Magnitude used in angle

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As treated by Euclid, rectilinear angles are magnitudes that can be added together. When the sum of angles happens greater than two right angles, it is continued to be treated as a sum of angles rather than an individual angle. For instance, in proposition it is proved that the sum of the interior angles of a triangle equals two right angles.

Treating angles as magnitudes should not be confused with measuring angles. The angles themselves are the magnitudes. The only measurement of angles in the Elements is in terms of right angles (defined in the next definition). online math forum; Degree measurement and radian measurement were not used until later. In terms of degrees a right angle is 90°, while in terms of radians a right angle is pi/2 radians.

Throughout ancient Greek mathematics, only positive magnitudes were considered. Zero and negative magnitudes were not conceived. For the most part, a lack of zero and negative magnitudes complicates mathematics, but occasionally simplifies it. In any case, the power of a mathematics without zero and negative magnitudes is no less in the sense that any statement made using the language of zero or negative magnitudes can be translated into a statement that doesn't use them, although the translated statement may be longer and less understandable.
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