945:
1916:
1893:
1760:
1728:
1668:
1616:
1560:
1506:
1437:
1256:
1226:
1190:is any constant, and
1134:
1076:
1025:
962:
916:
860:
816:
690:
129:Inventing the symbol
50:3 December [
5052:Linguists of English
4695:Godfrey Harold Hardy
4361:Works by John Wallis
4335:UK National Archives
4325:Galileo Project page
4305:Robertson, Edmund F.
4258:Historia Mathematica
4035:(June 1788): 479–480
3550:Kahn, David (1967),
3352:"Wallis, John"
2965:Nasir al-Din al-Tusi
2918:
2850:
2820:
2800:
2771:
2747:
2724:
2704:
2681:
2661:
2625:
2602:
2582:
2559:
2535:
2108:
2076:
2056:
1988:
1954:
1925:
1905:
1772:
1737:
1677:
1625:
1573:
1526:
1472:
1468:, whose equation is
1386:
1217:
1086:
1035:
972:
926:
870:
826:
792:
589:St Gabriel Fenchurch
554:Westminster Assembly
520:). At the school in
426:improve this article
306:. He similarly used
197:University of Oxford
78:28 October 1703]
74:(aged 86) [
5087:Westminster Divines
5042:History of calculus
5027:English Protestants
4896:William Abel Pantin
4884:Reginald Lane Poole
4607:Savilian Professors
4466:Savilian Professors
4449:Savilian Professors
4407:"John Wallis"
4397:10.3931/e-rara-8842
4370:John Wallis (1685)
4303:O'Connor, John J.;
4165:Smith, David Eugene
3584:. BBC. 26 July 2008
3298:Smith, David Eugene
3221:John Wallis Academy
3168:substitution cipher
3125:Louis XIV of France
3088:Glorious Revolution
2950:Pythagorean theorem
2933:{\displaystyle x=2}
2835:{\displaystyle x=0}
2720:Yards Forward; and
2621:designed the Point
2430:inelastic collision
2406:collision of bodies
2400:Collision of bodies
2224:continued fractions
1848:
1789:
1694:
1403:
1367: = 0 and
1349: = 0 and
669:Savilian Professors
601:Clavis Mathematicae
374:Anne, Lady Blencowe
162:Anne, Lady Blencowe
4878:Thomas Vere Bayne
4860:George Leigh Cooke
4848:Whittington Landon
4377:Linda Hall Library
4274:The Correspondence
4243:. Elsevier: 23–32.
3640:Scott, J.F. 1981.
3473:"Elizabeth Wallis"
3084:Stuart Restoration
3037:Institutio logicae
3033:
2969:parallel postulate
2930:
2904:
2871:
2832:
2806:
2786:
2784:
2753:
2736:{\displaystyle -3}
2733:
2710:
2693:{\displaystyle +3}
2690:
2667:
2646:
2631:
2614:{\displaystyle +3}
2611:
2588:
2571:{\displaystyle -3}
2568:
2551:, Wallis wrote in
2541:
2418:Christiaan Huygens
2404:The theory of the
2263:logarithmic spiral
2202:
2091:
2089:
2062:
2042:
2037:
2022:
2007:
1974:
1971:
1940:
1938:
1911:
1888:
1834:
1775:
1755:
1750:
1723:
1680:
1663:
1611:
1555:
1501:
1432:
1389:
1251:
1129:
1071:
1020:
957:
911:
855:
811:
720:continued fraction
696:
140:Coining the term "
5002:English logicians
4949:
4948:
4890:Strickland Gibson
4754:
4753:
4659:Abraham Robertson
4584:George Efstathiou
4560:Charles Pritchard
4536:Abraham Robertson
3857:978-0-07-338315-6
3813:978-0-14-027778-4
3781:978-0-691-12309-7
3619:, supplement, 10.
