Smaller than the Smallest Angle (formed by straight lines)

The angle a tangent line forms with the circumference of a circle is is least possible angle made with a straight line from that point of tangent (tangent line EA in the image). This is demonstrated in Book III, proposition 16 of Euclid’s Elements. The angle formed by the tangent is also known as a cornicular or … Continue reading Smaller than the Smallest Angle (formed by straight lines)

On Christian Doctrine: The Rule of Scripture and Knowledge of the Profane

We study the world that we may understand Scripture, and Scripture teaches us to truly read the world. Is this a conflict of principle or a vicious circle? No, it is the ordinary course of human learning elevated to a glorious pitch. God is pleased to use the things of His creation as a tutor unto … Continue reading On Christian Doctrine: The Rule of Scripture and Knowledge of the Profane

The Poetics of Faith and Learning, Part 1

Euclid The study of Euclid’s Elements serves as an excellent example of the contemplative learning process. Proposition 5, an early proposition in the text, marks a turning point for most students, where they must not only identify a chain of equalities (something akin to a hypothetical syllogism), but do so in transposition. Whereas students needed only identify equality by imposing … Continue reading The Poetics of Faith and Learning, Part 1