History of Science 206r (Spring 2011-2012)™

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Handouts

Amy's handout on Becker, Eudoxos Studien II
Amy's handout on Euclid 3.16
Connemara's handout on the *quadratrix*
Stephanie's handout on Lloyd, "Mathematics and narrative"
Alma on Plato's construction for doubling the cube
Barry's comments about some mathematical issues that came up in our seminar

Fun Links

Animations by Oliver Knill

Readings on Archimedes' "On the Equlibria of planes"

Archimedes, On the equilibria of planes, Intro. and props 1-5 (Mendell)
Archimedes, On the equilibria of planes, Props. 6-7 (Mendell)
Archimedes, On the equilibria of planes, intro. and props. 1-7 (Heiberg)
Archimedes, Loeb vol. 2
Eutocius' commentary on Archimedes, On the equilibria of planes, book 1
Ernst Mach, The science of mechanics, 4th ed. (1919)
Mach, The science of mechanics, 6th ed. (1960)
E. J. Dijksterhuis, Archimedes
P. Palmieri, The empirical basis of equilibrium: Mach, Vailati, and the lever
M. van Dyck, On the epistemological foundations of the law of the lever
P. Palmieri, Response to Maarten van Dyck's commentary
Andre Koch Torres Assis, Archimedes, the Center of Gravity, and the First Law of Mechanics
Barry's handout on Archimedes' proof of the law of the lever

Announcements

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Readings on the problem of finding mean proportionals ("doubling the cube")

Diocles On burning mirrors, ed. Toomer (Arabic-English)
Eutocius_Netz.pdf
Mean_proportionals_Loeb.pdf

Other readings

A. D. Steele, "Über die Rolle von Zirkel und Lineal in der griechischen Mathematik" (1936)
D. Nikulin, "Imagination and mathematics in Proclus"
R. Netz, "Imagination and layered ontology in Greek mathematics"

Readings on Descartes

Descartes, _Geometry_
M. Domski, "The intelligibility of motion and construction"
A. G. Molland, "Shifting the foundations: Descartes's transformation of ancient geometry"

Readings on the quadratrix

Pappus 4, 26-30 (ed. Sefrin-Weis)
Pappus' introduction of the quadratrix in Greek Mathematical Works I (Loeb)
Heath's discussion of squaring the circle

Web Links

Pappus on the quadratrix (Henry Mendell)
Hippocrates' quadrature of lunes (Henry Mendell)
Antiphon's attempt to square the circle (Henry Mendell)
Bryson's attempt to square the circle (Henry Mendell)
Euclid, Elements XII.2 (David Joyce)
Euclid, Elements XII.2 (Henry Mendell)

Additional Readings

Becker_Eudoxos_Studien_I.pdf
Oskar Becker, Eudoxos-Studien II: "Warum haben die Griechen die Existenz der vierten Proportionale angenommen?"
Becker_Eudoxos_Studien_III.pdf

Readings on Hippocrates of Chios

F. Rudio, Der Bericht des Simplicius über die Quadraturen des Antiphon und des Hippokrates
Hippocrates_Loeb.pdf
W. Knorr, The ancient tradition of geometrical problems, ch. 2

Course Documents

Syllabus
Motion and stasis in geometry (Barry)
Plutarch and Pappus on "mechanical" argument in mathematics
G.E.R. Lloyd's article: Mathematics and Narrative: An Aristotelian Perspective

Course Information

History of Science 206r: Geometry and Mechanics

Harvard College/GSAS: 111602

Spring 2011-2012

Mark Schiefsky and Barry C. Mazur

Meeting Time: Thursday 2:00pm - 4:00pm
Exam Group: 16,17

A seminar-course devoted to a philosophical and historical examination of appeals to motion and other "mechanical" notions in ancient geometry. We will read texts related to the three classical problems of Greek mathematics, the Mechanical Problems attributed to Aristotle, and the "mechanical method" of Archimedes, with examples and commentary drawn from early modern, and also contemporary, mathematics. Undergraduates and graduates welcome.

Announcements

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Course Documents