¶ A Corollary added by Orontius.
* 1.1Hereby is easily gathered, that such a perpendicular line in rectangle triangles falleth of necessitie vpon the side of the triangle, that is, neyther within the trian∣gle, nor without. But in obtuseangle triangles it falleth without, and in acuteangle triangles within. For the perpendicular line in obtuseangle triangles, and acute∣angle triangles can not exactly agree with the side of the triangle: for then an ob∣tuse & an acuteangle should be equal to a right angle, contrary to the eleuenth and twelfth definitions of the first booke. Likewise in obtuseangle triangles it can not fall within, nor in acuteangle triangles without: for then the outward angle of a triangle should be lesse then the inward and opposite angle, which is contrary to the 16. of the first.
* 1.2And this is to be noted, that although properly an acuteangle triangle, by the definition therof geuē in the first booke, be that triangle, whose angles be all acute: yet forasmuch as there is no triangle, but that it hath an acute angle, this propositi∣on is to be vnderstanded, & is true generally in all kindes of triangles whatsoeuer, and may be declared by them, as you may easily proue.