3432:(Subscription or
3232:Wallis' integrals
3216:Invisible College
3129:John III Sobieski
3104:Anthonie Heinsius
3029:Opera mathematica
3014:equal temperament
2954:similar triangles
2870:
2809:{\displaystyle x}
2783:
2756:{\displaystyle 3}
2713:{\displaystyle 3}
2670:{\displaystyle +}
2634:{\displaystyle C}
2591:{\displaystyle D}
2544:{\displaystyle A}
2426:elastic collision
2335:similar triangles
2197:
2184:
2171:
2158:
2145:
2132:
2119:
2088:
2065:{\displaystyle 1}
2036:
2021:
2006:
1972:
1970:
1937:
1914:{\displaystyle 1}
1832:
1828:
1749:
1714:
1553:
1499:
1127:
1069:
1018:
1013:
955:
909:
904:
853:
779:positive integers
766:Integral calculus
744:analytic geometry
726:Analytic geometry
716:Opera Mathematica
692:Opera mathematica
578:Gottfried Leibniz
502:
501:
494:
476:
379:Sir John Blencowe
229:
228:
220:William Brouncker
206:Academic advisors
169:Scientific career
5094:
4941:
4836:Benjamin Buckler
4818:Bernard Gardiner
4806:Gerard Langbaine
4781:
4774:
4767:
4758:
4757:
4746:
4578:Donald Blackwell
4494:Christopher Wren
4458:Sir Henry Savile
4443:
4436:
4429:
4420:
4419:
4415:
4409:
4400:
4357:
4343:
4338:
4321:
4299:
4291:
4232:
4198:
4188:
4160:
4154:
4146:
4144:
4142:
4136:
4124:
4122:
4120:
4091:
4081:
4074:W. W. Rouse Ball
4054:
4051:
4045:
4044:
4042:
4040:
4020:
4014:
4011:
4005:
4004:Smith, pp. 94-96
4002:
3996:
3995:Smith, pp. 89-93
3993:
3987:
3986:Smith, pp. 85-87
3984:
3978:
3977:Smith, pp. 83-84
3975:
3969:
3966:
3960:
3957:
3951:
3950:Smith, pp. 83-86
3948:
3942:
3939:
3930:
3927:
3921:
3914:
3908:
3907:
3888:
3882:
3867:
3861:
3860:
3843:
3837:
3824:
3818:
3817:
3799:
3793:
3792:
3790:
3788:
3765:
3759:
3758:
3744:
3738:
3737:
3723:
3711:
3705:
3704:
3694:
3654:
3645:
3638:
3632:
3626:
3620:
3613:
3607:
3600:
3594:
3593:
3591:
3589:
3578:
3572:
3569:
3563:
3562:
3547:
3541:
3540:
3529:
3523:
3522:
3494:
3488:
3487:
3485:
3483:
3469:
3463:
3462:
3460:
3458:
3444:
3438:
3437:
3429:
3427:
3425:
3406:
3396:
3390:
3389:
3369:
3363:
3362:
3354:
3343:
3332:
3331:
3321:
3294:
3288:
3280:
3274:
3267:
3251:
3248:
3210:31982 Johnwallis
3187:William Blencowe
3179:Natural language
3101:Grand pensionary
3086:, but after the
2958:Thabit Ibn Qurra
2939:
2937:
2936:
2931:
2913:
2911:
2910:
2905:
2897:
2896:
2872:
2869:
2855:
2841:
2839:
2838:
2833:
2815:
2813:
2812:
2807:
2795:
2793:
2792:
2787:
2785:
2776:
2762:
2760:
2759:
2754:
2742:
2740:
2739:
2734:
2719:
2717:
2716:
2711:
2699:
2697:
2696:
2691:
2676:
2674:
2673:
2668:
2643:
2640:
2638:
2637:
2632:
2620:
2618:
2617:
2612:
2597:
2595:
2594:
2589:
2577:
2575:
2574:
2569:
2550:
2548:
2547:
2542:
2414:Christopher Wren
2272:Christopher Wren
2211:
2209:
2208:
2203:
2198:
2190:
2185:
2177:
2172:
2164:
2159:
2151:
2146:
2138:
2133:
2125:
2120:
2112:
2100:
2098:
2097:
2092:
2090:
2081:
2071:
2069:
2068:
2063:
2051:
2049:
2048:
2043:
2038:
2029:
2023:
2014:
2008:
1999:
1983:
1981:
1980:
1975:
1973:
1963:
1961:
1949:
1947:
1946:
1941:
1939:
1930:
1920:
1918:
1917:
1912:
1897:
1895:
1894:
1889:
1877:
1876:
1867:
1866:
1847:
1842:
1833:
1830:
1826:
1818:
1817:
1808:
1807:
1788:
1783:
1764:
1762:
1761:
1756:
1751:
1742:
1732:
1730:
1729:
1724:
1715:
1713:
1712:
1697:
1693:
1688:
1672:
1670:
1669:
1664:
1662:
1661:
1652:
1651:
1620:
1618:
1617:
1612:
1610:
1609:
1600:
1599:
1567:geometrical mean
1564:
1562:
1561:
1556:
1554:
1552:
1551:
1536:
1510:
1508:
1507:
1502:
1500:
1498:
1497:
1482:
1462:binomial theorem
1441:
1439:
1438:
1433:
1421:
1420:
1416:
1402:
1397:
1362:
1344:
1329:
1314:
1260:
1258:
1257:
1252:
1250:
1249:
1236:
1234:
1138:
1136:
1135:
1130:
1128:
1126:
1121:
1120:
1111:
1106:
1105:
1101:
1080:
1078:
1077:
1072:
1070:
1068:
1060:
1055:
1054:
1050:
1029:
1027:
1026:
1021:
1019:
1016:
1014:
1012:
1007:
1006:
997:
992:
991:
987:
966:
964:
963:
958:
956:
951:
946:
945:
941:
920:
918:
917:
912:
910:
907:
905:
903:
902:
890:
885:
884:
864:
862:
861:
856:
854:
846:
841:
840:
820:
818:
817:
812:
804:
803:
783:rational numbers
648:Littlecote House
629:Savoy Conference
597:William Oughtred
497:
490:
486:
483:
477:
475:
434:
410:
402:
391:Elizabeth Wallis
367:
364:
262:
261:
258:
257:
254:
251:
248:
245:
242:
216:Notable students
210:William Oughtred
132:
116:
91:
79:
73:
42:
28:
27:
5102:
5101:
5097:
5096:
5095:
5093:
5092:
5091:
4952:
4951:
4950:
4945:
4931:
4908:Jeffrey Hackney
4791:
4785:
4755:
4750:
4736:
4641:Nathaniel Bliss
4608:
4601:
4476:John Bainbridge
4467:
4460:
4450:
4447:
4329:
4286:
4270:
4148:
4147:
4140:
4138:
4134:
4118:
4116:
4089:
4062:
4057:
4052:
4048:
4038:
4036:
4021:
4017:
4012:
4008:
4003:
3999:
3994:
3990:
3985:
3981:
3976:
3972:
3967:
3963:
3958:
3954:
3949:
3945:
3940:
3933:
3928:
3924:
3915:
3911:
3905:
3889:
3885:
3868:
3864:
3858:
3844:
3840:
3835:Wayback Machine
3825:
3821:
3814:
3800:
3796:
3786:
3784:
3782:
3766:
3762:
3745:
3741:
3721:
3712:
3708:
3692:1854/LU-1891046
3669:(9): 863–880 .
