sier. v.] DISSERTATION SECOND. 177 



it of his book on Opticks was always admitted, but he was 

 supposed to have borrowed much from Ptolemy, without 

 acknowledging it ; and the prejudices entertained in favour 

 of a Greek author, especially of one who had been for so 

 many years a legislator in science, gave a false impression, 

 both of the genius and the integrity of his modern rival. — 

 The work of Alhazen is, nevertheless, in many respects, su- 

 periour to that of Ptolemy, and in nothing more than in the 

 geometry which it employs. The problem known by his 

 name, to find the point in a spherical speculum, at which a 

 ray coming from one given point shall be reflecled to ano- 

 ther given point, is very well resolved in his book, though 

 a problem of so much difficulty, that Montucla hazards the 

 opinion, that no Arabian geometer was ever equal to the so- 

 lution of it. ' It is now certain, however, that the solution, 

 from whatever quarter it came, was not borrowed from Pto- 

 lemy, in whose work no mention is made of any such ques- 

 tion ; and it may very well be doubted, whether, had this 

 problem been proposed to him, the Greek geometer would 

 have appeared to as much advantage as the Arabian. 



The account which the latter gives of the augmentation 

 of the diameters of the heavenly bodies near the hoiizoi. 

 has been already mentioned. He treated also of the re- 

 fraction of light by transparent bodies, and particularly of 

 the atraospherick refraction, but not with the precision o! 

 Ptolemy, whose optical treatise Delambre seems to think it 



1 Barrow, in his 9th lecture, says of this Problem, that it maj 

 truly be called ^vixfA^xitvy as hardly any one more difficult had 

 then been attempted by geometers. He adds, that, after trying 

 the analysis in many different ways, he had found nothing prefera- 

 ble to the solution of Alhazen, which he therefore gives only 

 freed from the prolixness and obscurity with which the oiiginai 

 is chargeable. Lcctiones Opticae, Sect. 9. p. 65. A very elegant 

 solution of the same problem is given by Simson, at the end of 

 his Conick Sections. 



