Книга: John Wallis «Mathematical Tables»
Производитель: "Книга по Требованию" Viz. a table of logarithms, from 1 to 101000. To which is added (upon the same page) the differences and proportional parts, whereby the logarithm of any number under 10, 000, 000 may be easily found. Tables of natural sines, tangents, and secants, with their Logarithms, and logarithmick Differences to every Minute of the Quadrant. Tables of natural versed sines, and their Logarithms, to every minute of the Quadrant. With their construction and use Воспроизведено в оригинальной авторской орфографии издания 1726 года (издательство `London`). ISBN:978-5-8739-7847-2 Издательство: "Книга по Требованию" (2011)
ISBN: 978-5-8739-7847-2 |
John Wallis
Infobox Scientist
name = John Wallis
box_width = 300px
|300px
image_width = 300px
caption =
birth_date = birth date|1616|11|23
birth_place =
death_date = death date and age|1703|10|28|1616|11|23
death_place =
residence =
citizenship =
nationality = English
ethnicity =
field =
work_institutions =
alma_mater =
doctoral_advisor =
doctoral_students =
known_for =
author_abbrev_bot =
author_abbrev_zoo =
influences =
influenced =
prizes =
religion =
footnotes =
John Wallis (
Life
John Brehaut Wallis was born in
As it was intended that he should be a doctor, he was sent in 1632 to
Throughout this time, Wallis had been close to the
Returning to
Wallis joined the moderate Presbyterians in signing the remonstrance against the execution of Charles I, by which he incurred the lasting hostility of the Independents. In spite of their opposition he was appointed in 1649 to be the Savilian Chair of Geometry at Oxford University, where he lived until his death on October 28, 1703. Besides his mathematical works he wrote on
Mathematics
In 1655, Wallis published a treatise on
"Arithmetica Infinitorum", the most important of Wallis's works, was published in 1656. In this treatise the methods of analysis of Descartes and Cavalieri were systematised and extended, but some ideals were open to criticism. He begins, after a short tract on conic sections, by developing the standard notation for powers, extending them from
::::
Leaving the numerous algebraic applications of this discovery, he next proceeds to find, by integration, the area enclosed between the curve "y" = "x""m", the axis of "x", and any ordinate "x" = "h", and he proves that the ratio of this area to that of the parallelogram on the same base and of the same height is 1/("m" + 1). He apparently assumed that the same result would be true also for the curve "y" = "ax""m", where "a" is any constant, and "m" any number positive or negative; but he only discusses the case of the parabola in which "m" = 2, and that of the hyperbola in which "m" = −1. In the latter case, his interpretation of the result is incorrect. He then shows that similar results might be written down for any curve of the form
:
and hence that, if the ordinate "y" of a curve can be expanded in powers of "x", its area can be determined: thus he says that if the equation of the curve is "y" = "x"0 + "x"1 + "x"2 + ..., its area would be "x" + x2/2 + "x"3/3 + ... He then applies this to the quadrature of the curves "y" = ("x" − "x"2)0, "y" = ("x" − "x"2)1, "y" = ("x" − "x"2)2, etc., taken between the limits "x" = 0 and "x" = 1. He shows that the areas are respectively 1, 1/6, 1/30, 1/140, etc. He next considers curves of the form "y" = "x"1/m and establishes the theorem that the area bounded by this curve and the lines "x" = 0 and "x" = 1 is equal to the area of the rectangle on the same base and of the same altitude as "m" : "m" + 1. This is equivalent to computing
:
He illustrates this by the parabola, in which case "m" = 2. He states, but does not prove, the corresponding result for a curve of the form "y" = "x"p/q.
Wallis showed considerable ingenuity in reducing the equations of curves to the forms given above, but, as he was unacquainted with the
:
that is, 1 and ; this is equivalent to taking or 3.26... as the value of π. But, Wallis argued, we have in fact a series ... and therefore the term interpolated between 1 and ought to be chosen so as to obey the law of this series. This, by an elaborate method, which is not described here in detail, leads to a value for the interpolated term which is equivalent to taking: (which is now known as the
In this work also the formation and properties of
A few years later, in 1659, Wallis published a tract containing the solution of the problems on the
Early in 1658 a similar discovery, independent of that of Neil, was made by
The theory of the collision of bodies was propounded by the Royal Society in 1668 for the consideration of mathematicians. Wallis, Wren, and Huygens sent correct and similar solutions, all depending on what is now called the conservation of momentum; but, while Wren and Huygens confined their theory to perfectly elastic bodies, Wallis considered also imperfectly elastic bodies. This was followed in 1669 by a work on statics (centres of gravity), and in 1670 by one on dynamics: these provide a convenient synopsis of what was then known on the subject.
In 1685 Wallis published "Algebra", 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 "Opera", 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 "s" = "vt", where "s" 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 "s1 : s2 = v1t1 : v2t2". It is curious to note that Wallis rejected as absurd the now usual idea of a negative number as being less than nothing, but accepted the view that it is something greater than infinity — a viewpoint shared by Swiss mathematician
One aspect of Wallis's mathematical skills has not yet been mentioned, namely his great ability to do mental calculations. He slept badly and often did mental calculations as he lay awake in his bed. One night he calculated the square root of a number with 53 digits in his head. In the morning he dictated the 27 digit square root of the number, still entirely from memory. It was a feat which was rightly considered remarkable, and Oldenburg, 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 Philosophical Transactions of the Royal Society of 1685.
