MATH IN SIXTEEN CENTURY

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MATH IN SIXTEEN CENTURY
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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

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Math in different countries
The New World
The End
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ITALY

• Leonardo da Vinci (1452.-1519.)
• Distinguished between curves of single and double
  curvature

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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

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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

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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

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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

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• 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

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• 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

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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)

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• 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

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• 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
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• 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

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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

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• 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

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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

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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

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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.

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• Title- page of Recordes algebra

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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

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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

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Sumario

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

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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

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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

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• 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

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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

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• 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

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• 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

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THE CLASSICAL GROUP

• Philip Melanchton
• Joachim Camerarius
• Jacobus Micyllus
• Michael Neander
• Guilielmus Xylander

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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

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• 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

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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

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• 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

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• 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

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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

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• 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

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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

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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

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• This presentation was made by

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The Expert

• Antonija Milišic

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The New Guy

• Sanela Mitrovic

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The Supervisor

• Kristina Oremuš

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The Leader

• Sandra Stanišic

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The Joker

• Irena Užar

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