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         Mydorge Claude:     more detail
  1. Examen Du Livre Des Recreations Mathematiques (1639) (French Edition) by Claude Mydorge, 2010-09-10
  2. Examen Dv Livre Des Recreations Mathematiqves: Et De Ses Problemes En Geometrie, Mechanique, Optique, & Catoptrique. Où Sont Aussi Discutées & Restablies ... Physiques Y Proposees (French Edition) by Jean Leurechon, Claude Mydorge, 2010-03-16
  3. Examen Du Livre Des Recreations Mathematiques (1639) (French Edition) by Claude Mydorge, 2010-09-10

21. User:Gerritholl/mathematicians - Wikipedia, The Free Encyclopedia
Gabriel Mouton Nasir Muhaqqiq-i - Thomas Muir - Müller - David Mumford -Francis Murnaghan - claude mydorge - claude Mylon - Yurii Mytropolshy - Mark
http://en.wikipedia.org/wiki/User:Gerritholl/mathematicians
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Mathematicians
Ernst Abbe Niels Henrik Abel Abraham bar Hiyya Max Abraham ... Antoni Zygmund Retrieved from " http://en.wikipedia.org/wiki/User:Gerritholl/mathematicians Views Personal tools Navigation Search Toolbox

22. The Galileo Project
mydorge, claude. 1. Dates Born Paris, 1585 Died Paris, July 1647 DateinfoDates Certain Lifespan 62; 2. Father Occupation Lawyer, Government
http://galileo.rice.edu/Catalog/NewFiles/mydorge.html
Mydorge, Claude
1. Dates
Born: Paris, 1585
Died: Paris, July 1647
Dateinfo: Dates Certain
Lifespan:
2. Father
Occupation: Lawyer, Government Official
Mydorge belonged to one of France's richest and most illustrious families. His father was conseiller at the Parlement of Paris and Judge of the Grand Chambre. His mother was the sister of the "président Chrétien de Lamoignon."
3. Nationality
Birth: French
Career: French
Death: French
4. Education
Schooling: No University
5. Religion
Affiliation: Catholic
6. Scientific Disciplines
Primary: Mathematics, Optics
Subordinate: Astronomy
His work in geometry was directed to the study of conic sections. His work on the subject, first published in two volumes in 1631 and enlarged to four in 1639, was reprinted several times under the title De sectionibus conicis. His works on conic sections contain hundreds of problems published for the first time, as well as a multitude of ingenious and original methods that later geometers frequently used. According to Baillet, he succeeded Viète as the premier mathematician of his day.
He studied the properties and nature of light and refraction, and he studied vision.

23. AIP Niels Bohr Library
mydorge s Examen (in first part of work only) follows each probleme discusses, Cyriaque de Mangin, Clément, d. 1642. mydorge, claude, 15851647.
http://www.aip.org/history/catalog/19774.html
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Item Information Holdings More by this author Leurechon, Jean, 1591-1670. Subjects Science Early works to 1800. Scientific recreations Early works to 1800. Fireworks Early works to 1800. Browse Catalog by author: Leurechon, Jean, 1591-1670. by title: Examen du livre des ... MARC Display by Leurechon, Jean, 1591-1670. Paris : Chez Antoine Robinot, 1639. 1639. Call Number: (Z)N8 LEU Description: [6], [8], 432 p. : ill. ; 18 cm. Notes: Mydorge's "Examen" (in first part of work only) follows each "probleme" discusses, in italics. The second and third parts are paged continuously, but each part has separate t.p. Added Author: Mydorge, Claude, 1585-1647. Edition: 2e ed. Copy/Holding information Location Collection Call No. Status Niels Bohr Library Books Special Collections (Z)N8 LEU In NBL
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24. René Descartes (1596-1650)
Descartes also made friends with the mathematician claude mydorge and with FatherMarin Mersenne, a man of universal learning who during his lifetime wrote
http://www.hfac.uh.edu/gbrown/philosophers/leibniz/BritannicaPages/Descartes/Des
born March 31, 1596, La Haye, Touraine, France
died February 11, 1650, Stockholm, Sweden Latin Renatius Cartesius Family and regional background Descartes was born in La Haye (now Descartes), France. Although La Haye was in Touraine, Descartes's family connections were south across the Creuse River in Poitou Poitiers Education, travels, and early influences Henri IV. (1553-1610) In 1614 Descartes went to Poitiers , where he took a law degree in 1616. At this time Huguenot Poitiers was in virtual revolt against Louis XIII. Descartes's father probably expected him to enter Parlement, but, because the legal age for that was 27, Descartes had seven years to wait. In 1618 he went to Breda in the Netherlands for 15 months as a student in mathematics and military architecture in the peacetime army of the Protestant ruler, Maurice, prince of Orange. There Descartes met the physicist Isaac Beeckman, who encouraged him in science and mathematics and for whom Descartes wrote his Musicae Compendium (written 1618, published 1650; Compendium of Music During the period 1619 to 1628, Descartes traveled in northern and southern Europe, saying that he was studying the book of the world. While in Bohemia in 1619, he had three dreams that defined for him his career as a scientist and a philosopher seeking knowledge for the benefit of humanity. By 1620 he had conceived of a universal method of deductive reasoning, applicable to all the sciences. He had also investigated reports of esoteric knowledge such as theosophical claims to command nature. Although disappointed with the followers of the magician Raymond Lulle and the alchemist Cornelius Agrippa, Descartes was impressed by the German mathematician and Rosicrucian Johann Faulhaber.

