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MATH 5400, History of Mathematics Lecture 3: Roman, Byzantine and Arab Empires Professor: Peter Gibson [email protected] http://people.math.yorku.ca/pcgibson/math5400 September 29, 2016

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Page 1: MATH 5400, History of Mathematicspeople.math.yorku.ca/.../math5400files/Lectures/Lecture3.pdfAfter Euclid’s Elements the next important compilation of Greek mathematics from antiquity

MATH 5400, History of MathematicsLecture 3: Roman, Byzantine and Arab Empires

Professor: Peter Gibson

[email protected]

http://people.math.yorku.ca/pcgibson/math5400

September 29, 2016

Page 2: MATH 5400, History of Mathematicspeople.math.yorku.ca/.../math5400files/Lectures/Lecture3.pdfAfter Euclid’s Elements the next important compilation of Greek mathematics from antiquity

Leptis Magna

P. Gibson (YorkU) Math 5400 29.9.2016 2 / 11

Page 3: MATH 5400, History of Mathematicspeople.math.yorku.ca/.../math5400files/Lectures/Lecture3.pdfAfter Euclid’s Elements the next important compilation of Greek mathematics from antiquity

Roman Empire 117AD

P. Gibson (YorkU) Math 5400 29.9.2016 3 / 11

Page 4: MATH 5400, History of Mathematicspeople.math.yorku.ca/.../math5400files/Lectures/Lecture3.pdfAfter Euclid’s Elements the next important compilation of Greek mathematics from antiquity

Roman Empire 271AD

P. Gibson (YorkU) Math 5400 29.9.2016 4 / 11

Page 5: MATH 5400, History of Mathematicspeople.math.yorku.ca/.../math5400files/Lectures/Lecture3.pdfAfter Euclid’s Elements the next important compilation of Greek mathematics from antiquity

Roman Empire 555 AD

P. Gibson (YorkU) Math 5400 29.9.2016 5 / 11

Page 6: MATH 5400, History of Mathematicspeople.math.yorku.ca/.../math5400files/Lectures/Lecture3.pdfAfter Euclid’s Elements the next important compilation of Greek mathematics from antiquity

German invasions

P. Gibson (YorkU) Math 5400 29.9.2016 6 / 11

Page 7: MATH 5400, History of Mathematicspeople.math.yorku.ca/.../math5400files/Lectures/Lecture3.pdfAfter Euclid’s Elements the next important compilation of Greek mathematics from antiquity

The Islamic conquest

Expansion under the Prophet Mohammad, 622-632

Expansion during the Patriarchal Caliphate, 632-661

Expansion during the Umayyad Caliphate, 661-750

P. Gibson (YorkU) Math 5400 29.9.2016 7 / 11

Page 8: MATH 5400, History of Mathematicspeople.math.yorku.ca/.../math5400files/Lectures/Lecture3.pdfAfter Euclid’s Elements the next important compilation of Greek mathematics from antiquity

Both Euclid of Alexandria and Appolonius of Perga are known for havingeach authored a compilation of mathematics.

Euclid wrote the Elements, consisting of thirteen volumes mainlyconcerning geometry (but also other mathematics)

Appolonius is famous for the eight volumes entitled Conics

These works were highly influential in later eras.

P. Gibson (YorkU) Math 5400 29.9.2016 8 / 11

Page 9: MATH 5400, History of Mathematicspeople.math.yorku.ca/.../math5400files/Lectures/Lecture3.pdfAfter Euclid’s Elements the next important compilation of Greek mathematics from antiquity

Ptolemy

After Euclid’s Elements the next important compilation of Greekmathematics from antiquity is Ptolemy’s Almagest.

Ptolemy of Alexandria (85-165AD) was known for

the Almagest, consisting of 13 books, coveringI geometrical theorems, trigonometric tablesI the motion of the sunI the moonI eclipsesI the fixed starsI the motion of the planets

Geography

P. Gibson (YorkU) Math 5400 29.9.2016 9 / 11

Page 10: MATH 5400, History of Mathematicspeople.math.yorku.ca/.../math5400files/Lectures/Lecture3.pdfAfter Euclid’s Elements the next important compilation of Greek mathematics from antiquity

Ptolemy

After Euclid’s Elements the next important compilation of Greekmathematics from antiquity is Ptolemy’s Almagest.Ptolemy of Alexandria (85-165AD) was known for

the Almagest, consisting of 13 books, coveringI geometrical theorems, trigonometric tablesI the motion of the sunI the moonI eclipsesI the fixed starsI the motion of the planets

Geography

P. Gibson (YorkU) Math 5400 29.9.2016 9 / 11

Page 11: MATH 5400, History of Mathematicspeople.math.yorku.ca/.../math5400files/Lectures/Lecture3.pdfAfter Euclid’s Elements the next important compilation of Greek mathematics from antiquity

The geocentric theory of Ptolemy held sway for 14 centuries, until thetime of Copernicus, who in 1543 proposed a heliocentric theory.(By contrast, Euclid’s Elements endure.)

P. Gibson (YorkU) Math 5400 29.9.2016 10 / 11

Page 12: MATH 5400, History of Mathematicspeople.math.yorku.ca/.../math5400files/Lectures/Lecture3.pdfAfter Euclid’s Elements the next important compilation of Greek mathematics from antiquity

DiophantusDiophantus of Alexandria (c. 3rd century AD) is known for is compilation,entitled the Arithmetica, of 130 algebraic problems.

P. Gibson (YorkU) Math 5400 29.9.2016 11 / 11

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