Christiani Hugenii ...Theoremata De Quadratura Hyperboles, Ellipsis Et Circuli, Ex Dato Portionum Gravitatis Centro

by a path that was intended, indeed, but hindered and difficult. Afterward, seeking a shorter way, I fell upon this method which would also pertain to the ellipse and the circle, and that constant and wonderful correspondence in related figures occurred conveniently. Indeed, the only thing that causes this not to have a place universally in all these cases is the newest proposition, that supernumerary one, as it were, and taken up beyond the original proposal, to which it is fair that only this much be attributed to me: that I have shown how it can be proven from the preceding ones by a not-inelegant method. For the most acute geometer, J. Della Faille, anticipated us here long ago and gave an excellent theorem demonstrated nineteen years ago. He was fortunate, in my opinion, to have perceived before others how the quadrature depends upon the center of gravity of the sectors. And while I acknowledge that he earned primary praise regarding the circle, I was not equally pleased by the discovery of a similar connection in the remaining segments of this