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

always existed within them, which we now bring forth, even though it is clear that they were not known or determined by anyone, so far as has reached us. However, we do not provide a determination similar to that of Archimedes, which we have mentioned, nor does the very nature of things seem to have left any hope—after the failed attempts of so many subtle men—of ever expecting such a thing concerning the figures we have taken up to be treated. Yet, we profess to have achieved what is expressed in the very title, and a little bit more, if one may be permitted to anticipate the fair judgment of the reader. For it is not the ultimate goal of these theorems to reduce hyperbolas, ellipses, and circles to squares from given centers of gravity, but only a consequence; and for that reason, they should be especially pleasing, because they demonstrate a certain ratio of the three portions to the inscribed triangles to some extent. It happened that I first discovered this in the hyperbola,