385L34

BRONZE AGE 3000-1100 BCE Minoan and Mycenaean civilizations DARK AGE 1100-800 BCE economic collapse migration into Aegean ARCHAIC PERIOD 800-480 BCE trade and economic renewal literacy rise of polis Presocratic speculation CLASSICAL PERIOD 480-323 BCE Athenian supremacy scientific advances: logic, astronomy, medicine, physics, mathematics, biology… research institutes (Academy, Lyceum) HELLENISTIC PERIOD 323-31 BCE Alexander the Great syncretism research libraries (Alexandria, Pergamon) ROMAN REPUBLIC 509-31 BCE Roman conquest of Greece (150) expansion of Empire ROMAN EMPIRE 31 BCE — 476 CE collapse of Republic imperial rule religious cults “fall” of Rome

Alexandrian Museum and Library • Alexandria founded 331 BCE • state patronage of arts and sciences under Ptolemaic rulers • Museum and Library founded early 3rd century BCE • competition between Alexandria and Pergamum • estimates range from 40,000-400,000 scrolls • Museum as research institute: physics, mathematics, astronomy, engineering, zoology, medicine • library partially destroyed 48 BCE; also 270s CE

Anaximander 6th cent. BCE concentrism; symmetrical distances Empedokles ca. 450 BCE reflected light; solar eclipse Philolaos 5th cent. BCE pyrocentrism; Counter-Earth Plato 427-348 BCE Spindle of Necessity; geocentric model Eudoxus 410-355 BCE 27 spheres Kallippos 370-300 BCE 34 spheres Aristotle 384-322 BCE 5th element (aither); 56 spheres; Unmoved Mover Herakleides ca. 350 BCE Earth axial rotation; Mercury and Venus orbit Sun; epicycles Aristarchus 310-230 BCE heliocentrism Eratosthenes 276-194 BCE circumference of Earth Apollonius 262-190 BCE equivalence of epicyclic and eccentric models

Stations & Retrogression of Mars (13.10.96-26.7.97)

Epicycle and Deferent

Epicycle and Deferent

Eudoxus & Herakleides (1:29+)

Aristarchus (310-230 BCE) • heliocentrism! • Earth rotates on axis • Moon orbits Earth • Sun and stars remain immobile • Earth and planets orbit Sun • all orbits circular • Eudoxan 27 spheres  7 spheres

Failure of Heliocentrism • inertia of geocentric paradigm • authority of Plato • circular orbits, immobile Earth • authority of earlier models (Eudoxus, Herakleides) • authority of Aristotle • 5-element theory • physics of movement • 4 causes • religious/cultural resistance • Earth rotation counter-experiential • inequality of seasonal lengths • failure to account for varying brightness

skaphê/gnômon

Eratosthenes • summer solstice at Syene (TC): noon sun at zenith • noon angle at Alexandria 7 degrees 12’ (1/50 of circle) north of zenith • distance Alexandria to Syene = 5000 stades • 50 x 5000 = 25,000 stades (46,620 km / 28,968.3 mi) • actual circumference 40,075 km (24,901 mi)

Apollonius : Eccentric

Uniform & Eccentric Orbits