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         Bernoulli Jacob:     more books (24)
  1. The Art of Conjecturing, together with Letter to a Friend on Sets in Court Tennis by Jacob Bernoulli, 2005-12-20
  2. Die Streitschriften von Jacob und Johann Bernoulli: Variationsrechnung (Gesammelten Werke der Mathematiker Und Physiker der Familie Bernoulli) (German Edition) by Jakob Bernoulli, Johann I Bernoulli, 1991-06-01
  3. Die Streitschritfen Von Jacob Und Johann Bernoulli: Variationsrechnung by Bearbeitet Von Kommentiert, Herman H. Goldstine, 1991-09
  4. Der Briefwechsel von Johann I. Bernoulli: Band 1: Der Briefwechsel mit Jacob Bernoulli, dem Marquis de l'Hôpital u.a. (German Edition) (Vol 1) by Johann I Bernoulli, 1955-01-01
  5. 1654 Births: Jacob Bernoulli, Johann Friedrich, Margrave of Brandenburg-Ansbach, Joshua Barnes, Kangxi Emperor, Michiel de Swaen
  6. Leibnizens mathematische Schriften. Abteilung 2. Band III. Briefwechsel zwischen Leibniz, Jacob Bernoulli, Johann Bernoulli und Nicolaus Bernoulli, Folge 3: Mathematik, Band 3, Abt. 2 by Gottfried Wilhelm von Leibniz, 2010
  7. 17th-Century Swiss People: Francesco Borromini, Jacob Bernoulli, Paracelsus, Jakob Abbadie, Johann Bernoulli, Maria Sibylla Merian
  8. Leibnizens mathematische Schriften. Abteilung 1. Band III. Briefwechsel zwischen Leibniz, Jacob Bernoulli, Johann Bernoulli und Nicolaus Bernoulli, Folge 3: Mathematik, Band 3, Abt. 1 by Gottfried Wilhelm von Leibniz, 2010
  9. People From Basel-City: Leonhard Euler, Theodor Zwinger, Jacob Bernoulli, Auguste Piccard, Matthäus Merian, Edwin Fischer, Johann Bernoulli
  10. Swiss Calvinists: Henry Dunant, Daniel Bernoulli, Jacob Bernoulli, Johann Bernoulli, Karl Barth, Philip Schaff, Nicolaus Ii Bernoulli
  11. Leibnizens mathematische Schriften. Abteilung 2. Band III. Briefwechsel zwischen Leibniz, Jacob Bernoulli, Johann Bernoulli und Nicolaus Bernoulli, Folge 3: Mathematik, Band 3, Abt. 2 by Gottfried Wilhelm von Leibniz, 2010
  12. Swiss Scientists: Jacob Bernoulli, Emil Theodor Kocher, Kenneth Hsu, Edward Kofler, Catherine Kousmine, Alfred Métraux, Marie-Louise Von Franz
  13. 18th-Century Latin Writers: Isaac Newton, Carl Linnaeus, Leonhard Euler, Gottfried Leibniz, Daniel Bernoulli, Jacob Bernoulli, Ludvig Holberg
  14. Leibnizens mathematische Schriften. Abteilung 1. Band IV. Briefwechsel zwischen Leibniz, Jacob Bernoulli, Johann Bernoulli und Nicolaus Bernoulli, Folge 3: Mathematik, Band 4 by Gottfried Wilhelm von Leibniz, 2010

41. Great Mathematicians - In Alphabetical Order.
l'Hôpital wrote the first textbook on calculus in 1696 which was much influencedby the lectures of his teacher Johann bernoulli, jacob bernoulli, and Leibniz
http://www.sp.edu.sg/departments/ms/Math/Great Mathematicians/greatmath-alpha.ht
Mathematics Science Computing Home ... Enquiry Great Mathematicians - in alphabetical order Love them, hate them...
but first, get to know them... Materials summarised from:
MacTutor History of Mathematics archive

