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MATH IN SIXTEEN CENTURY

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Title: MATH IN SIXTEEN CENTURY


1
MATH IN SIXTEEN CENTURY
2
General conditions
  • In 15th century printing having only just been
    invented and in 16th century the printed page
    began to prepetuate names
  • The world moved rapidly, and influences that bear
    upon the development of mathematics become more
    difficult to trace
  • Mathematical conditions
  • - attempt the solution of cubic
    eqations
  • - a better symbolism
  • - more rapid development of
    trigonometry

3
Math in different countries
The New World
The End
4
ITALY
  • Leonardo da Vinci (1452.-1519.)
  • Distinguished between curves of single and double
    curvature

5
Scipione del Ferro (1465.-1526.)
  • professor of mathematics in Bologna
  • In geometry he was interested in constructions
    depending on a single opening of the compasses
  • In algebra he found a method of solving the cubic
    equation for the special case x3axb

6
Girolamo Cardano (1501.-1576.)
  • Frist of the two prime movers in the solution of
    the cubic
  • Man of remarkable contrast
  • Wrote a number of books on a wide variety of
    subjects
  • Wrote Ars Magna,the frist great Latin treatise
    devoted solely to algebra

7
Girolamo Cardano (1501.-1576.)
  • Solved all the other types of cubics and solved
    the quartic equation
  • He approached Tartaglia for help
  • With his pupil Ludovico Ferrari had discovered
    the solution of the biquadric

8
Tartaglia (1500. 1557.)
  • Real name Nicolo Fontana
  • One of the greatest mathematicians of Italy in
    the 16th century
  • He have completed the solution of cubic equation
  • Wrote the best treatize on arithmetic
  • Published editions of Euclid and Archimedes
    (1543.)
  • He was challenged by Antonio Maria Fior in
    solving 30 mathematician problems,and he won

9
  • Lodovico Ferarri (1522.-1560.)
  • Was taken into Cardans household in Milan when
    he was fifteen
  • professor of matematics in Bologna
  • Rafael Bombelli (1526.-1572.)
  • Wrote LAlgebra parte maggiore
  • dell aritmetica divisia in tre libri
  • He put rules for calculating with
  • imaginary expressions

10
  • Francesco Maurolico (1494.-1575.)
  • He was interested in the Greek writers,so he
    translated into Latin works of Theodosius,
    Menelaus, Euclid, Apollonius and Archimeds
  • Also wrote various general works of mathematics
    and arithmetic
  • Italian geometers
  • Federigo Commandino of Urbino
  • Francesco Barozzi
  • Giambatista Benedetti
  • Cosimo Bartoli
  • Pietro Antonio Cataldi
  • Matteo Ricci
  • Minor writers
  • Sivlio Belli
  • Petrus Bongus
  • Italian arithmeticians
  • Girolamo and Giannantonio Tagliente
  • Francesco Feliciano da Lazesio
  • Giovanni Sfortunati
  • Giovani Mariani

BACK
11
FRANCE
  • Jacques le Fevre dEstaples
  • Wrote an intoduction to the arithmetic of
    Boethius
  • Work on geometry
  • Edited Sacroboscos Sphere
  • Description of the number game of Rithmomachia
    (rithmo-arithmetic, numbers machia-battle)

12
  • Charles de Bouelles
  • Wrote on geometry and the theory of numbers
  • Book on perfect numbers
  • Work on cycloid
  • Wrote on regular convex and stellar polygons
  • Oronce Fine
  • Wrote on astronomy
  • Works on arithmetic and geometry
  • Quadrature of the circle

13
  • Jean Fernel
  • Published a work of the Boethian type on
    proportion
  • His computation of the length of a degree of the
    meridian was so satisfactory as to entitle him to
    a worthy place in the history of geodesy
  • Claude de Boissiere
  • Wrote on poetry, music and astronomy
  • Arithmetic related to the science of warfare