In his "Opera Mathematica" I (1695) Wallis introduced the term "
In fiction
Wallis is portrayed as the villain of the historical mystery novel
See also
*
Footnotes
References
The initial text of this article was taken from the
* Scriba, C J, 1970, "The autobiography of John Wallis, F.R.S.," "Notes and Records Roy. Soc. London" 25: 17-46.
*Stedall, Jacqueline, 2005, "Arithmetica Infinitorum" in
External links
*
Источник: John Wallis
Другие книги схожей тематики:
Автор | Книга | Описание | Год | Цена | Тип книги |
---|---|---|---|---|---|
John Wallis | Mathematical Tables | Viz. a table of logarithms, from 1 to 101000. To which is added (upon the same page) the differences and proportional parts, whereby the logarithm of any number under 10, 000, 000 may be easily… — Книга по Требованию, Подробнее... | 2011 | 1474 | бумажная книга |
Merriman Mansfield | Mathematical tables for class-room use | Книга представляет собой репринтное издание. Несмотря на то, что была проведена серьезная работа по… — Книга по Требованию, - Подробнее... | 2011 | 686 | бумажная книга |
Fischer Louis Albert | 1. Mathematical Tables | Книга представляет собой репринтное издание. Несмотря на то, что была проведена серьезная работа по… — Книга по Требованию, - Подробнее... | 2011 | 689 | бумажная книга |
Hussey William Joseph | Logarithmic and other mathematical tables | Книга представляет собой репринтное издание. Несмотря на то, что была проведена серьезная работа по… — Книга по Требованию, - Подробнее... | 2011 | 689 | бумажная книга |
Institution Smithsonian | Smithsonian Mathematical Tables. Hyperbolic Functions | Книга представляет собой репринтное издание. Несмотря на то, что была проведена серьезная работа по… — Книга по Требованию, - Подробнее... | 2011 | 1315 | бумажная книга |
Knott Cargill Gilston | Four-figure mathematical tables | Книга представляет собой репринтное издание. Несмотря на то, что была проведена серьезная работа по… — Книга по Требованию, - Подробнее... | 2011 | 412 | бумажная книга |
Bottomley John Thomson | Four figure mathematical tables | Книга представляет собой репринтное издание. Несмотря на то, что была проведена серьезная работа по… — Книга по Требованию, - Подробнее... | 2011 | 684 | бумажная книга |
Galbraith Joseph Allen | Manual of Mathematical Tables, by J. a. Galbraith and S. Haughton | Книга представляет собой репринтное издание. Несмотря на то, что была проведена серьезная работа по… — Книга по Требованию, - Подробнее... | 2010 | 1311 | бумажная книга |
John Shynk J. | Mathematical Foundations for Linear Circuits and Systems in Engineering | Extensive coverage of mathematical techniques used in engineering with an emphasis on applications in linear circuits and systems Mathematical Foundations for Linear Circuits and Systems in… — John Wiley&Sons Limited, электронная книга Подробнее... | 10810.32 | электронная книга | |
Wrapson James P | Mathematical and physical tables, for the use of students in technical schools and colleges | Книга представляет собой репринтное издание. Несмотря на то, что была проведена серьезная работа по… — Книга по Требованию, - Подробнее... | 2011 | 1308 | бумажная книга |
См. также в других словарях:
Mathematical Tables Project — The Mathematical Tables Project was one of the largest and most sophisticated computing organizations that operated prior to the invention of the digital electronic computer. Begun in 1938 as a project of the Works Progress Administration (WPA),… … Wikipedia
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables — Titelseite der Ausgabe von 1965 Abramowitz Stegun oder Abramowitz und Stegun ist die häufig verwendete umgangssprachliche Bezeichnung für ein bekanntes mathematisches Nachschlagewerk mit dem (englischen) Originaltitel Handbook of Mathematical… … Deutsch Wikipedia
Mathematical table — Before calculators were cheap and plentiful, people would use mathematical tables lists of numbers showing the results of calculation with varying arguments to simplify and drastically speed up computation. Tables of logarithms and trigonometric… … Wikipedia
Mathematical constant — A mathematical constant is a special number, usually a real number, that is significantly interesting in some way .[1] Constants arise in many different areas of mathematics, with constants such as e and π occurring in such diverse contexts as… … Wikipedia
mathematical — adj. 1 of or relating to mathematics. 2 (of a proof etc.) rigorously precise. Phrases and idioms: mathematical induction = INDUCTION 3b. mathematical tables tables of logarithms and trigonometric values etc. Derivatives: mathematically adv.… … Useful english dictionary
Mathematical anxiety — is anxiety about one s ability to do mathematics independent of skill. Contents 1 Math anxiety 2 Performance anxiety 3 Anxiety Rating Scale 4 Math and c … Wikipedia