25. Jean Leurechon - Recreation Mathematique - Presented By Olivier THILL.
First edition with 13 pages of notes added by DALG (claude mydorge) on problems1, 5, 10, 11, 20, 35 and 71. This is the first edition to have the
http://members.aol.com/OlivThill/leurechon.htm
Jean Leurechon (1591-1670)
Notes by Olivier Thill His Life His Works Documents Questions ... Sources Foreword An interesting source about Leurechon is Antonella Romano, La contre-réforme mathématique , which is quite rare, although it dates from 1999. Another valuable source is the study by Albrecht Heeffer about Recreations mathematiques . Don't hesitate to send me an e-mail if I am wrong or have omitted something. Hoping this site will help for the advancement of the past His Life Born in 1591, at Bar le Duc, Lorraine, Jean Leurechon is the son of a physician. On 17 Aug. 1609, when he is 18 years old, he enters as a novice in the Jesuit college of Tournai, Belgium.
His parents accuse the Jesuits of having abducted him. The Parliament of Paris ordains his release. Nevertheless, he continues to study theology in Jesuit colleges, at Nancy, and then at Pont-à-Mousson. In 1614 or 1615, he begins his career as a professor of mathematics, at Pont-à-Mousson. He stays at Pont-à-Mousson till 1627. He observes the comet of 1618, and he writes a booklet about it, printed at Pont-à-Mousson and reprinted at Paris. It is read by Peiresc, Aleandro, and probably also by other astronomers.

26. Earliest Known Uses Of Some Of The Words Of Mathematics (P)
claude mydorge used the word parameter with the meaning of latus rectum in 1631according to two Italian scientific encyclopedias (Dizionario
http://members.aol.com/jeff570/p.html
Earliest Known Uses of Some of the Words of Mathematics (P)
Last revision: July 28, 2005 p-ADIC INTEGER was coined by Kurt Hensel (1861-1941) (Katz, page 824). P-VALUE and prob-value. David (1995) discusses the difficulties in dating P -value, the idea of which goes back to Laplaceat leastbefore opting for a reference from 1960! Subsequently David (1998) chose W. E. Deming's Statistical Adjustment of Data of 1943. When Deming wrote the phrase "value of P " was current. It was used in Karl Pearson's (1900) "On the Criterion that a Given System of Deviations from the Probable in the Case of Correlated System of Variables is such that it can be Reasonably Supposed to have Arisen from Random Sampling" ( Philosophical Magazine , 157-175) and used very heavily in R. A. Fisher's Statistical Methods for Research Workers (1925). The use of P -values (or prob-values) is often set against the use of fixed significance levels, especially 5%. It is ironical then that the "value of P " should feature so strongly in Fisher's book when that work also did so much to popularise the use of the 5% level. [John Aldrich]

