For several millenia, "Euclid’s Elements" was considered the indispensable gateway to higher studies. Like St. Thomas’s "Summa Theologiae", the Elements is that rare work that is both an excellent textbook attentive to the needs of new students and one of the great masterpieces of geometry. This course will lead participants on a broad tour of the first ten books of the Elements, which encompasses all of Euclid’s plane geometry. Participants will get a taste of demonstrating prepositions, while seeing proofs for fundamental equalities concerning triangles, parallelograms, and circles. Then attention will be turned to Euclid’s treatment of measurement, similarity, and incommensurability. Discussions will center on understanding Euclid’s arguments & order, with comparisons to modern developments in mathematics. Dr. Andrew Seeley has decades of experience in leading discussions of great texts of all kinds, including original texts in ancient and modern mathematics and science.

QUAD 100


Week 1 – Elements, Book I, Definitions, Postulates, Common Notions, Propositions 1-4
Watch Geogebra demonstration of I.1; Submit demonstration for I.2

Week 2 – Read I.5 to I.17, Submit demonstrations of  I.5, 9, & 16.

Week 3 – Read I.27-35, & 46. Submit demonstrations of I.27, 29, 32, 35.

Week 4 – Read I.42, 47; II.4, 5, 12, 14.

Week 5 – Book III, Read definitions. Submit demonstrations of III.16. Read III.1, III.3, III.7, III.31, III.35, IV.5

Week 6 – Books V & VII definitions. Read V.1, 4, 7, 8; VII. 4

Week 7 – Book VI, definitions, VI.1, 2, 4, 6, 8, 13, 16, 31

Week 8 – Book X, definitions, X.1, 2, 7, 8, handout, Lemma before 19, X.20, 21, X.115.

Course Content

About Instructor

Andrew Seeley

For more than two decades, Dr. Andrew Seeley has been a Tutor at Thomas Aquinas College in California, where his love has been teaching and learning with his fellow faculty and students from the greatest minds of Western Civilization. A 1987 graduate of Thomas Aquinas, Dr. Seeley received his Licentiate from the Pontifical Institute in Medieval Studies (Toronto) and a Ph.D. in Medieval Studies from the University of Toronto (1995). His dissertation was a study in St. Thomas’s teaching about the Gifts of the Holy Spirit. His teaching experience includes courses in Biblical Studies; Patristics; Logic; Language; Natural Philosophy; Biology; Geometry; Cartesian Algebra; Differential Calculus; Number Theory; non-Euclidean Geometry; Ancient, Medieval and Modern Philosophy and Literature; Classical Physics and Relativity; and Music Theory. Desiring to share his love of learning, in 2005 Dr. Seeley became Executive Director of the Institute for Catholic Liberal Education. He has spoken at conferences, led in-service workshops, offered consultations to schools and colleges and directed the Institute’s Academic Retreat for Teachers. Dr. Seeley is on the National Policy Advisory Board for the Catholic High School Honor Roll, Wyoming Catholic College’s Catholic Scholars Advisory Board, and a number of Catholic liberal arts schools around the country. His articles have been published on-line in Crisis, First Things and The Imaginative Conservative, among others. He is co-author of Declaration Statesmanship: A Course in American Government. Dr. Seeley is married to Lisa Seeley and is father to six children and grandfather to three.

1 Course

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Course Includes

  • 8 Lessons
  • Course Certificate