Thales's theorem
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In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ∠ ABC is a right angle. Thales's theorem is a special case of the in
Non si est dare primum motum esse o se del mezzo cerchio far si puote triangol sì c'un recto nonauesse. – Dante's Paradiso, Canto 13, lines 100–102 Non si est dare primum motum esse, Or if in semicircle can be made Triangle so that it have no right angle. – English translation by Longfellow
Q.E.D.
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Q.E.D. is an initialism of the Latin phrase quod erat demonstrandum, meaning "that which was to be demonstrated". Literally, it states "what was to be shown". Traditionally, the abbreviation is placed
Thales's theorem
…β = ∠ OBC. The three internal angles of the ∆ABC triangle are α, (α + β), and β. Since the sum of the angles of a triangle is equal to 180°, we have Q.E.D. The theorem may also be proven using trigonometry: Let O = (0, 0), A = (−1, 0), and C = (1, 0). Then B is a point on the unit circle (cos θ, sin θ…
Spinoza's original text of Ethics, Part 1, Q.E.D. is used at the end of Demonstratio of Propositio III on the right hand page