Thales's theorem theorem is named after Thales because he was said by ancient sources to have been the first to prove the theorem, using his own results that the base angles of an isosceles triangle are equal, and that the sum of angles in a triangle is equal to 180°. Dante's "Paradiso" (canto 13, lines 101–102) refers to Thales's theorem in the course of a speech. The following facts are used: the sum of the angles in a triangle is equal to 180° and the base angles of an isosceles triangle are equal. Since = = , ∆OBA and ∆OBC are isosceles
Euler angles reached as follows: In sum, the three elemental rotations occur about "z", "x" and "z". Indeed, this sequence is often denoted "z-x-z" (or 3-1-3). Sets of rotation axes associated with both proper Euler angles and Tait–Bryan angles are commonly named using this notation (see above for details). There are six possibilities of choosing the rotation axes for proper Euler angles. In all of them, the first and third rotation axes are the same. The six possible sequences are: Angles are commonly defined according to the right-hand rule. Namely, they have positive values when they represent a rotation that appears clockwise