"The archive contains the biographies of more than 1100 mathematicians...
and more extensive references ... + Alphabetical or Chronological Biographical indexes ." Alphabetical Order Chronological Order
Ampère André Marie Ampère
Born: 20 Jan 1775 in Lyon, France
Died: 10 June 1836 in Marseilles, France He worked on electromagnetism and analysis. He also made contributions to line geometry extending ideas of Binet.
Archimedes Archimedes of Syracuse
Born: 287 BC in Syracuse, Sicily
Died: 212 BC in Syracuse, Sicily Archimedes greatest contributions were in geometry. His methods anticipated the integral calculus 2,000 years before Newton and Leibniz. Barrow Isaac Barrow Born: Oct 1630 in London, England Died: 4 May 1677 in London, England

42. EE126 Home Page: Jean Walrand
Bayes, Thomas. Bayesian Detection. bernoulli, jacob. bernoulli Process. BrownianMotion Process. as scaled bernoulli process. C. Cards – 52-card deck.
http://robotics.eecs.berkeley.edu/~wlr/126/
EECS 126 - Probability and Random Processes J. Walrand INDEX
This page is an index for the commentaries and the notes. A B C D ... J K L M N O P Q R S T U ... w XY Z A Additive countably A periodic Markov chain B Balance equations continuous time discrete time detailed in discrete or continuous time Bayes, Thomas Bayes’ Rule Bayesian Detection Bernoulli, Jacob ... Brownian Motion Process as scaled Bernoulli process C Cards – 52-card deck Central Limit Theorem Approximate Chebychev Inequality ... Continuous – Probability Confidence Intervals Countable Set Additivity Conditional Probability Expectation o Smoothing property o Of jointly Gaussian rvs Continuous random variable Convergence of random variables: see limits Correlation uncorrelation implies independence for jointly Gaussian rvs D De Moivre, Abraham Detection Discrete random variable E Ergodicity of random process of Markov chain Estimation Properties of estimator MMSE LLSE ... Conditional Of function of random variable F First passage time of Markov chain Fortune process Function of random variable of Markov process may not be Markov G Gambling system: Impossibility of Gambler’s ruin problem Gauss, Carl Friedrich

43. EE126 Commentaries 1: Jean Walrand
bernoulli (jacob, 1654 – 1705). De Moivre found a useful approximationof the probability that preoccupied jacob bernoulli.
http://robotics.eecs.berkeley.edu/~wlr/126/w1.htm
EECS 126 - Probability and Random Processes J. Walrand UNCERTAINTY AND RANDOMNESS Models and Physical Reality Concepts and Calculations Function of Hidden Variable
Models and Physical Reality
Probability Theory is a mathematical model of uncertainty. In these lectures, we introduce examples of uncertainty and we explain how the theory models them. It is important to appreciate the difference between uncertainty in the physical world and the models of Probability Theory. That difference is similar to that between laws of theoretical physics and the real world: even though mathematicians view the theory as standing on its own, when engineers use it, they see it as a model of the physical world. Consider flipping a fair coin repeatedly. Designate by and 1 the two possible outcomes of a coin flip (say for head and 1 for tail). This experiment takes place in the physical world. The outcomes are uncertain. This week, we try to appreciate the probability model of this experiment and to relate it to the physical reality.
Concepts and Calculations
In my twenty years of teaching probability models, I have always found that what is most subtle is the