27. Matematiske Portrett
mydorge, claude 15851647. Newton , Isaac 1642-1727. Noether, EmmyAmalie 1882-1935. Pascal, Blaise 1623-1662
http://www.matematikk.org/artikkel/biografi/
Matematiske portrett
Matematiske portrett
Abel, Niels Henrik Al-Khwarizmi , Abu Ja'far Muhammad ibn Musa [ca. 780-ca. 850] av Alexandria , Diofantus [ca. 200-ca. 284] av Alexandria , Euklid [ca. 325 f.kr. -ca. 265 f.kr.] av Alexandria , Pappus [ca. 290-ca. 350] av Perga, Apollonius [ca. 260 f.kr.-ca. 190 f.kr.] av Syracuse, Pythagoras [mellom 590 og 570 f.Kr-ca 500 f.Kr] av Syracuse , Arkimedes [287 f.kr.-212 f.kr.] Babbage, Charles Bayes , Thomas Bernoulli , Jacob (Jacques) Cantor, Georg Ferdinand Ludwig Philipp ... Fibonacci , Leonardo [ca 1170-ca 1240] Fourier, Josep Galilei , Galileo Galois, Evariste Gauss, Carl Friedrich ... Wiles , Andrew John
Ansvarlig for denne siden er matematikk.org ( om matematikk.org
Kontakt oss: post@matematikk.org
Nettstedet er et samarbeidsprosjekt mellom HiA HiO UiTø NTNU ... UiB og UiO
Postadresse: Matematisk institutt, Postboks 1053 Blindern, 0316 Oslo
Prosjektledelse: Hege Kaarstein (22 85 58 90) og Annette Hessen (22 85 58 81) Samarbeidspartnere: BP og Norges Forskningsråd

28. CLAUDE MYDORGE
Translate this page mydorge, claude. Nasceu em 1585 em Paris, França, onde faleceu em Julho de 1647.mydorge foi educado como advogado mas realmente pouco necessitava trabalhar
http://www.geocities.com/cobra_pages/fm-mydorge.html
COBRA PAGES
e seus
objetivos
reg. COBRA PAGES páginas em Educação e Cultura
ÍNDICE
Filosofia Moderna Filosofia Contemporânea Temas de Filosofia ...
mais frequentes
NOTAS

Vultos e episódios da Época Moderna Para retornar
à página de
COBRA PAGES
em que estava,
use a seta de
volta do seu
navegador Mydorge, Claude
. Nasceu em 1585 em Paris, França, onde faleceu em Julho de 1647. Mydorge foi educado como advogado mas realmente pouco necessitava trabalhar, por pertencer a uma família rica. Podia devotar a maioria de sua vida à pesquisa em matemática geometria e física. Publicou livros sobre o sistema ótico, seções cônicas, De sectionibus conicis , e recreações matemáticas Examen du livre des récréations mathématiques publicado em 1630. Mydorge deixou um manuscrito não publicado sobre 1000 problemas geométricos e suas soluções. Seu interesse nos sistemas óticos ajustava-se ao seu interesse em fazer observações astronômicas. Foi um amigo próximo de Descartes e fazia um grande número instrumentos óticos para ele; os dois compartilharam um grande interesse em explicar a visão e os instrumentos e as lentes deviam ajudá-los a desenvolver suas teorias. Um dos resultados famosos de Mydorge foi uma medida extremamente exata da latitude de Paris. R.Q.Cobra

29. M Index
Marston (287*) Mostowski, Andrzej (168*) Moufang, Ruth (445*) Mouton, Gabriel (147)Muir, Thomas (267) Mumford, David (617*) mydorge, claude (255) Mytropolshy
http://intranet.woodvillehs.sa.edu.au/pages/resources/maths/History/M.htm