3655:
3648:
3639:
3635:
3627:
3623:
3614:
3610:
3606:3, pp. 665–668.
3601:
3597:
3587:
3585:
3580:
3579:
3575:
3570:
3566:
3548:
3544:
3530:
3526:
3495:
3491:
3481:
3479:
3471:
3470:
3466:
3456:
3454:
3446:
3445:
3441:
3431:
3423:
3421:
3397:
3393:
3370:
3366:
3344:
3335:
3295:
3291:
3281:
3277:
3268:
3264:
3260:
3255:
3254:
3249:
3245:
3240:
3206:
3159:Harbord Harbord
3148:Richard Hampden
3092:lord Nottingham
3053:
3045:English grammar
3022:
3010:Henry Oldenburg
3002:
2990:Henry Oldenburg
2985:
2946:
2919:
2916:
2915:
2914:, evaluated at
2892:
2888:
2859:
2853:
2851:
2848:
2847:
2821:
2818:
2817:
2801:
2798:
2797:
2774:
2772:
2769:
2768:
2763:Yards Backward.
2748:
2745:
2744:
2725:
2722:
2721:
2705:
2702:
2701:
2682:
2679:
2678:
2662:
2659:
2658:
2641:
2626:
2623:
2622:
2603:
2600:
2599:
2583:
2580:
2579:
2560:
2557:
2556:
2536:
2533:
2532:
2525:
2517:
2511:
2504:
2498:
2491:
2484:
2446:
2402:
2189:
2176:
2163:
2150:
2137:
2124:
2111:
2109:
2106:
2105:
2079:
2077:
2074:
2073:
2057:
2054:
2053:
2027:
2012:
1997:
1989:
1986:
1985:
1960:
1955:
1952:
1951:
1928:
1926:
1923:
1922:
1906:
1903:
1902:
1872:
1868:
1862:
1858:
1843:
1838:
1831: and
1829:
1813:
1809:
1803:
1799:
1784:
1779:
1773:
1770:
1769:
1740:
1738:
1735:
1734:
1708:
1704:
1696:
1689:
1684:
1678:
1675:
1674:
1657:
1653:
1647:
1643:
1626:
1623:
1622:
1605:
1601:
1595:
1591:
1574:
1571:
1570:
1547:
1543:
1535:
1527:
1524:
1523:
1493:
1489:
1481:
1473:
1470:
1469:
1412:
1408:
1404:
1398:
1393:
1387:
1384:
1383:
1354:
1331:
1316:
1301:
1245:
1241:
1235:
1230:
1218:
1215:
1214:
1122:
1116:
1112:
1110:
1097:
1093:
1089:
1087:
1084:
1083:
1064:
1059:
1046:
1042:
1038:
1036:
1033:
1032:
1015:
1008:
1002:
998:
996:
983:
979:
975:
973:
970:
969:
950:
937:
933:
929:
927:
924:
923:
906:
898:
894:
889:
877:
873:
871:
868:
867:
845:
833:
829:
827:
824:
823:
799:
795:
793:
790:
789:
768:
728:
712:infinite series
685:
661:
644:English grammar
498:
487:
481:
478:
435:
433:
423:
411:
400:
365:
355:
333:
328:
239:
235:
201:
139:
134:
130:
127:
112:
92:
82:
80:
71:
70:8 November 1703
69:
61:
55:
33:
24:
17:
12:
11:
5:
5100:
5090:
5089:
5084:
5079:
5074:
5069:
5064:
5059:
5054:
5049:
5044:
5039:
5034:
5029:
5024:
5019:
5014:
5009:
5004:
4999:
4997:Deaf education
4994:
4989:
4984:
4979:
4974:
4969:
4964:
4947:
4946:
4936:
4933:
4932:
4930:
4929:
4923:
4917:
4911:
4905:
4899:
4893:
4887:
4881:
4875:
4872:John Griffiths
4869:
4863:
4857:
4851:
4845:
4842:Thomas Wenman
4839:
4833:
4827:
4821:
4815:
4809:
4803:
4796:
4793:
4792:
4784:
4783:
4776:
4769:
4761:
4752:
4751:
4741:
4738:
4737:
4735:
4734:
4731:Frances Kirwan
4728:
4722:
4719:Richard Taylor
4716:
4710:
4707:Michael Atiyah
4704:
4698:
4692:
4686:
4680:
4674:
4668:
4665:Stephen Rigaud
4662:
4656:
4650:
4644:
4638:
4632:
4626:
4620:
4613:
4611:
4603:
4602:
4600:
4599:
4593:
4587:
4581:
4575:
4572:Harry Plaskett
4569:
4566:Herbert Turner
4563:
4557:
4554:William Donkin
4551:
4548:George Johnson
4545:
4542:Stephen Rigaud
4539:
4533:
4530:Thomas Hornsby
4527:
4521:
4515:
4509:
4503:
4500:Edward Bernard
4497:
4491:
4485:
4479:
4472:
4470:
4462:
4461:
4455:
4452:
4451:
4446:
4445:
4438:
4431:
4423:
4417:
4416:
4401:
4379:
4367:
4358:
4344:
4327:
4322:
4300:
4284:
4269:
4268:External links
4266:
4265:
4264:
4261:
4254:
4244:
4233:
4199:
4161:
4125:
4100:(1): 133–156.
