172 DISSERTATION SECOND. [part i. 



respects imperfect, the reasoning often unsound, and the 

 whole hardly worthy of the great geometer whose name it 

 bears. There is, however, no doubt that Euclid wrote on 

 the subject of opticks, and many have supposed that this 

 treatise is a careless extract, or an unskilful abridgment of 

 the original work. 



Antiquity furnished another mathematical treatise on 

 opticks, that of the astronomer Ptolemy. This treatise, 

 though known in the middle ages, and quoted by Roger 

 Bacon, had disappeared, and was supposed to be entirely 

 lost, till within these few years, when a manuscript on 

 opticks, professing to be the work of Ptolemy, and to be 

 translated from the Arabick, was found in the King's libra- 

 ry at Paris. The most valuable part of this work is that 

 which relates to refraction, from whence it appears that 

 many experiments had been made on that subject, and the 

 angles of incidence and refraction, for different transparent 

 substances, observed with so much accuracy, that the 

 same ratio very nearly of the sines of these angles, from 

 air into water, or into glass, is obtained from Ptolemy's 

 numbers, which the repeated experiments of later times 

 have shown to be true. The work, however, in the state 

 in which it now appears, is very obscure, the reasoning 

 often deficient in accuracy, and the mathematical part 

 much less perfect than might have been expected. Mo- 

 dern writers, presuming partly on the reputation of Ptole- 

 my, and partly guided by the authority of Roger Bacon, 

 had ascribed to this treatise more merit than it appears 

 to possess ; and, of consequence, had allowed less to 

 the Arabian author Alhazen, who comes next in the 

 order of time, than of right belongs to him. Montucla, 

 on the authority of Bacon, says, that Ptolemy ascribed 

 the increase of the apparent magnitude of the heaven- 

 ly bodies near the horizon, to the greater distance at 