30. References For Mydorge
References for claude mydorge. Version for printing Biography in Dictionaryof Scientific Biography (New York 19701990). Articles
http://www-groups.dcs.st-andrews.ac.uk/history/References/Mydorge.html
References for Claude Mydorge
Version for printing
  • Biography in Dictionary of Scientific Biography (New York 1970-1990). Articles:
  • Janus
  • M Cantor, II (Leipzig, 1913), 673-674; 768-769.
  • Main index Birthplace Maps Biographies Index
    History Topics
    ... Anniversaries for the year
    JOC/EFR June 2004 School of Mathematics and Statistics
    University of St Andrews, Scotland
    The URL of this page is:
    http://www-history.mcs.st-andrews.ac.uk/References/Mydorge.html
  • 31. Hardy_Claude
    claude Hardy was a practising lawyer and took part in the weekly meetings of Roberval,Mersenne and others. He was also a friend of Gassendi and mydorge.
    http://www.gap-system.org/~history/Mathematicians/Hardy_Claude.html
    Claude Hardy
    Born: 1598 in Le Mans, France
    Died: 5 April 1678 in Paris, France
    Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index
    Version for printing
    Claude Hardy was a practising lawyer and took part in the weekly meetings of Roberval Mersenne and others. He was also a friend of Gassendi and Mydorge . Hardy introduced Mydorge to Descartes Hardy, in his capacity as a lawyer, worked for the Parliament in Paris from 1625. A year later he was certainly attached to the court of justice in Paris as a counsellor. In 1630 he published Examen and in 1638 Refutation . These works dealt with the problem of the duplication of the cube and Hardy pointed out a fallacy which had arisen regarding this problem. Hardy took part in many of the mathematical discussions and arguments of the time but his greatest contribution was his knowledge of Arabic and other languages which enabled him to make important Latin translations of Euclid 's Data and other books. Despite the fact that he introduced Mydorge to Descartes , Hardy supported Descartes when the two had a dispute over Fermat 's method of maxima and minima, a forerunner to the calculus.

    32. List Of Scientists By Field
    Translate this page Musschenbroek, Petrus van. Mutis y Bossio, José Celestino Bruno. Mutis y Bossio,José Celestino Bruno. mydorge, claude. mydorge, claude. Mylon, claude.
    http://www.indiana.edu/~newdsb/m.html
    Maanen, Adriaan van Macallum, Archibald Byron Macallum, Archibald Byron MacArthur, Robert Helmer Macaulay, Francis Sowerby Macbride, David Macbride, David MacBride, Ernest William MacCullagh, James MacCulloch, John MacCulloch, John Mach, Ernst Mach, Ernst Mach, Ernst Machatschki, Felix Karl Ludwig Machatschki, Felix Karl Ludwig Machatschki, Felix Karl Ludwig Macheboeuf, Michel Macheboeuf, Michel Maclaurin, Colin Maclean, John Maclear, Thomas MacLeod, Colin Munro MacLeod, Colin Munro Macleod, John James Rickard Maclure, William MacMahon, Percy Alexander Macmillan, William Duncan Macmillan, William Duncan Macquer, Pierre Joseph Macrobius, Ambrosius Theodosius Magalotti, Lorenzo Magati, Cesare Magellan, Jean-Hyacinthe de Magellan, Jean-Hyacinthe de Magellan, Jean-Hyacinthe de Maggi, Bartolomeo Magini, Giovanni Antonio Magini, Giovanni Antonio Magini, Giovanni Antonio Magiotti, Raffaello Magiotti, Raffaello Magiotti, Raffaello Magnenus, Johann Chrysostom Magnenus, Johann Chrysostom Magni, Valeriano Magnitsky, Leonty Filippovich Magnol, Pierre Magnus, Heinrich Gustav

    33. Lawyers In Engineering
    claude mydorge, Educated as an attorney in France. Prolific writer in the areas of.(1585 1647), geometry and optics. Designed and built optical
    http://www.cs.ccsu.edu/~boconnel/lawyers.htm
    Ibn Sina (Avicenna) 12th Century physician and jurist who wrote extensively on topics ranging from Aristotle to astronomy. U. of St. Andrews: History of Mathematics Nicolaus Copernicus Studied canon law at Bologna and was appointed a canon. He eventually received his doctorate in law from Ferrara and served as counsel to his uncle, a bishop, before engaging in full time scientific pursuits. U. of St. Andrews: History of Mathematics François Viète Received his law degree from the University of Poitiers. After brief period of practice, he became engaged as councillor to various governments and eventually, Henry IV of France. A self-professed non-mathematician, he was nonetheless actively involved in numerous, seminal practical and theoretical projects. He introduced the first cohesive symbolic algebra system, which influenced Descartes' work. He is sometimes called "the father of algebra". U. of St. Andrews: History of Mathematics

    34. Vol. 1 Ch. 2
    Marin Mersenne, Blaise Pascal, claude mydorge and Girard Desargues, Descartes Mersenne Pascal Desargues mydorge E. Pascal Roberval P. de Fermat
    http://www.sumscorp.com/perspective/Vol1/ch2.htm
    Dr. Kim H. Veltman II Centres Introduction
    Europe