4082:
4070:
4061:
4058:
4056:
4055:
4046:
4015:
4006:
3997:
3988:
3979:
3970:
3961:
3952:
3943:
3931:
3922:
3909:
3903:
3883:
3862:
3856:
3838:
3819:
3812:
3794:
3780:
3760:
3755:MPIWG:GK8U243K
3739:
3706:
3646:
3633:
3621:
3608:
3595:
3573:
3564:
3542:
3524:
3489:
3464:
3439:
3391:
3380:(5): 373–374.
3364:
3349:, ed. (1911).
3347:Chisholm, Hugh
3333:
3289:
3275:
3261:
3259:
3256:
3253:
3252:
3242:
3241:
3239:
3236:
3235:
3234:
3229:
3224:
3218:
3213:
3205:
3202:
3163:James Johnston
3116:Black Chambers
3052:
3049:
3043:was a work on
3021:
3018:
3001:
3000:Musical theory
2998:
2984:
2981:
2974:He found that
2945:
2942:
2929:
2926:
2923:
2903:
2900:
2895:
2891:
2887:
2884:
2881:
2878:
2875:
2868:
2865:
2862:
2858:
2844:Leonhard Euler
2831:
2828:
2825:
2805:
2782:
2779:
2752:
2732:
2729:
2709:
2689:
2686:
2666:
2630:
2610:
2607:
2587:
2567:
2564:
2540:
2524:
2521:
2520:
2519:
2515:
2509:
2502:
2496:
2489:
2482:
2469:
2468:
2445:
2442:
2401:
2398:
2367:of the point (
2217:Wallis product
2213:
2212:
2201:
2196:
2193:
2188:
2183:
2180:
2175:
2170:
2167:
2162:
2157:
2154:
2149:
2144:
2141:
2136:
2131:
2128:
2123:
2118:
2115:
2087:
2084:
2061:
2041:
2035:
2032:
2026:
2020:
2017:
2011:
2005:
2002:
1996:
1993:
1969:
1966:
1959:
1936:
1933:
1910:
1899:
1898:
1887:
1884:
1881:
1875:
1871:
1865:
1861:
1857:
1854:
1851:
1846:
1841:
1837:
1825:
1822:
1816:
1812:
1806:
1802:
1798:
1795:
1792:
1787:
1782:
1778:
1754:
1748:
1745:
1722:
1719:
1711:
1707:
1703:
1700:
1692:
1687:
1683:
1660:
1656:
1650:
1646:
1642:
1639:
1636:
1633:
1630:
1608:
1604:
1598:
1594:
1590:
1587:
1584:
1581:
1578:
1550:
1546:
1542:
1539:
1534:
1531:
1496:
1492:
1488:
1485:
1480:
1477:
1443:
1442:
1431:
1428:
1425:
1419:
1415:
1411:
1407:
1401:
1396:
1392:
1300:of the curves
1262:
1261:
1248:
1244:
1240:
1233:
1229:
1225:
1222:
1140:
1139:
1125:
1119:
1115:
1109:
1104:
1100:
1096:
1092:
1081:
1067:
1063:
1058:
1053:
1049:
1045:
1041:
1030:
1011:
1005:
1001:
995:
990:
986:
982:
978:
967:
954:
949:
944:
940:
936:
932:
921:
901:
897:
893:
888:
883:
880:
876:
865:
852:
849:
844:
839:
836:
832:
821:
810:
807:
802:
798:
767:
764:
740:René Descartes
732:conic sections
727:
724:
684:
681:
660:
657:
652:William Holder
566:François Viète
500:
499:
414:
412:
405:
399:
396:
395:
394:
388:
382:
359:Susanna Glynde
354:
351:
350:
349:
346:
343:
340:
337:
332:
329:
327:
324:
227:
226:
223:
222:
217:
213:
212:
207:
203:
202:
200:
199:
194:
188:
186:
182:
181:
176:
172:
171:
165:
164:
158:
154:
153:
150:
146:
145:
125:Wallis product
122:
121:Known for
118:
117:
109:Felsted School
106:
102:
101:
98:
94:
93:
81:
67:
63:
62:
56:
48:
44:
43:
35:
34:
31:
15:
9:
6:
4:
3:
2:
5099:
5088:
5085:
5083:
5080:
5078:
5075:
5073:
5070:
5068:
5065:
5063:
5060:
5058:
5055:
5053:
5050:
5048:
5045:
5043:
5040:
5038:
5035:
5033:
5030:
5028:
5025:
5023:
5020:
5018:
5015:
5013:
5010:
5008:
5005:
5003:
5000:
4998:
4995:
4993:
4990:
4988:
4985:
4983:
4980:
4978:
4975:
4973:
4970:
4968:
4965:
4963:
4960:
4959:
4957:
4944:
4940:
4934:
4927:
4924:
4921:
4918:
4915:
4912:
4909:
4906:
4903:
4900:
4897:
4894:
4891:
4888:
4885:
4882:
4879:
4876:
4873:
4870:
4867:
4864:
4861:
4858:
4855:
4852:
4849:
4846:
4843:
4840:
4837:
4834:
4831:
4828:
4825:
4822:
4819:
4816:
4813:
4810:
4807:
4804:
4801:
4798:
4797:
4794:
4789:
4782:
4777:
4775:
4770:
4768:
4763:
4762:
4759:
4749:
4745:
4739:
4732:
4729:
4726:
4725:Nigel Hitchin
4723:
4720:
4717:
4714:
4711:
4708:
4705:
4702:
4699:
4696:
4693:
4690:
4689:William Esson
4687:
4684:
4681:
4678:
4675:
4672:
4669:
4666:
4663:
4660:
4657:
4654:
4651:
4648:
4645:
4642:
4639:
4636:
4635:Edmond Halley
4633:
4630:
4627:
4624:
4621:
4618:
4615:
4614:
4612:
4610:
4604:
4597:
4596:Steven Balbus
4594:
4591:
4588:
4585:
4582:
4579:
4576:
4573:
4570:
4567:
4564:
4561:
4558:
4555:
4552:
4549:
4546:
4543:
4540:
4537:
4534:
4531:
4528:
4525:
4524:James Bradley
4522:
4519:
4516:
4513:
4510:
4507:
4506:David Gregory
4504:
4501:
4498:
4495:
4492:
4489:
4486:
4483:
4480:
4477:
4474:
4473:
4471:
4469:
4463:
4459:
4453:
4444:
4439:
4437:
4432:
4430:
4425:
4424:
4421:
4413:
4408:
4402:
4398:
4394:
4390:
4389:
4384:
4380:
4378:
4374:
4373:
4368:
4366:
4362:
4359:
4356:
4352:
4348:
4345:
4342:
4336:
4332:
4328:
4326:
4323:
4320:
4316:
4315:
4310:
4309:"John Wallis"
4306:
4301:
4297:
4296:
4290:
4285:
4283:
4279:
4275:
4272:
4271:
4262:
4259:
4255:
4253:
4250:66(1): 3–17.
4249:
4245:
4242:
4238:
4234:
4230:
4226:
4222:
4218:
4214:
4210:
4209:
4204:
4200:
4196:
4192:
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4170:
4166:
4162:
4158:
4152:
4133:
4132:
4126:
4115:
4111:
4107:
4103:
4099:
4095:
4088:
4083:
4080:(4 ed.).
4079:
4075:
4071:
4068:
4067:public domain
4064:
4063:
4050:
4034:
4030:
4026:
4019:
4010:
4001:
3992:
3983:
3974:
3965:
3956:
3947:
3938:
3936:
3926:
3919:
3913:
3906:
3904:9781135028541
3900:
3896:
3895:
3887:
3881:
3877:
3873:
3866:
3859:
3853:
3849:
3842:
3836:
3832:
3829:
3823:
3815:
3809:
3805:
3798:
3783:
3777:
3773:
3772:
3764:
3756:
3752:
3751:
3743:
3735:
3731:
3727:
3720:
3716:
3715:Núñez, Rafael
3710:
3702:
3698:
3693:
3688:
3684:
3680:
3676:
3672:
3668:
3664:
3660:
3653:
3651:
3643:
3637:
3630:
3625:
3618:
3612:
3605:
3599:
3583:
3577:
3568:
3561:
3557:
3553:
3546:
3538:
3534:
3528:
3520:
3516:
3512:
3508:
3504:
3500:
3493:
3478:
3474:
3468:
3453:
3449:
3443:
3435:
3420:
3416:
3412:
3411:
3405:
3404:
3395:
3387:
3383:
3379:
3375:
3368:
3360:
3359:
3353:
3348:
3342:
3340:
3338:
3329:
3325:
3320:
3315:
3311:
3307:
3303:
3299:
3293:
3286:
3285:
3279:
3272:
3266:
3262:
3247:
3243:
3233:
3230:
3228:
3225:
3222:
3219:
3217:
3214:
3211:
3208:
3207:
3201:
3199:
3194:
3192:
3188:
3183:
3180:
3176:
3171:
3169:
3164:
3160:
3157:
3151:
3149:
3144:
3142:
3137:
3134:
3130:
3126:
3122:
3118:
3117:
3112:
3107:
3105:
3102:
3097:
3093:
3089:
3085:
3080:
3078:
3074:
3070:
3066:
3062:
3058:
3048:
3046:
3042:
3038:
3030:
3026:
3017:
3015:
3011:
3007:
2997:
2995:
2991:
2980:
2977:
2972:
2970:
2966:
2961:
2959:
2955:
2951:
2941:
2927:
2924:
2921:
2901:
2898:
2893:
2889:
2885:
2882:
2879:
2876:
2873:
2866:
2863:
2860:
2856:
2845:
2829:
2826:
2823:
2803:
2780:
2777:
2764:
2750:
2730:
2727:
2707:
2687:
2684:
2664:
2653:
2651:
2628:
2608:
2605:
2585:
2565:
2562:
2554:
2538:
2529:
2514:
2508:
2501:
2495:
2488:
2481:
2478:
2477:
2476:
2474:
2466:
2462:
2459:
2458:
2457:
2455:
2451:
2441:
2439:
2435:
2431:
2427:
2423:
2419:
2415:
2411:
2410:Royal Society
2407:
2397:
2395:
2390:
2386:
2382:
2378:
2374:
2370:
2366:
2362:
2359:
2355:
2352:. Therefore,
2351:
2347:
2343:
2339:
2336:
2332:
2328:
2324:
2320:
2316:
2312:
2308:
2304:
2300:
2296:
2292:
2288:
2284:
2280:
2275:
2273:
2268:
2264:
2260:
2256:
2255:William Neile
2252:
2248:
2244:
2240:
2239:Blaise Pascal
2236:
2231:
2229:
2225:
2220:
2218:
2199:
2194:
2191:
2186:
2181:
2178:
2173:
2168:
2165:
2160:
2155:
2152:
2147:
2142:
2139:
2134:
2129:
2126:
2121:
2116:
2113:
2104:
2103:
2102:
2085:
2082:
2059:
2039:
2033:
