PHYSICAL AND MATHEMATICAL SCIENCES. Q5

Haroun-el-Reschid, a little before a.d. 800; and was atits height under Kl-Mamoun, soon after that period.This last sovereign ordered a new measurement of thelength of a degree, which we are told was performed inthe plains of Mesopotamia ; but the result is lost to us,owing to an uncertainty about the kind of measure em-ployed. The great work of Ptolemy was also translatedinto Arabic by his command, under the title of Alma-gest , a.d. 827- 4

The two centuries following this sera were fruitful inastronomers, who particularly devoted themselves to ac-curate observation: the records of their labours are ofgreat extent. Among these Albategnius (or El Batani)discovered the motion of the point of the sun’s apogee.He also corrected Ptolemy ’s determination of the pre-cession of equinoxes.

Ibn Junis made his observations at Cairo t about a. d.1000. It appears that about this time the Arabianastronomers were aware of the properties of the pen-dulum, and employed it in their observations as a mea-sure of time.

In trigonometry, the Arabian mathematicians certainlyintroduced some improvements. The most valuable,perhaps, was the substitution of the sine in their calcu-lations instead of the chord used by the Greeks. AboulWefa made tables of tangents and cotangents abouta. d. 1000. They do not seem to have used the cosinetill about a century later, when Geber , a MahometanSpaniard, gives a formula into which it enters.

It may indeed excite our surprise that such apparentlyobvious improvements should not have been introducedearlier; and that the speculative genius of the Greekgeometry, even without any reference to the practicaluse of trigonometrical formula; for astronomical purposes,should not have pursued the innumerable curious rela-tions they present, as matters of abstract contemplation.That the mathematicians of Greece did not do this is,perhaps, to be traced partly to the fastidious dread theyalways appear to have entertained of mixing up their