    Greater Europe

    Britain
    ...
    Conclusions

    1. Introduction
    The importance of centres in the development and diffusion of Renaissance culture, assumed by Vasari (1550),1 and discussed by Burckhardt (1860),2 became the topic of an important book by Chastel (1965),3 who acknowledged that there were problems with the approach. For while Florence, Lombardy, Rome, Naples, Venice and Padua were of enormous significance, smaller cities such as Lodi and Prato were also important. In a subsequent book on Italy's workshops (1969)4 Chastel gave greater emphasis to these smaller cities surrounding the larger ones, as, for example, Bergamo, Brescia, Como, Vigevano and Pavia in the case of Milan. Since then there has been increasing attention in the relation between centre and periphery. Ginzburg and Castelnuovo,5 in a fundamental study, have challenged the very notion of a centre. A detailed study would need to confront these problems of method, and might draw parallels between criticism of great centres and the fashion to criticize great individuals. Our concern is more modest: to outline the development of the major centres of publication regarding perspective and to trace how these shift with time. Centres in cities were usually due to the presence of a court, university and/or a workshop. They could be centres in at least three different senses: as places of production, as places which attracted painters to meet, or as places of transit. Nor was it just a question of painters. As Settis has shown, humanist counselors played an important part in these developments.

    35. SUMS V0.1
    claude mydorge (1585 1647). Author Variants
    http://www.sumscorp.com/develop/pages/person.php?PersonID=2074

    36. Universal Book Of Mathematics: List Of Entries
    mydorge, claude (15851647) myriad Nagel point Napier, John (1550-1617) NapoleonBonaparte (1769-1821) narcissistic number Nash, John Forbes Jr. (1928-)
    http://www.daviddarling.info/works/Mathematics/mathematics_entries.html
    WORLDS OF DAVID DARLING ENCYCLOPEDIA NEWS ARCHIVE ... E-MAIL
    THE UNIVERSAL BOOK OF MATHEMATICS
    From Abracadabra to Zeno's Paradoxes
    More details on the book
    Alphabetical List of Entries
    abacus
    Abbott, Edwin Abbott (1838-1926)
    ABC conjecture
    Abel, Niels Henrik (1802-1829)
    Abelian group
    abracadabra
    abscissa
    absolute
    absolute value
    absolute zero abstract algebra Abu’l Wafa (A.D. 940-998) abundant number Achilles and the Tortoise paradox. See Zeno's paradoxes Ackermann function acre acute adjacent affine geometry age puzzles and tricks Agnesi, Maria Gaetana (1718-1799) Ahmes papyrus. See Rhind papyrus Ahrens, Wilhelm Ernst Martin Georg (1872-1927) Alcuin (735-804) aleph Alexander’s horned sphere algebra algebraic curve algebraic fallacies algebraic geometry algebraic number algebraic number theory algebraic topology algorithm algorithmic complexity Alhambra aliquot part al-Khowarizmi (c.780-850) Allais paradox almost perfect number alphamagic square alphametic Altekruse puzzle alternate altitude ambiguous figure ambiguous connectivity.

    37. Pepper, Claude --  Britannica Student Encyclopedia
    claude mydorge University of St Andrews Brief biography of this French mathematiciansupplemented with references. claude Simon Nobel eMuseum
    http://www.britannica.com/ebi/article-9312936
    Home Browse Newsletters Store ... Subscribe Already a member? Log in This Article's Table of Contents Pepper, Claude Print this Table of Contents Shopping Price: USD $1495 Revised, updated, and still unrivaled. The Official Scrabble Players Dictionary (Hardcover) Price: USD $15.95 The Scrabble player's bible on sale! Save 30%. Merriam-Webster's Collegiate Dictionary Price: USD $19.95 Save big on America's best-selling dictionary. Discounted 38%! More Britannica products Pepper, Claude
     Student Encyclopedia Article Page 1 of 1
    Pepper, Claude... (75 of 370 words) var mm = [["Jan.","January"],["Feb.","February"],["Mar.","March"],["Apr.","April"],["May","May"],["June","June"],["July","July"],["Aug.","August"],["Sept.","September"],["Oct.","October"],["Nov.","November"],["Dec.","December"]]; To cite this page: MLA style: "Pepper, Claude." Britannica Student Encyclopedia http://www.britannica.com/ebi/article-9312936