44. A Short History Of Probability And Statistics: 18th Century
Still to do. 1705, jacob bernoulli dies. It contains large parts of text that aredirectly copied from jacob bernoulli's Meditationes and the Ars Conjectandi.
http://www.leidenuniv.nl/fsw/verduin/stathist/sh_18.htm
Load Home page + menu
18th century
Introduction
Still to do Jacob Bernoulli dies. A eulogy by Fontenelle which contains a summary of his Ars Conjectandi is published the following year. Due to family disputes, it will take another 8 years before the Ars Conjectandi is published. The sad part is that the main text was already finished in 1690. Nicolaus Bernoulli's dissertation De Usu Artis Conjectandis in Jure dated june 1709, is published. It contains large parts of text that are directly copied from Jacob Bernoulli's Meditationes and the Ars Conjectandi John Arbuthnot reads his paper An Argument for Divine Providence, taken from the constant Regularity observed in the Births of both Sexes (published 1712) to the Royal Society. He presents the number of yearly christenings for males and females for the period 1629-1710. He notes that there are more males then females and that the proportion is almost constant. The original part is that he then calculates the probability, given no difference in number, of this outcome which is 0.5 . Extrapolating this result to ...Ages and Ages...and...all over the World he concludes ... that it is Art, not Chance, that governs.

45. Bernoulli
bernoulli, jacob Wahrscheinlichkeitsrechung (Ars conjectandi).
http://www.kk.s.bw.schule.de/mathge/bernoull.htm
Die Familie Bernoulli Nikolaus
Ratsherr in Basel
Jakob I

Professor in Basel
Nicolaus
Maler
Nikolaus I
Johann I

Nicolaus II

Prof. in Bern, Mitglied der Petersburger Akademie
Daniel I
Professor in Basel, Mitglied der Petersburger Akademie Johann II Professor in Basel (1710 - 1790) Johann III , Berliner Akademie Daniel II Jakob II , Petersburger Akademie Jakob Bernoulli (1654 - 1705) Lebensdaten Literatur Stammbaum
Lebensdaten
am 27.12.1654 geboren in Basel. am 16.08.1705 gestorben in Basel Beendigung der theologischen Studien 1. Arbeiten zur Differentialrechung Ars conjectandi
  • Arbeiten zur Infinitesimalrechung Variationsrechnung : Brachistochone: Zykloide. Isoperimetrische Aufgabe Wahrscheinlichkeitsrechung : Ars conjectandi (Vermutungskunst). Gedruckt 1713. Geschrieben ab 1680.
      I. Teil: Huygens: De ratiociniis in ludo aleae, mit Kommenatren von Jakob II. Teil: Kombinatorik (Permutationen, Kombinationen, Variationen). Darin: "Bernoullische Zahlen"
    Variationsrechnung
    Johann Bernoulli Lebensdaten Urheberrechte-Verkauf Stammbaum Literatur ... Seitenanfang
    Lebensdaten
    am 27.07.1667 geboren in Basel.

46. Mathem_abbrev
Isaac Battani, Abu al Bayes, Thomas Bell, Eric Temple ben Ezra, Abraham ben Gerson,Levi ben Tibbon, jacob, bernoulli, Daniel bernoulli, jacob bernoulli, jacob
http://www.pbcc.cc.fl.us/faculty/domnitcj/mgf1107/mathrep1.htm
Mathematician Report Index Below is a list of mathematicians. You may choose from this list or report on a mathematician not listed here. In either case, you must discuss with me the mathematician you have chosen prior to starting your report. No two students may write a report on the same mathematician. I would advise you to go to the library before choosing your topic as there might not be much information on the mathematician you have chosen. Also, you should determine the topic early in the term so that you can "lock-in" your report topic!! The report must include: 1. The name of the mathematician. 2. The years the mathematician was alive. 3. A biography. 4. The mathematician's major contribution(s) to mathematics and an explanation of the importance. 5. A historical perspective during the time the mathematician was alive.
Some suggestions on the historical perspective might be:
(a) Any wars etc.
(b) Scientific breakthroughs of the time
(c) Major discoveries of the time
(d) How did this mathematician change history etc.

