For the wave of light DN, being likewise represented by a straight line, it will be seen that all the points of this wave, travelling as far as the surface KD along lines parallel to DB, will advance subsequently towards the point B, and will arrive there at the same time.

As for the Ellipse which served for reflexion, it is evident that it will here become a parabola, since its focus A may be regarded as infinitely distant from the other, B, which is here the focus of the parabola, towards which all the reflexions of rays parallel to AB tend.

And the demonstration of these effects is just the same as the preceding.
But that this curved line CDE which serves for refraction is an Ellipse, and is such that its major diameter is to the distance between its foci as 3 to 2, which is the proportion of the refraction, can be easily found by the calculus of Algebra.

For DB, which is given, being called _a_; its undetermined perpendicular DT being called _x_; and TC _y_; FB will be _a - y_; CB will be sqrt( _xx + aa -2ay + yy_).

But the nature of the curve is such that 2/3 of TC together with CB is equal to DB, as was stated in the last construction: then the equation will be between _( 2/3)y + sqrt( xx + aa - 2ay + yy)_ and _a_; which being reduced, gives _( 6/5)ay - yy_ equal to _( 9/5)xx_; that is to say that having made DO equal to 6/5 of DB, the rectangle DFO is equal to 9/5 of the square on FC.