Huygens demonstrated that the centre of gravity of a segment of any hyperbola, ellipse, or circle was directly related to the area of that segment. He was then able to show the relationships between triangles inscribed in conic sections and the centre of gravity for those sections. By generalizing these theorems to cover all conic sections, Huygens extended classical methods to generate new results.
Huygens demonstrated that the centre of gravity of a segment of any hyperbola, ellipse, or circle was directly related to the area of that segment. He was then able to show the relationships between triangles inscribed in conic sections and the centre of gravity for those s!ections. By generalizing these theorems to cover all conic sections, Huygens extended classical methods to generate new results.