Euclid/Lobachevski Course Syllabus

Dr. Lynda L. Myers

Reading List:
Euclid, The Elements, Book I (Thomas Heath translation). Recommended edition:  Green Lion Press.
Proclus, Selections from Commentary on the First Book of Euclid’s Elements, Glenn  Morrow translation. To be handed out.
Girolamo Sacchieri, Selections from Euclides Vindicatus (Euclid Freed of Every Fleck),  George Halstead translation.  To be handed out.
Nicholas Lobachevski, Geometrical Researches on the Theory of Parallels, George  Halstead translation. To be handed out.
Stephen F. Barker, “Geometry,” from The Encyclopedia of Philosophy, Paul Edwards,  Editor in Chief (New York: 1967), Vol. III, pp. 285-290.  To be handed out.

Schedule:

Week 1
Session
A.  Euclid, Elements, Book 1, Definitions 1-22 (overview)
B.  Def. 1-7
C.  Postulates 1-3; Common Notions; Proposition 1 (introduction)

Week 2
Session
A. Propositions 1-3; Def. 15
B. Structure of a Euclidean proposition; problems v. theorems
C. Proposition 4; Common Notion 4

Week 3
Session
A. Prop. 5-6; logic of immediate inference; reductio ad absurdum
B. Prop. 7-8
C. Prop. 9-12 (First essay due)

Week 4
Session
A. Prop. 13-15; Postulate 4
B. Prop. 16-17
C. Postulate 5 

Week 5
Session
A. Prop. 18-21
B. Prop. 22-23; (read 24-25); Prop. 26
C. Review theory of congruence

Week 6
Session
A. Prop. 27-28; Definition 23
B. Prop. 29; Postulate 5
C. Prop. 30 (cf. Playfair’s axiom); Prop. 31; Prop. 32 (cf. Props. 16-17)

Week 7
Session
A. Prop. 33-35 (Read 36-41)
B. Prop. 42-43
C. Prop. 44-45

Week  8
Session
A. Prop. 46-8
B. Overview of Euclid, Elements, Book I
C. Overview continued  (Second essay due)

Week 9
Session
A. Proclus, Commentary on the First Book of Euclid’s Elements, paragraph 175-177; 191-193
B. Ibid., para. 361-368
C. Ibid., para. 369-373.

Week 10
Session
A. Saccheri, Euclid Freed of Every Fleck, Preface, Book I, Propositions 1-2
B. Ibid., Prop. 3
C. Ibid., Corollaries 1-3

Week 11
Session
A. Lobachevski, Theory of Parallels, Author’s preface, Theorems 1-10
B. Idem
C. Idem

 

Week 12
Session
A. Theorem 16
B. Idem
C. Th. 17

Week 13
Session
A. Th. 18; Euclid X.1, Lob. Th. 19
B. Th. 20
C.  Idem (Third essay due)

Week 14
Session
A. Th. 21-22
B.  Th. 23
C.  Idem

Week 15
Session
A. Th. 24
B. Original proofs
C. Idem

Week 16
Session
A.  “Geometry”
B.  Idem
C.  Idem; Final essay due

Week 17
Session
A.  Review and Conclusion
B.  Idem
C.  Meetings with individual students to discuss final essay

Week 18
Session
A. Meetings with individual students to discuss final essay
B. Continued
C. Continued

 

 

Evaluation of Students’ Work: This class will be a discussion (seminar-style) class, not a lecture class. Therefore regular attendance, preparation and class participation are essential.  When called upon, students will be expected to present at the blackboard demonstrations of the propositions that they have studied.  These demonstrations will be the basis for our conversations about important details of our authors’ mathematical arguments. In our conversations, students will be expected to raise questions about the text and to be willing to suggest and explore possible answers to those questions.  Our more general, philosophical discussions will arise out of these explorations.  Thus, the evaluation of students’ work will be based on several factors: regular class attendance, ability to demonstrate propositions at the board carefully and accurately, willingness to raise and explore thoughtful questions about the details of the texts, and willingness to speculate about more general philosophical issues raised by the texts.  Students will be required to write four short (2-3 page) papers on topics assigned by Mrs. Myers.  There will be no quizzes or final exam.