| To eliminate the residual aberration in the spherical lens, we need to increase the refractive index of the glass. |
| In Treatise on the quadrilateral al-Tusi gave the first extant exposition of the whole system of plane and spherical trigonometry. |
| Adding an aplanatic meniscus lens to an achromatic lens can increase relative aperture without introducing additional spherical aberration. |
| In the introduction he pointed out that a plane was a special case of a spherical surface, that is a sphere with infinite radius. |
| A single very small spherical shell is characterized by a lumpy to ragged surface and numerous short spines. |
| Menelaus's work formed the basis for Ptolemy's numerical solutions of spherical astronomy problems in the Almagest. |