2030:
2024:
2018:
2015:
2009:
2003:
2000:
1994:
1991:
1967:
1964:
1957:
1934:
1931:
1908:
1885:
1882:
1879:
1873:
1863:
1859:
1855:
1852:
1844:
1839:
1835:
1823:
1820:
1814:
1804:
1800:
1796:
1793:
1785:
1780:
1776:
1768:
1767:
1766:
1752:
1746:
1743:
1720:
1717:
1709:
1705:
1701:
1698:
1690:
1685:
1681:
1658:
1648:
1644:
1640:
1637:
1631:
1628:
1606:
1596:
1592:
1588:
1585:
1579:
1576:
1568:
1548:
1544:
1540:
1537:
1532:
1529:
1522:
1518:
1517:interpolation
1514:
1494:
1490:
1486:
1483:
1478:
1475:
1467:
1463:
1458:
1456:
1452:
1448:
1429:
1426:
1423:
1417:
1413:
1409:
1405:
1399:
1394:
1390:
1382:
1381:
1380:
1378:
1374:
1370:
1366:
1361:
1357:
1352:
1348:
1342:
1338:
1334:
1327:
1323:
1319:
1312:
1308:
1304:
1299:
1295:
1291:
1287:
1283:
1279:
1275:
1271:
1267:
1246:
1242:
1238:
1231:
1227:
1223:
1220:
1213:
1212:
1211:
1209:
1205:
1201:
1197:
1193:
1189:
1185:
1181:
1177:
1173:
1169:
1165:
1161:
1157:
1153:
1149:
1145:
1123:
1117:
1113:
1107:
1102:
1098:
1094:
1090:
1082:
1065:
1061:
1056:
1051:
1047:
1043:
1039:
1031:
1009:
1003:
999:
993:
988:
984:
980:
976:
968:
952:
947:
942:
938:
934:
930:
922:
899:
895:
891:
886:
881:
878:
874:
866:
850:
847:
842:
837:
834:
830:
822:
808:
805:
800:
796:
788:
787:
786:
784:
780:
776:
772:
763:
761:
756:
752:
747:
745:
741:
737:
733:
723:
721:
717:
713:
709:
705:
701:
693:
689:
680:
678:
677:Royal Society
674:
670:
666:
656:
653:
649:
645:
641:
637:
632:
630:
626:
622:
618:
614:
610:
605:
602:
598:
594:
593:Royal Society
590:
585:
583:
579:
575:
571:
567:
561:
559:
555:
551:
547:
543:
539:
535:
531:
527:
523:
519:
515:
511:
507:
506:Ashford, Kent
496:
493:
485:
474:
471:
467:
464:
460:
457:
453:
450:
446:
443: –
442:
441:"John Wallis"
438:
437:Find sources:
431:
427:
421:
420:
415:This section
413:
409:
404:
403:
392:
389:
386:
383:
380:
376:
375:
371:
370:
369:
360:
347:
344:
341:
338:
335:
334:
323:
321:
317:
313:
312:infinitesimal
309:
305:
301:
297:
293:
292:cryptographer
288:
286:
282:
281:mathematician
278:
274:
270:
266:
260:
233:
224:
221:
218:
214:
211:
208:
204:
198:
195:
193:
190:
189:
187:
183:
180:
177:
173:
170:
166:
163:
160:3, including
159:
155:
151:
147:
143:
138:
133:
126:
123:
119:
115:
110:
107:
103:
99:
95:
89:
85:
77:
68:
64:
59:
58:Ashford, Kent
53:
49:
45:
41:
36:
29:
26:
22:
4928: (2020)
4922: (2000)
4920:Simon Bailey
4916: (1995)
4914:David Vaisey
4910: (1987)
4904: (1969)
4902:Trevor Aston
4898: (1946)
4892: (1927)
4886: (1909)
4880: (1885)
4874: (1857)
4868: (1826)
4866:Philip Bliss
4862: (1818)
4856: (1815)
4854:James Ingram
4850: (1796)
4844: (1781)
4838: (1777)
4832: (1767)
4830:John Swinton
4826: (1726)
4824:Francis Wise
4820: (1703)
4814: (1658)
4811:
4808: (1644)
4802: (1634)
4733: (2017)
4727: (1997)
4721: (1995)
4715: (1969)
4709: (1963)
4703: (1931)
4697: (1919)
4691: (1897)
4685: (1883)
4679: (1861)
4673: (1827)
4671:Baden Powell
4667: (1810)
4661: (1797)
4655: (1766)
4649: (1765)
4647:Joseph Betts
4643: (1742)
4637: (1704)
4631: (1649)
4628:
4625: (1631)
4623:Peter Turner
4619: (1619)
4617:Henry Briggs
4598: (2012)
4592: (1999)
4586: (1994)
4580: (1960)
4574: (1932)
4568: (1893)
4562: (1870)
4556: (1842)
4550: (1839)
4544: (1827)
4538: (1810)
4532: (1763)
4526: (1721)
4520: (1712)
4514: (1709)
4512:John Caswell
4508: (1691)
4502: (1673)
4496: (1661)
4490: (1649)
4484: (1642)
4482:John Greaves
4478: (1620)
4468:of Astronomy
4411:
4387:
4383:Wallis, John
4382:
4371:
4312:
4293:
4247:
4240:
4212:
4206:
4179:(2): 82–96.