Jean Fernel
14
  • Pierre de la Ramee
  • All that Aristotle has said is false.
  • Orator and a skillful debater
  • Edited the Elements of Euclid
  • Theoretical arithmetic, geometry and optics

15
Francois Viéte
  • The greatest of all the French mathematicians of
    the 16th century
  • Letters represent numbers in algebra vowels
    unknowns consonants knowns
  • Formula for sin n? in terms of sin ?
  • Equation of the n-th degree is made up of n
    linear factors

16
  • The relation between the problems of the
    trisection of an angle and the solution of a
    cubic equation
  • Formulas which relate the coefficients of a
    polinomyal to signed sums and products of its
    roots
  • Evaluating p by infinite
  • products

17
Minor Writers
  • Joannes Butteo
  • Francesco dal Sole
  • Pierre Forcadel
  • Estienne de la Roche
  • Jacques Peletier
  • Ian Trenchant
  • Monte Regal Piedmontois
  • Tables-products of numbers to 100 1000

BACK
18
ENGLAND
  • Tonstall
  • dedicated the book to one of greatest scolars and
    one of the noblest men of his generation, Sir
    Thomas More
  • His aritmetic was not original, the material
    being confessedly drawn from such Italian writers
    as Picioli

19
Recorde
  • most influential English mathematician
  • The four mathematical works were written in
    dialogue
  • The Ground of Artes- This was one of the most
    popular arithmetics printed in the 16th century.
  • The Castle of Knowledge- a work on astronomy, and
    one of the first to bring the Copernican system
    to the attention of English readers
  • The pathewaie to knowledge-containing an
    abridgment of Euclid's elements
  • The whetstone of witte-containyng the extraction
    of Rootes The Cossike practise, with the rule of
    Equationand the woorkers of Surde Nombers.

20
  • Title- page of Recordes algebra

21
MINOR WRITERS
  • Leonard Diggers
  • Thomas Diggers
  • John Dee
  • wrote the preface to the first England
    translation of Euclid's Elements (picture)
  • Thomas Masterson
  • Thomas Blundeville

BACK
22
THE NEW WORLD
  • Juan Diez
  • He was of a literary turn of mind, as is shown by
    three or four books which he published. One of
    these works was on mathematics, and this appeared
    in Mexico under the folowing title

23
Sumario
  • The matematical text consists of twenty-four
    pages besides the colophon

24
BACK
25
GERMANY
  • Nature of the German Mathematics
  • the mathematics of Germany was Gotic, unpolished,
    but strong
  • Germany produced a notable group of
    arithmeticians, two strong algebraists
  • Germany made a definite advance in geometry, in
    the study of higer plane curves
  • the greatest influence for advance in 16th
    century was printing, Erasmus and Martin Luther
  • it was a century of intellectual awakening and of
    breaking away from traditions

26
The Margarita Phylosophica
  • the first modern encyclopedia of any note
  • published at Freiburg in 1503 by Gregorius Reisch
  • it consists of 12 books and includes considerable
    material upon arithmetic, geometry and astronomy
  • there were 16 editions of this book in the 16th
    century

27
  • Albrecht Dürer
  • showed in his treaties on geometry, fortification
    and human porportion his mathematical powers
  • Johann Stöffler
  • showed how the Julian calendar could be brought
    into harmony with astronomical events
  • predicted that the Deluge would be repeated in
    1524 but he was wrong

28
Michael Stifel
  • the first German writer of the century to devote
    his life to mathematics and to acquire an
    enviable reputation in this field
  • Stifel made the error of predicting the end of
    the world and, when it was seen that he was
    wrong, he was arrested

29
  • Christoff Rudolff
  • worked on algebra
  • published three books Coss (1525), Kunstliche
    rechnung (1526) and a collection of problems
    (1530)
  • Johann Scheubel
  • gave the so-called Pascal Triangle a century
    before Pascal wrote upon it, and extracted roots
    as high as the 24th by a process similar to the
    one which employs the Binomial Theorem
  • Ludolf van Ceulen
  • he is known for his value of ??, at first given
    to 20 and then to 35 decimal places

