It is a consectary drawne out of the [xiij. e ij]. Because a tangent is a very perpendicular.
Euclide propoundeth this more specially thus; that no other right line may possibly fall betweene the periphery and the tangent.
And
24 A touch-angle is lesser than any rectilineall acute angle, è 16 p ij.
Angulus contractus, A touch angle is an angle of a straight touch-line and a periphery. It is commonly called Angulus contingentiæ: Of Proclus it is named Cornicularis, an horne-like corner; because it is made of a right line and periphery like unto a horne. It is lesse therefore than any acute or sharpe right-lined angle: Because if it were not lesser, a
right line might fall between the periphery and the perpendicular.
And
25 All touch-angles in equall peripheries are equall.
But in unequall peripheries, the cornicular angle of a lesser periphery, is greater than the Cornicular of a greater.
