Reducing Quotes - page 6
The King, after the decease of his son, marched his army towards Runtunbhore, to quell an insurrection in those parts, leaving his son Arkully Khan in Dehly, to manage affairs in his absence. The enemy retired into the fort of Runtunbhore, and the King reconnoitred the place, but, despairing of reducing it, marched towards Oojein, which he sacked. At the same time also, he broke down many of the temples of Malwa, and after plundering them of much wealth, returned to Runtunbhore.
Firishta
Hippocrates also attacked the problem of doubling the cube. ...Hippocrates did not, indeed, solve the problem, but he succeeded in reducing it to another, namely, the problem of finding two mean proportionals in continued proportion between two given straight lines, i. e. finding x, y such that a:x=x:y=y:b, where a, b are the two given straight lines. It is easy to see that, if a:x=x:y=y:b, then b/a = (x/a)3, and, as a particular case, if b=2a, x3=2a3, so that the side of the cube which is double of the cube of side a is found.
Thomas Little Heath