    38. Malet, Claude Francois De --  Encyclopædia Britannica
    Malet, claude Francois de French general who conspired against Napoleon andattempted an almost successful coup claude mydorge University of St Andrews
    http://www.britannica.com/eb/article-9050321
    Home Browse Newsletters Store ... Subscribe Already a member? Log in Content Related to this Topic This Article's Table of Contents Claude François de Malet Print this Table of Contents Shopping Price: USD $1495 Revised, updated, and still unrivaled. The Official Scrabble Players Dictionary (Hardcover) Price: USD $15.95 The Scrabble player's bible on sale! Save 30%. Merriam-Webster's Collegiate Dictionary Price: USD $19.95 Save big on America's best-selling dictionary. Discounted 38%! More Britannica products
     Encyclopædia Britannica Article Page 1 of 1
    born June 28, 1754, Dole, Fr.
    died Oct. 29, 1812, Paris
    (75 of 308 words) var mm = [["Jan.","January"],["Feb.","February"],["Mar.","March"],["Apr.","April"],["May","May"],["June","June"],["July","July"],["Aug.","August"],["Sept.","September"],["Oct.","October"],["Nov.","November"],["Dec.","December"]]; To cite this page: MLA style: http://www.britannica.com/eb/article-9050321

    39. History Of Astronomy: Persons (M)
    mydorge, claude (15851647). Biographical data and references Short biographyand references (MacTutor Hist. Math.)
    http://www.astro.uni-bonn.de/~pbrosche/persons/pers_m.html
    History of Astronomy Persons
    History of Astronomy: Persons (M)
    Deutsche Fassung

    40. History Of Astronomy: Index Of Persons
    Mutis, José Celestino (17321808); mydorge, claude (1585-1647) 1935);Peirce, Benjamin (1809-1880); Peiresc, Nicolas claude Fabri de (1580-1637)
    http://www.astro.uni-bonn.de/~pbrosche/persons/pers-index.html
    History of Astronomy Persons
    History of Astronomy: Index of Persons
    A
  • Aaronson, Marc (1950-1987)
  • Abbadie, Antoine Thompson d' (1810-1897)
  • Abbe, Cleveland (1838-1916)
  • Abbe, Ernst (1840-1905)
  • Abbon de Fleury [Abbo of Fleury; Albo; Albon Floriacensis] (c. 945-1004)
  • Abbot, Charles Greeley (1872-1973)
  • Abbott, Francis (1799-1883)
  • Abbott, Francis (jnr) (1834-1903)
  • Abel, Niels Henrik (1802-1829)
  • Abell, George Ogden (1927 - 1983)
  • Abetti, Antonio (1846-1928)
  • Abetti, Giorgio (1882-1982)
  • Abiosi [Abbiosi], Giovanni Battista [Jean-Baptiste] (fl. 1490-1520) Ablufarabius: see al-Farabi, Mohammed (ca. 870-950)
  • Abney, Sir William de Wiveleslie (1843-1920)
  • Abraham bar Hiyya Ha-Nasi [Abraham Ben Chaja [Chija]; Abraham Judaeus] (ca. 1070-1136(?))
  • Abraham Ben Dior [Ben David, Harischon; Josophat Ben Levi] (12th c.) Abraham ben Meir ibn Ezra: see Ezra, Abraham ben Meir ibn (1092-1167)
  • Abraham Zachut (15th c.) Abu Abdallah al-Battani (868-929): see al-Battani
    Abu al-Hasan: see Ali Ibn Rabban al-Tabari (838-870)
    Abu Ali Hasan Ibn al-Haitham (965-1040): see al-Haitham
    Abu al-Nasr al-Farabi (870-950): see al-Farabi
  • Abu Dschaasar Almansur (712-775) Abu Hamid al-Ghazali (1058-1128): see al-Ghazali
    Abu Mashar: see Albumazar (787-885)
    Abu Raihan al-Biruni (973-1048): see al-Biruni
  • Abu'l Fida [Abulfeda], Ismail (1273-1331)
  • 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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