47. Bernoulli_Jacob
jacob bernoulli was the first to use the term integral. jacob bernoulli wasthe brother of Johann bernoulli and the uncle of Daniel bernoulli.
http://sfabel.tripod.com/mathematik/database/Bernoulli_Jacob.html
Jacob (Jacques) Bernoulli
Born: 27 Dec 1654 in Basel, Switzerland
Died: 16 Aug 1705 in Basel, Switzerland
Show birthplace location Previous (Chronologically) Next Biographies Index
Previous
(Alphabetically) Next Welcome page Jacob Bernoulli was the first to use the term integral. He studied the catenary, the curve of a suspended string. He was an early user of polar coordinates and discovered the isochrone. Jacob Bernoulli was the brother of Johann Bernoulli and the uncle of Daniel Bernoulli . He graduated with a theology degree from Basel in 1676. He received training in mathematics and astronomy against the wishes of his parents. Between 1676 and 1682 Jacob travelled widely in France, England and the Netherlands. He met Boyle and Hooke in England. Jacob returned to Switzerland and taught mechanics at the University in Basel from 1683. He was appointed professor of mathematics in Basel in 1687. Jacob was the first to use the term integral in 1690. In 1691 he studied the catenary, the curve of a suspended string. He was an early user of polar coordinates and discovered the isochrone, the curve along which a body with uniform vertical velocity will fall.

48. Hollis: Differential Equations
Abel, Niels Henrik Airy, George Banach, Stefan Bendixson, Ivar bernoulli, Danielbernoulli, jacob bernoulli, Johann Bessel, Wilhelm Borda, Jean Cauchy
http://www.math.armstrong.edu/faculty/hollis/dewbvp/
Differential Equations
with Boundary Value Problems by Selwyn Hollis
Contents and Preface
Marketing Blurb Book Site @ Prentice Hall ... Solutions Manual Technology Mathematica Maple Java M ... ATLAB Sundry Items Problem graphics and extra graphical problems for Section 3.1.
Please send bug reports here
Professors: Please send me an email
Some Biographical References
The following are links to information on most of the mathematicians/scientists whose names appear in the book. Unless otherwise noted, each of these is a link to the MacTutor History of Mathematics Archive at the University of St Andrews, Scotland.
Abel, Niels Henrik

Airy, George

Banach, Stefan

Bendixson, Ivar
... Edelstein-Keshet, Leah (U. BC) Euler, Leonhard Fourier, Joseph Frobenius, Georg Gauss, Carl Friedrich ... Hertz, Heinrich Rudolf (Google search) Hodgkin, Alan Nature Hooke, Robert Huxley, Andrew (sfn.org) Jacobi, Carl Jordan, Camille Kirchhoff, Gustav Kutta, Martin Wilhelm ... Lorenz, Edward N. (xrefer.com) Lotka, Alfred (Google search) Lyapunov, Aleksandr Maclaurin, Colin Malthus, Thomas (Google search) Menten, Maud

49. Bernoulli
physics; his son, Johann bernoulli, 1746–1807, who was astronomer royal at Berlinand also studied mathematics and geography; and jacob bernoulli, 1759–89
http://www.infoplease.com/ce5/CE005708.html

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Newsletter You've got info! Help Site Map Visit related sites from: Family Education Network Encyclopedia Bernoulli [both: bern OO y E Pronunciation Key Bernoulli or Bernouilli , name of a family distinguished in scientific and mathematical history. The family, after leaving Antwerp, finally settled in Basel, Switzerland, where it grew in fame. Jacob, Jacques, or James Bernoulli, calculus and of the calculus of variations , he was the first to use the word integral in solving Leibniz's problem of the isochronous curve. He wrote an important treatise on the theory of probability (1713) and discovered the series of numbers that now bear his name, i.e., the coefficients of the exponential series expansion of x e -x ). He was succeeded at Basel by his brother

