Chapter 1: Geometry, philosophy and world order
Understanding God
Thales of Myletus (624-548)
Rich and wealthy man who became politically active
Often called the first mathematician
Geometry as part of philosophy to understand divine reasons
Pythagoras of Samos (571-500)
Part of the pythagorean sect
Numbers represent the divine world order
Musica (length of the snare)
Connection between musica and the theory of ratios
Ratios part of arithmetica or geometria
Mythical connection between numbers and reality
Plato (428-348)
Real knowledge came from logos, not the senses
Cave projections
Ideai, the “real world”
Aristotle (384-322)
Arithmetica and geometria are abstractions of ideas given by our senses
Four blocks: earth, fire, water and air
Quadrature of the circle
Square similar in area to a given circle
Hippocrates of Chios (470-410)
Wealthy merchant who liked geometria
Tried to solve the quadrature of the circle
Euclid (~300BC)
Writer of Elements
No exact copies, we don’t know what the original looked like
Five platonic solids
Axioms and hypotheses
Archimedes (287-212)
Founder of cylinder and cones, inscribed by an orb
More practically inclined (upward force of an object in water
Introduction of abstract counting system (count until you don’t know)
Pragmatic interest from king (useful in war)
,Apollonius of Perga (252-190)
Writer of de Konika
Hyperboles, closer to the quadrature of circles
Romans more practically minded about geometria
Only the most well educated man would learn arithmetic
Others used the abacus
Hipparchos of Nicaea (190-120)
Calculate local time
Pax romana
Spread of roman and greek culture
Early Christians distanced themselves from the pagan Greek philosophers
Saint Augustine (354-430)
Ideal icon to Christianity since he was not versed in the Greek philosophers
Was impressed about geometria and arithmetica
Comparing knowledge in arithmatica to divine revelation
Intepreted as sanctifying this form of knowledge
God revealed aritmetica to Abraham
Boethius(480-525)
Perpendicular to Augustine
Wealthy and politically influential, so he knew the Greek philosophers
Translations of Aritstotle and Plato
Pythagorean number theory
Offering the rules of computus (calculation of time)
Trying to establish biblical calendar
Artes liberales
The arts that had to be mastered by any free man
Trivium(trivial matters)
The trivial matters
Grammar, rhetorics, dialectics
Quadrivium
Arithmetica, geometria, musica and astronomia
Gerbert of Aurillac (946-1003)
Important to the rise of mathematical thinking in europe
Gerbert illustrates the new kind of purpose for the field of geometria and arithmetica
New ideals of studying: understand something new by studying different sources
Popularised studying since he was an influential christian thinker
Important at the imperial court
Stark contrast with people from those days who didnt trust the heretic sources
Gerbert took non christian knowledge serious
, Monasteries (cathedral schools)
Where knowledge in the shapes of books and scrolls was located
Universitas
Starting to pop up
Greatly valued by city or court officials (benefit from knowledge)
A subculture within society.
Understanding God
Thales of Myletus (624-548)
Rich and wealthy man who became politically active
Often called the first mathematician
Geometry as part of philosophy to understand divine reasons
Pythagoras of Samos (571-500)
Part of the pythagorean sect
Numbers represent the divine world order
Musica (length of the snare)
Connection between musica and the theory of ratios
Ratios part of arithmetica or geometria
Mythical connection between numbers and reality
Plato (428-348)
Real knowledge came from logos, not the senses
Cave projections
Ideai, the “real world”
Aristotle (384-322)
Arithmetica and geometria are abstractions of ideas given by our senses
Four blocks: earth, fire, water and air
Quadrature of the circle
Square similar in area to a given circle
Hippocrates of Chios (470-410)
Wealthy merchant who liked geometria
Tried to solve the quadrature of the circle
Euclid (~300BC)
Writer of Elements
No exact copies, we don’t know what the original looked like
Five platonic solids
Axioms and hypotheses
Archimedes (287-212)
Founder of cylinder and cones, inscribed by an orb
More practically inclined (upward force of an object in water
Introduction of abstract counting system (count until you don’t know)
Pragmatic interest from king (useful in war)
,Apollonius of Perga (252-190)
Writer of de Konika
Hyperboles, closer to the quadrature of circles
Romans more practically minded about geometria
Only the most well educated man would learn arithmetic
Others used the abacus
Hipparchos of Nicaea (190-120)
Calculate local time
Pax romana
Spread of roman and greek culture
Early Christians distanced themselves from the pagan Greek philosophers
Saint Augustine (354-430)
Ideal icon to Christianity since he was not versed in the Greek philosophers
Was impressed about geometria and arithmetica
Comparing knowledge in arithmatica to divine revelation
Intepreted as sanctifying this form of knowledge
God revealed aritmetica to Abraham
Boethius(480-525)
Perpendicular to Augustine
Wealthy and politically influential, so he knew the Greek philosophers
Translations of Aritstotle and Plato
Pythagorean number theory
Offering the rules of computus (calculation of time)
Trying to establish biblical calendar
Artes liberales
The arts that had to be mastered by any free man
Trivium(trivial matters)
The trivial matters
Grammar, rhetorics, dialectics
Quadrivium
Arithmetica, geometria, musica and astronomia
Gerbert of Aurillac (946-1003)
Important to the rise of mathematical thinking in europe
Gerbert illustrates the new kind of purpose for the field of geometria and arithmetica
New ideals of studying: understand something new by studying different sources
Popularised studying since he was an influential christian thinker
Important at the imperial court
Stark contrast with people from those days who didnt trust the heretic sources
Gerbert took non christian knowledge serious
, Monasteries (cathedral schools)
Where knowledge in the shapes of books and scrolls was located
Universitas
Starting to pop up
Greatly valued by city or court officials (benefit from knowledge)
A subculture within society.