4176:
4172:
4139:. Retrieved
4130:
4117:. Retrieved
4097:
4093:
4049:
4037:. Retrieved
4032:
4028:
4018:
4009:
4000:
3991:
3982:
3973:
3964:
3959:Smith, p. 87
3955:
3946:
3929:Smith, p. 83
3925:
3917:
3912:
3893:
3886:
3875:
3871:
3865:
3847:
3841:
3822:
3803:
3797:
3785:. Retrieved
3770:
3763:
3749:
3742:
3725:
3709:
3666:
3662:
3641:
3636:
3624:
3616:
3611:
3603:
3598:
3586:. Retrieved
3576:
3567:
3551:
3545:
3536:
3527:
3505:(1): 74–82.
3502:
3498:
3492:
3480:. Retrieved
3476:
3467:
3455:. Retrieved
3451:
3442:
3422:. Retrieved
3408:
3402:
3394:
3377:
3373:
3367:
3356:
3312:(2): 82–96.
3309:
3305:
3292:
3283:
3278:
3270:
3265:
3246:
3195:
3191:survivorship
3184:
3172:
3152:
3145:
3138:
3115:
3108:
3081:
3073:St. Martin's
3054:
3040:
3036:
3034:
3028:
3003:
2993:
2986:
2973:
2962:
2947:
2766:
2743:, signifies
2700:, signifies
2655:
2647:
2552:
2512:
2506:
2499:
2493:
2486:
2479:
2472:
2470:
2464:
2460:
2453:
2449:
2447:
2403:
2388:
2384:
2380:
2376:
2372:
2368:
2360:
2357:
2353:
2349:
2345:
2341:
2337:
2330:
2326:
2322:
2318:
2314:
2310:
2306:
2302:
2298:
2294:
2290:
2286:
2283:van Schooten
2276:
2250:
2246:
2242:
2232:
2221:
2214:
1900:
1512:
1459:
1454:
1450:
1446:
1444:
1376:
1372:
1368:
1364:
1359:
1355:
1350:
1346:
1340:
1336:
1332:
1325:
1321:
1317:
1310:
1306:
1302:
1293:
1289:
1285:
1281:
1277:
1273:
1269:
1265:
1263:
1207:
1202:= 2 and the
1199:
1191:
1187:
1183:
1179:
1171:
1167:
1163:
1159:
1155:
1151:
1141:
770:
769:
754:
750:
748:
729:
715:
700:trigonometry
697:
691:
673:Peter Turner
662:
633:
625:Presbyterian
606:
600:
586:
562:
545:
503:
488:
479:
469:
462:
455:
448:
436:
424:Please help
419:verification
416:
390:
384:
372:
358:
356:
289:
231:
230:
185:Institutions
168:
72:(1703-11-08)
25:
4967:1703 deaths
4962:1616 births
4926:Faye McLeod
4812:John Wallis
4800:Brian Twyne
4629:John Wallis
4609:of Geometry
4590:Joseph Silk
4278:John Wallis
4203:Scriba, C J
3175:linguistics
3096:William III
3069:St. Gabriel
3020:Other works
2956:. However,
2650:number line
2523:Number line
2279:van Heuraët
1144:integration
518:Scriba 1970
385:John Wallis
366: 1600
320:mathematics
232:John Wallis
179:Mathematics
97:Nationality
88:Oxfordshire
32:John Wallis
4956:Categories
4713:Ioan James
4653:John Smith
4518:John Keill
4252:Jstor link
3436:required.)
3258:References
3111:Williamite
2983:Calculator
1298:quadrature
1017: etc.
908: etc.
742:' work on
582:Hanoverian
482:April 2024
452:newspapers
296:Parliament
135:Extending
4488:Seth Ward
4229:145393357
4215:: 17–46.
4151:cite book
4114:162387765
4069:resource:
4039:20 August
3701:120058064
3482:21 August
3457:21 August
3424:21 August
3106:in 1689.
3057:Chicester
2902:⋯
2864:−
2728:−
2563:−
2555:that "...
2287:Geometria
2274:in 1658.
2228:Brouncker
2200:⋯
2187:⋅
2174:⋅
2161:⋅
2148:⋅
2135:⋅
2114:π
1901:that is,
1856:−
1836:∫
1797:−
1777:∫
1753:π
1733:which is
1702:−
1682:∫
1641:−
1589:−
1541:−
1487:−
1391:∫
1228:∑
1206:in which
1204:hyperbola
1198:in which
879:−
835:−
775:Cavalieri
714:. In his
609:Charles I
570:algorithm
510:Tenterden
326:Biography
269:Wallisius
105:Education
90:, England
60:, England
5047:Infinity
4992:Calculus
4385:(1685).
4167:(1917).
4141:4 August
4119:3 August
4076:(1908).
