8 The plaine angles comprehending a solid angle, are lesse than foure right angles. 21. p xj.
For if they should be equall to foure right angles, they would fill up a place by the [27 e, iiij]. neither would they at all make an angle, much lesse therefore would they doe it if they were greater.
9 If three plaine angles lesse than foure right angles, do comprehend a solid angle, any two of them are greater
than the other: And if any two of them be greater than the other, then may comprehend a solid angle, 21. and 23. p xj.
It is an analogy unto the [10 e vj]. and the cause is in a readinesse. For if two plaine angles be equall to the remainder, they shall with that third include no space betweene them: But if thou shalt conceit to fit the plaine to the shankes, with the congruity they should of two make one: but much lesse if they be lesser.
The converse from hence also is manifest.
Euclide doth thus demonstrate it: First if three angles are equall, then by and by two are conceived to be greater than the remainder. But if they be unequall, let the angle aei, be greater than the angle aeo: And let aeu, equall to aeo, be cut off from the greater aei: And let eu, be equall to eo. Now by the [2 e, vij]. two triangles aeu, and aeo, are equall in their bases au, and ao. Item ao, and ei, are greater than ai, and ao: And ao, is equall to au. Therefore oi, is greater than iu. Here two triangles, uei, and ieo, equall in two shankes; and the base oi, greater than the base iu. Therefore, by the [5 e vij]. the angle oei, is greater than the angle ieu. Therefore two angles aeo, and oei, are greater than aei.
