Of an angle, which is of two lines whatsoever they be, meeting in one point, the digression or openness in other points, it may be asked how great is that digression? This question is answered also by quantity. An angle therefore hath quantity, though it be not the subject of quantity; for the body only can be the subject, in which body those straddling lines are marked. And because two lines may be made to divaricate by two causes; one, when having one end common and immoveable, they depart one from another at the other ends circularly, and this is called simply an angle; and the quantity thereof is the quantity of the arch, which the two lines intercept. The other cause is the bending of a straight line into a circular or other crooked line, till it touch the place of the same line, whilst it was straight, in one only point. And this is called an angle of contingence. And because the more it is bent, the more it digresseth from the tangent, it may be asked _how much_ more? And therefore the answer must be made by quantity; and consequently an angle of contingence hath its quantity as well as that which is called simply an angle. And in case the digression of two such crooked lines from the tangent be uniform, as in circles, the quantity of their digression may be determined. For, if a straight line be drawn from the point of contact, the digression of the lesser circle will be to the digression of the greater circle, as the part of the line drawn from the point of contact, and intercepted by the circumference of the greater circle is to the part of the same line intercepted by the circumference of the lesser circle, or, which is all one, as the greater radius is to the lesser radius. You may guess by this what will become of that part of your last book, where you handle the question of the quantity of an angle of contingence. Also there lieth a question of _how much comparatively_ one magnitude is to another magnitude, as how much water is in a tun in respect of the ocean, how much in respect of a pint; _little_ in the first respect, _much_ in the latter. Therefore the answer must be made by some respective quantity. This respective quantity is called _ratio_ and proportion, and is determined by the quantity of their differences; and if their differences be compared also with the quantities themselves that differ, it is called simply proportion, or proportion geometrical. But if the differences be not so compared, then it is called proportion arithmetical. And where the difference is none, there is no quantity of the proportion, which in this case is but a bare comparison.