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Whence it is easy to recognize this chief property of refraction, namely that the Sine of the angle DAE has always the same ratio to the Sine of the angle NAF, whatever be the inclination of the ray DA: and that this ratio is the same as that of the velocity of the waves in the transparent substance which is towards AE to their velocity in the transparent substance towards AF. For, considering AB as the radius of a circle, the Sine of the angle BAC is BC, and the Sine of the angle ABN is AN. But the angle BAC is equal to DAE, since each of them added to CAE makes a right angle.
On March 11, 1916, English outposts had advanced again about seven miles toward Kut-el-Amara to the neighborhood of Abn Roman, among the sand hills on the right bank of the Tigris. There they surprised at dawn a small Turkish force and made some fifty prisoners, including two officers.
Abn al Casem, the terror of southern Italy, and numbers of his Arab followers, were left dead upon the field. On the 13th of July, 982, the emperor again met the Greeks and their Arab allies in battle, and now occurred that singular adventure and reverse of fortune which has made this engagement memorable.
And the angle ABN is equal to NAF, since each of them with BAN makes a right angle.
His tongue, primed with the satirical sayings of Abn Zayd el Helali, and Humayd ibn Mansur , is the terror of men upon whom repartee imposes. His father was a wealthy shipowner in his day; but, cursed with Abdy and another son, the old man has lost all his property, his children have deserted him, and he now depends entirely upon the charity of the Zayla chief.
Abn Thaher, shocked at the obstinacy of the prince of Persia, left him hastily, and going to his own house, recalled his former reflections, and began to think seriously what he should do. In the mean time a jeweller, one of his intimate friends, came to see him.
Some historians even speak of this period as the "dynasty of the Amirites," from Al-mansur's father, Abn Amir. But this daring usurpation was in part redeemed by qualities in the usurper worthy of a king.
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