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.
(was on http://isites.harvard.edu/icb/icb.do?keyword=k83402)
- 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
- 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
- Diocles On burning mirrors, ed. Toomer (Arabic-English)
- Eutocius_Netz.pdf
- Mean_proportionals_Loeb.pdf
- 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"
- Descartes, _Geometry_
- M. Domski, "The intelligibility of motion and construction"
- A. G. Molland, "Shifting the foundations: Descartes's transformation of ancient geometry"
- 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
- 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
- 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
- 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