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MATH IN SIXTEEN CENTURY

MATH IN SIXTEEN CENTURY. 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

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MATH IN SIXTEEN CENTURY

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  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 oftrigonometry

  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 x3+ax=b

  6. Giro’lamo Carda’no (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 Cardan’s household in Milan when he was fifteen • professor of matematics in Bologna • Rafael Bombelli (1526.-1572.) • Wrote L’Algebra 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 d’Estaples • Wrote an intoduction to the arithmetic of Boethius • Work on geometry • Edited Sacrobosco’s 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 nФ in terms of sin Ф • 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 π 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 Equation:and the woorkers of Surde Nombers.

  20. Title- page of Recorde’s 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 𝜋, 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 π 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 π

  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 Euclid’s 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 Mōri Kambei Shigeyoshi, a scholar in the servise of two of the powerful lords of Japan • The great hero Toyotomi Hideyoshi (Taikō) sent Mōri to China to acquire and bring back mathematical knowledge (most famous mathematicion from China was K’u Ying-hsiang wrote on algebra and geometry) • Mōri’s 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 Milišić

  43. The New Guy Sanela Mitrović

  44. The Supervisor Kristina Oremuš

  45. The Leader Sandra Stanišić

  46. The Joker Irena Užar

  47. Let’s smile:

  48. THE END Just to mention that All those mathematicians didn’t die, they just losed their functions…

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