50. Biografias
Translate this page Barrow, Isaac. Boyle, Robert. Berkeley, George. bernoulli, Daniel. bernoulli, jacob.bernoulli, Johann (II). bernoulli, Nicolás. Bolzano, Bernhard. Boole, George.
http://www.sectormatematica.cl/biografias.htm
B I O G R A F Í A S Las biografías que aquí se muestran corresponden exclusivamente a los aportes efectuados en el área de la matemática. Abel, Niels Agnesi, María Aitken, Alexander Al-Khuarizmi ... Principal

51. Bernojacob
Translate this page jacob bernoulli. 1654-1705. Matemático suizo, hermano de Johann bernoulli, trabajócomo profesor de matemáticas en la Universidad de Basilea en el año 1687.
http://www.sectormatematica.cl/biografias/bernojacob.htm
Jacob Bernoulli Matemático suizo, hermano de Johann Bernoulli, trabajó como profesor de matemáticas en la Universidad de Basilea en el año 1687.
Jacob fue el primero en usar el término integral en el año 1690. Utilizó tempranamente las coordenadas polares y descubrió el isócrono, la curva que se forma al caer verticalmente un cuerpo con velocidad uniforme.
En una disputa matemática con su hermano Johann, inventó el cálculo de las variaciones. Trabajó en la Teoría de la Probabilidad y la distribución de Bernoulli, la ecuación diferencial de Bernoulli, los números de Bernoulli fueron nominados por Jacob; quien también publicó muchos artículos de series finitas.
Al morir, su puesto en Basilea fue ocupado por su hermano Johann.

52. Biography Of Johann Bernoulli
1,1748). The bernoulli family was probably the most notable mathematical familyin world history. The three most significant were jacob, Daniel, and Johann.
http://www.andrews.edu/~calkins/math/biograph/bioberno.htm
Back to the Table of Contents
Johann Bernoulli
(Aug. 6, 1667 - Jan. 1,1748)
The Bernoulli family was probably the most notable mathematical family in world history. There were ten notable intellectuals over three generations. The three most significant were Jacob, Daniel, and Johann. Also of importance were Johann's brother Nicolaus I, Nicolaus I's son Nicolaus II, Johann's sons Nicolaus III and Johann II, and his grandsons Johann III, Jacob II, and Daniel II. However, Johann made the biggest name for himself, so we will focus on his life, and methods that resulted in his contributions to modern mathematics. Below is a list of his personal information.
PERSONAL FACTS
He was born in Basel, Switzerland on August 6, 1667. He died in Basel, Switzerland on January 1, 1748. He enrolled in Basel in 1683; began to study medicine in 1685. He was schooled at Basel University and earned a M.A. and M.D. He received the medicine license in 1690. In 1694, he received a doctoral dissertation in Iatromathematics. He was called the "Grandseigneur of the science of mathematics" On a darker note he had a rocky relationship with Jacob and Daniel; he frequently took part in belittling chatter with the former, and once deliberately plagiarized one of the latter's papers.

53. Bioberno
The bernoulli family was probably the most notable mathematical family in worldhistory. The three most significant were jacob, Daniel, and Johann.
http://www.andrews.edu/~calkins/math/biograph/199899/bioberno.htm
Back to the Table of Contents
Johann Bernoulli
(Aug 6,1667-Jan 1,1748)
The Bernoulli family was probably the most notable mathematical family in world history. There were ten notable intellectuals over three generations. The three most significant were Jacob, Daniel, and Johann. Also of importance were Johann's brother Nicolaus I, Nicolaus I's son Nicolaus II, Johann's sons Nicolaus III and Johann II, and his grandsons Johann III, Jacob II, and Daniel II. Here is a family tree to help straighten things out. However, Johann made the biggest name for himself, so we will focus on his life, and methods that resulted in his contributions to modern mathematics. Below is a list of his personal information.
PERSONAL FACTS
He was born in Basel, Switzerland on August 6, 1667. He died in Basel, Switzerland on January 1, 1748. He enrolled in Basel in 1683; began to study medicine in 1685. He was schooled at Basel University and earned a M.A. and M.D. He received the medicine license in 1690. In 1694, he received a doctoral dissertation in iatromathematics. He was called the "Grandseigneur of the science of mathematics" On a darker note he had a rocky relationship with Jacob and Daniel; he frequently took part in belittling chatter with the former, and once deliberantly plagarized one of the latter's papers.

