Download - MATH IN SIXTEEN CENTURY
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MATH IN SIXTEEN CENTURY
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General conditionsIn 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 x3+ax=b
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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
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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 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
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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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FRANCEJacques 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)
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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 nФ in terms of sin Ф
• 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 π by infinite
products:
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Minor WritersJoannes ButteoFrancesco dal SolePierre ForcadelEstienne de la RocheJacques PeletierIan TrenchantMonte Regal Piedmontois
• Tables-products of numbers to 100 × 1000
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ENGLANDTonstall
• 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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Recordemost influential English mathematicianThe four mathematical works were written in
dialogue:1. The Ground of Artes- This was one of the most
popular arithmetics printed in the 16th century.2. The Castle of Knowledge- a work on astronomy, and
one of the first to bring the Copernican system to the attention of English readers
3. The pathewaie to knowledge-containing an abridgment of Euclid's elements
4. The whetstone of witte-containyng the extraction of Rootes: The Cossike practise, with the rule of Equation:and the woorkers of Surde Nombers.
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• Title- page of Recorde’s algebra
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MINOR WRITERSLeonard DiggersThomas DiggersJohn Dee
• wrote the preface to the first England translation of Euclid's Elements (picture)
Thomas MastersonThomas Blundeville
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THE NEW WORLDJuan 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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BACK
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GERMANYNature 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 𝜋
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 ApianusGeorg Jaochim
RhæticusChristopher 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
BACK
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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 liberaliumOrtega
• 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
BACK
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NetherlandsJoachim 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
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Adriaen AdriaenszoonGiel Vander Hoecke
• Plus and minus signs as symbol operations
Gemma FrisiusValentin Menher
• Arithmetic (geometry and trigonometry)
Jodocus ClichtoveusSimon Stevin
• The theory of decimal fractions BACK
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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 Euclid’s Elements and wrote a
mathematical dictionary
BACK
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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 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
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This presentation was made by:
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The Expert
Antonija Milišić
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The New Guy
Sanela Mitrović
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The Supervisor
Kristina Oremuš
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The Leader
Sandra Stanišić
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The Joker
Irena Užar
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Let’s smile:
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THE END
Just to mention that
All those mathematicians didn’t die, they just losed their functions…