| They are also subject to sharp revision, often in ways which suggest that political factors were at work in the numerical reckoning. |
| Mathematical proofs of conjectures, however, require more than overwhelming numerical evidence. |
| If a major interval is made a half step smaller without changing its numerical name, it becomes a minor interval. |
| York were disappointed not to have made more of a clear numerical advantage after Boston Spa players were yellow-carded. |
| Menelaus's work formed the basis for Ptolemy's numerical solutions of spherical astronomy problems in the Almagest. |
| Patients with acalculia are unable to perform mathematical calculations, although some other numerical processing may still be available to them. |