54. INDEX
Translate this page Berkeley, George Berkovitz, LD Bernardini, Angelo Bernardini, Gilberto Bernardini,Riccardo Bernays, Paul bernoulli, Daniel bernoulli, jacob I bernoulli, jacob
http://www.cwi.nl/~wouter/DATA/pictures/names.html
INDEX PICTURE DATABASE
A
B C D ... Z
A
Aazhang, Behnaam
Abadi, M.

Abadi, Martin

Abbadi, Amr el
...
Azbelev, N. V.
B
B"achtold, Martin
B"olcskei, Helmut

Baayen, P. C.

Babbage, Charles
...
Bürgi, Jost
C
Cacciabue, Pietro Carlo
Caccioppoli, Renato
Caffarelli, L.A. Cahill, Patrick T. ... Córdoba, António
D
D"urre, Karl D'Andrea, Aldo N. D'Atri, J. Da Costa, Newton C. A. ... Dürre, Karl P.
E
Eberle, Karin Eberlein, W.F. Eberstark, Hans Ebrahimi, Touradj ... Ezhkova, Irina Vasilyevna
F
F"urstenberg, Harry Fabes, Eugene B. Faci, Mohammed Faddeev, Lyudvig Dmitrievich ... Fuster Casas, D. Jose
G
G"odel, K. G"odel, Kurt G"ortler, H. G"unter, Paul ... Gödel, Kurt
H
H"older, Ernst H"older, Otto H"ormander, Lars Haantjes, J. ... Hülsemann, Johannes
I
I, Chih-Lin Ibnkahla, Mohamed Ienne, Paolo Iinatti, Jari H. ... Izzard, Martin
J
J"orgens, Konrad Jaaksoo, Ülo Jablonsky, Boleslav Jackson, Michael ... Jwo, Jung-Sing
K
K"ahler, Erich K"ohler, Torsten K"onig, Heinz K"onigsberger, Leo ... Kühn, Johannes
L
L"owig, H.F.J. L"owner, Karl L'Abbé, M.A. L'Ecuyer, Pierre ... Lück, Wolfgang
M
M"obius, August Ferdinand M"oller, Rolf M"uhll-His Karl von der M"uller, Claus ... Müntzer, Thomas
N
Nacabal, Francois

55. BiblioDb
Translate this page Bayes, Rev. Thomas. bernoulli, Daniel. bernoulli, jacob (Jacques). bernoulli,Johan II. bernoulli, Johann. bernoulli, Johann III. bernoulli, Nicolaus II.
http://aleasrv.cs.unitn.it/bibliodb.nsf/Pernome?OpenForm

56. Web Links For Chapter 4
Andrews, Scotland. http//wwwhistory.mcs.st-and.ac.uk/history/Mathematicians/bernoulli_jacob.html(bernoulli – jacob). Page 275.
http://www.mhhe.com/math/advmath/rosen/student/webres/ch4links.mhtml
Web Links for Chapter 4 Section 4.1. The Basics of Counting Page 236 Details of the North American Numbering Plan (NANP) , the numbering plan for the Public Switched Telephone Network in North America and the Caribbean, can be found at http://www.nanpa.com (North American Numbering Plan Administration) http://www-comm.itsi.disa.mil/itu/e164.html Section 4.2. The Pigeonhole Principle Page 244 A variety of applications of the pigeonhole principle can be found on the Interactive Mathematics and Miscellany site. http://www.cut-the-knot.com/do_you_know/pigeon.html (Pigeonhole Principle) A biography and a portrait of Dirichlet can be found at the History of Mathematics Archive at the University of St Andrews, Scotland. http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Dirichlet.html (Dirichlet) Page 248 A biography and a photo of Frank Plumpton Ramsey can be found at the History of Mathematics Archive at the University of St Andrews, Scotland. http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Ramsey.html (Ramsay) Section 4.3. Permutations and Combinations

