I don't think I have ever seen that idea put forth
And two posts later, there it is put forth, by Kepler, as I had suggested.
No, he didn't put forth the point you think he did, he just worded it badly. What he meant is that the cumulative bending effect (i.e. the change in gradient) gets larger over time, not the rate of bending. He agrees with me that, for a parabola, the second derivative is constant:
dy^2/dx^2 = 2
That is to say, the rate of change of gradient is constant with respect to horizontal distance travelled everywhere along the curve. This is
not the same as a circle, where the rate of change of angle to the horizontal is constant with respect to distance travelled by the light ray. Regardless, it does not depend on where the light ray was emitted or where it is going to.
Although, I might also add that in light of more recent calculations, a parabola is a poor approximation to the shape light takes. In actuality, it is a curve which, on large scales, is approximately of the form y = Ax
4/3, which has a second derivative of the form dy
2/d
2x = Bx
-2/3, which means that the greatest curvature is seen where the curve is closest to horizontal (although the actual expression is significantly more complicated and I haven't fully analysed it yet; this is just an approximation that works on large scales).