Transcript 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
Mathematical conditions:
- attempt the solution of cubic eqations
- a better symbolism
- more rapid development of
trigonometry
Math in different countries:
The New World
The End
ITALY
• Leonardo da Vinci
(1452.-1519.)
• Distinguished between curves
of single and double curvature
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
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
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
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
 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
 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:
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Federigo Commandino of Urbino
Francesco Barozzi
Giambatista Benedetti
Cosimo Bartoli
Pietro Antonio Cataldi
Matteo Ricci
 Minor writers:
• Sivlio Belli
• Petrus Bongus
 Italian arithmeticians:
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Girolamo and Giannantonio Tagliente
Francesco Feliciano da Lazesio
Giovanni Sfortunati
Giovani Mariani
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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)
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
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
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
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
• 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:
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
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
Recorde
most influential English mathematician
The 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.
• Title- page of Recorde’s
algebra
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:
Sumario
• The matematical text
consists of twenty-four
pages besides the
colophon
BACK
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
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
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
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
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
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
THE CLASSICAL
GROUP
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Philip Melanchton
Joachim Camerarius
Jacobus Micyllus
Michael Neander
Guilielmus Xylander
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
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
 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
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
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
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 Euclid’s 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 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
This presentation was made by:
The Expert
Antonija Milišić
The New Guy
Sanela Mitrović
The Supervisor
Kristina Oremuš
The Leader
Sandra Stanišić
The Joker
Irena Užar
Let’s smile:
THE END
Just to mention that
All those mathematicians didn’t die, they just losed their
functions…