30
  • Grammateus
  • Real name Heinrich Scheyber
  • his best known work was an arithmetic in the
    German language
  • first German writter to make free use of the
    signs and in the treatment of algebraic
    expressions
  • Pitiscus
  • his trigonometry was the first satisfactory
    textbook published on the subject and the first
    book to bear this title

31
THE CLASSICAL GROUP
  • Philip Melanchton
  • Joachim Camerarius
  • Jacobus Micyllus
  • Michael Neander
  • Guilielmus Xylander

32
MATHEMATICAL ASTRONOMERS
  • Petrus Apianus
  • Georg Jaochim Rhæticus
  • Christopher Clavius
  • he was engaged in the reform of the calendar
    under direction of Pope Gregory XIII (picture)
  • Johann and Andreas Schoner

33
  • Adam Riese
  • the greatest of all the Rechenmeisters of this
    century
  • The only other Rechenmeister of the century to
    deserve special mention is Simon Jacob who wrote
    two commercial arithmetics

BACK
34
SPAIN
  • The intellectual atmosphere was not favorable to
    the development of mathematics, however, many
    Spanish scholars settled in France and Italy or
    at least published their works abroad

35
  • Ciruelo
  • The earliest Spanish mathematician of the century
    was Pedro Sánchez
  • general work of mathematics Cursus quattuor
    mathematicarum artium liberalium
  • Ortega
  • wrote A Tractado subtilisimo d'arithmetica y de
    geometria which was published in 1512, in
    Barcelona and Lyons, being the first book on
    commercial computation known to have been printed
    in France

36
  • Joannes Martinus Blasius
  • an astrologer and arithmetician
  • published in Paris (1513) a work on computation
  • Juan Perez de Moya
  • his Arithmetica includes calculation, applied
    arithmetic, algebra, principal geometry and
    contains a considerable amount of interesting
    historical material

BACK
37
Netherlands
  • Joachim Fortius Ringelbergius
  • Astronomy, optics, arithmetic
  • Adriaen van Roomen
  • Gave the value of p to seventeen decimal places
  • Other works
  • Treatment of the circle by Archimedes
  • Spherical triangles
  • Adriaen Anthoniszoon
  • Known as Metius
  • Suggested 355/113 as a convenient value of p

38
  • Adriaen Adriaenszoon
  • Giel Vander Hoecke
  • Plus and minus signs as symbol operations
  • Gemma Frisius
  • Valentin Menher
  • Arithmetic (geometry and trigonometry)
  • Jodocus Clichtoveus
  • Simon Stevin
  • The theory of decimal fractions

BACK
39
Switzerland
  • Henricus Loritus Glareanus
  • He wrote on arithmetic, meterology and music
  • Canradus Dasypodius
  • He had in mind the ending of all the Greek
    mathematical works
  • He only edited Euclids Elements and wrote a
    mathematical dictionary

BACK
40
Japan
  • The 16th century in Japan corresponds mostly to
    the 13th century in the West it was century of
    preparation
  • Probably the chief cause which contributed to
    this preparation in the field of mathematichs was
    the jouney to China made by one Mori Kambei
    Shigeyoshi, a scholar in the servise of two of
    the powerful lords of Japan
  • The great hero Toyotomi Hideyoshi (Taiko) sent
    Mori to China to acquire and bring back
    mathematical knowledge (most famous mathematicion
    from China was Ku Ying-hsiang wrote on algebra
    and geometry)
  • Moris mission was not successful, but he bring
    back with him a considerable amount of material

BACK
41
  • This presentation was made by

42
The Expert
  • Antonija Milišic

43
The New Guy
  • Sanela Mitrovic

44
The Supervisor
  • Kristina Oremuš

45
The Leader
  • Sandra Stanišic

46
The Joker
  • Irena Užar

47
Lets smile
48
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49
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50
THE END
Just to mention that All those mathematicians
didnt die, they just losed their functions
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