3831:Archived
3717:(2017).
3615:Holder,
3560:63016109
3386:27955680
3300:(1917).
3204:See also
3127:to king
2944:Geometry
2505: :
2485: :
2438:dynamics
2348: :
2340: :
2325:, where
2321: :
2313: :
1375: :
1292:+ x/2 +
1196:parabola
1186:, where
708:geometry
704:calculus
636:theology
621:chaplain
304:infinity
157:Children
142:momentum
4349:at the
4260:28: 73.
4239:, ed.,
4195:1560009
4060:Sources
3671:Bibcode
3519:3087253
3328:1560009
3065:Livings
3006:Ptolemy
2450:Algebra
2444:Algebra
2434:statics
2259:ellipse
2235:cycloid
1565:is the
522:Felsted
466:scholar
310:for an
100:English
4227:
4193:
4112:
3901:
3854:
3810:
3787:9 June
3778:
3699:
3558:
3517:
3430:
3384:
3326:
3133:Poland
3077:London
3031:, 1657
2952:using
2642:
2471:where
2416:, and
2394:Fermat
1827:
1521:circle
1146:, the
736:degree
694:, 1699
538:Hebrew
536:, and
530:French
514:plague
468:
461:
454:
447:
439:
353:Family
316:Newton
300:symbol
175:Fields
149:Spouse
84:Oxford
4225:S2CID
4135:(PDF)
4110:S2CID
4090:(PDF)
3722:(PDF)
3697:S2CID
3588:5 May
3515:JSTOR
3382:JSTOR
3238:Notes
2598:; as
2454:Opera
2365:locus
640:logic
534:Greek
526:Latin
473:JSTOR
459:books
265:Latin
4282:EMLO
4157:link
4143:2023
4121:2023
4041:2023
3899:ISBN
3852:ISBN
3808:ISBN
3789:2013
3776:ISBN
3590:2018
3556:LCCN
3484:2023
3459:2023
3426:2023
3198:Anne
3071:and
3035:His
2354:h ds
2072:and
1921:and
1621:and
1148:area
663:The
617:O.S.
445:news
398:Life
294:for
277:O.S.
273:O.S.
76:O.S.
66:Died
52:O.S.
47:Born
4393:doi
4363:at
4280:in
4276:of
4217:doi
4181:doi
4102:doi
3730:doi
3687:hdl
3679:doi
3507:doi
3415:doi
3314:doi
3131:of
3075:in
3067:of
2219:).
2034:140
1335:= (
1320:= (
1305:= (
781:to
760:1/∞
749:In
722:".
599:'s
574:key
546:act
428:by
308:1/∞
4958::
4410:.
4333:.
4317:,
4311:,
4307:,
4292:.
4223:.
4213:25
4211:.
4191:MR
4189:.
4177:24
4175:.
4171:.
4153:}}
4149:{{
4108:.
4098:42
4096:.
4092:.
4033:63
4031:.
4027:.
3934:^
3876:15
3874:,
3695:.
3685:.
3677:.
3667:20
3665:.
3661:.
3649:^
3535:.
3513:.
3501:.
3475:.
3450:.
3407:.
3378:51
3376:.
3355:.
3336:^
3324:MR
3322:.
3310:24
3308:.
3304:.
3156:MP
3079:.
2492:=
2465:vt
2463:=
2389:ax
2387:=
2381:ax
2379:=
2371:,
2361:dx
2356:=
2344:=
2342:dx
2338:ds
2331:ds
2317:=
2305:,
2293:,
2251:ay
2249:=
2019:30
1457:.
1453:=
1358:=
1339:−
1330:,
1324:−
1315:,
1309:−
1284:+
1280:+
1276:=
1184:ax
1182:=
1166:=
1158:,
1154:=
785::
746:.
706:,
702:,
650:.
642:,
638:,
631:.
532:,
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322:.
287:.
267::
263:;
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2874:=
2867:x
2861:1
2857:1
2830:0
2827:=
2824:x
2804:x
2781:x
2778:1
2751:3
2731:3
2708:3
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2665:+
2629:C
2609:3
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2461:s
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2377:y
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2247:x
2195:7
2192:6
2182:5
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2127:2
2122:=
2117:2
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2083:1
2060:1
2040:,
2031:1
2025:,
2016:1
2010:,
2004:6
2001:1
1995:,
1992:1
1968:3
1965:2
1958:4
1935:3
1932:2
1909:1
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1597:2
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1580:=
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1533:=
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1476:y
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1451:y
1447:m
1430:.
1427:x
1424:d
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1414:/
1410:1
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1373:m
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1311:x
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1224:=
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1208:m
1200:m
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1168:h
1164:x
1160:x
1156:x
1152:y
1124:q
1118:p
1114:x
1108:=
1103:q
1099:/
1095:p
1091:x
1066:n
1062:x
1057:=
1052:n
1048:/
1044:1
1040:x
1010:3
1004:2
1000:x
994:=
989:3
985:/
981:2
977:x
953:x
948:=
943:2
939:/
935:1
931:x
900:n
896:x
892:1
887:=
882:n
875:x
851:x
848:1
843:=
838:1
831:x
809:1
806:=
801:0
797:x
495:)
489:(
484:)
480:(
470:·
463:·
456:·
449:·
422:.
361:(
259:/
256:s
253:ɪ
250:l
247:ɒ
244:w
241:ˈ
238:/
234:(
144:"
131:∞
23:.
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