As aei, is a semicircle: The other sections, as oyu, and oeu, are unequall sections: that greater; this lesser.
21 The angle in a semicircle is a right angle: The angle of a semicircle is lesser than a rectilineall right angle: But greater than any acute angle: The angle in a greater section is lesser than a right angle: Of a greater, it is a greater. In a lesser it is greater: Of a lesser, it is lesser, è 31. and 16. p iij.
Or thus: The angle in a semicircle is a right angle, the angle of a semicircle is lesse than a right rightlined angle, but
greater than any acute angle: The angle in the greater section is lesse than a right angle: the angle of the greater section is greater than a right angle: the angle in the lesser section is greater than a right angle, the angle of the lesser section, is lesser than a right angle: H.
There are seven parts of this Element: The first is that The angle in a semicircle is a right angle: as in aei: For if the ray oe, be drawne, the angle aei, shall be divided into two angles aeo, and oei, equall to the angles eao, and eio, by the [17 e vj]. Therefore seeing that one angle is equall to the other two, it is a right angle, by the [6 e viij]. Aristotle saith that the angle in a semicircle is a right angle, because it is the halfe of two right angles, which is all one in effect.
The second part, That the angle of a semicircle is lesser than a right angle; is manifest out of that, because it is the part of a right angle. For the angle of the semicircle aie, is part of the rectilineall right angle aiu.
The third part, That it is greater than any acute angle; is manifest out of the [23. e xv]. For otherwise a tangent were not on the same part one onely and no more.
The fourth part is thus made manifest: The angle at i, in the greater section aei, is lesser than a right angle; because it is in the same triangle aei, which at a, is a right angle. And if neither of the shankes be by the center, not withstanding an angle may be made equall to the assigned in the same section.