57. Los Grandes Matemáticos. E. T. Bell
Translate this page jacob I tenía una predisposición mística, cosa que posee cierta significaciónpara el estudio de la herencia de los bernoulli, y que afloró en una forma
http://www.geocities.com/grandesmatematicos/cap08.html
C O N T E N I D O
Aclaraciones

Citas

Introducción

Zenón, Eudoxio y Arquímedes
...
Bajar Parte 3
LOS BERNOULLI
Johannes Bernoulli tories principio de Ars Conjectandi. Jacob I y su hermano Johannes I no siempre se llevaron bien. Eadem mutata resurgo (Aunque cambiada, surjo la misma). El lema de Jacob fue Invito patre sidera verso Magister artium

58. Definizioni
Translate this page il 1678. Anche Johann bernoulli, jacob bernoulli, de L'Hôpital,Quaterlet e Lagrange studiarono le curve caustiche. Evoluta L
http://www.geocities.com/Heartland/Plains/4142/definitions.html
Definizioni
Alcune definizioni sono date in basso. Un elenco piu' completo e' disponibile. Curve Caustiche: Quando la luce si riflette da una curva allora l'involucro dei raggi riflessi e' una caustica per riflesso o "catacaustica". Quando la luce e' rifratta, allora l'involucro dei raggi rifratti e' una caustica per rifrazione o "diacaustica". Essero vennero studiate per primi da Huygens e Tschirnhaus circa il 1678. Anche Johann Bernoulli Jacob Bernoulli , Quaterlet e Lagrange studiarono le curve caustiche. Evoluta : L'involucro delle normali a una data curva. Si puo' anche pensarla come il luogo dei centri di curvatura. L'idea ne appare in una forma primitiva nel libro V delle Coniche di Apollonio . Appare nella sua forma corrente in un lavoro di Huygens del 1673. Curva Inversa : Dato un cerchio C di centro O e raggio r allora due punti P e Q sono inversi rispetto a C se OP.OQ = r . Se P descrive una curva C allora Q descrive una curva C chiamata l'inverso del cerchio C . Benche' geometricamente non significhi molto avere un cerchio C con raggio negativo, cio' non fa differenza alla definizione dell'inverso di un punto, tranne che in questo caso P e Q sono ai lati opposti di O mentre quando r e' positivo, P e Q sono sullo stesso lato di O. Involuta : Se C e' una curva e C' e' la sua evoluta, allora C e' chiamata una involuta di C'. Qualsiasi curva parallela a C e' pure una involuta di C'. Percio' una curva ha una sola evoluta ma infinite involute. Detto in altro modo, una involuta puo' essere pensata come una curva qualsiasi ortogonale a tutte le tangenti ad una data curva.

59. History Of Astronomy: What's New At This Site On June 22, 2000
Brit.). bernoulli, Johann Jean (16671748) Short biography (Encycl. Brit.).bernoulli, jacob Jakob, Jacques (1654-1705) Short biography (Encycl.
http://www.astro.uni-bonn.de/~pbrosche/new/new000622.html
History of Astronomy What's new
History of Astronomy:
What's new at this site on June 22, 2000
Welcome / About
History of astronomy

60. History Of Astronomy: Persons (B)
Brit.); Short biography and reference (Eric Weisstein's Treasure Trove).bernoulli, jacob Jakob, Jacques (16541705) Biographical
http://www.astro.uni-bonn.de/~pbrosche/persons/pers_b.html
History of Astronomy Persons
History of Astronomy: Persons (B)
Deutsche Fassung

A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z  

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