542 
OPT 
this angle is an important element ill that judgment; and 
Euclid, by difcovering this, came into the poffeflioh of a 
valuable truth ; but, b)La fpecies of fophiftry very conge¬ 
nial to the human mind, he extended the principle too 
far, and fuppofed it to be the only circumftance which de¬ 
termines our judgment of vifible magnitude. It is in¬ 
deed the only meafure which we are furnifhed with di- 
reCHy b}' the eye itfelf; but there are few cafes in which 
we form our eftimate without firffc appealing to the com- 
mentapy afforded by the fenfations of touch, or the cor¬ 
rections derived from our own motion. Another princi¬ 
ple, laid down by the fame geometer, is in circumftances 
nearly fimilar to the preceding. According to it, the 
place of any point of an objeCt feen by reflection, is always 
the interfeClion of the reflected ray with the perpendi¬ 
cular drawn from that point to the reflecting furface. 
The proof offered is obfcure and defective ; the propofi- 
tion, however, is true, of plain fpeculums always, and 
of fpherisul, as far as Euclid’s inveltigations extended; 
that is, while the rays fall on the fpecuium with no great 
obliquity. His afi’umption, therefore, did not affeCt the 
truth of his conclutions, though it would have been a 
very unfafe guide in more general inveftigations. The 
book is in many other refpeCts imperfeCt, the reafoning 
often unfound, and the whole hardly worthy of the great 
geometer whofe name it bears. There is, however, no 
doubt that Euclid wrote on the fubjeCt of optics ; but 
many have fuppofed that this treatife is a carelefs extraCt, 
or an unfkilful abridgment, of the original work. 
From the time of Euclid to Seneca, who repeats the 
crude fentiments of Ariflotle, together with fome of his 
own, concerning the rainbow, we find nothing worthy of 
being particularly detailed on the fubjeCt of optics. Pto¬ 
lemy, who lived 150 years after Chrift, wrote a treatife 
on optics. This treatife, though known in the middle 
ages, and quoted by Roger Bacon, had difappeared, and 
was fuppofed to be entirely loft, till within thefe few 
years, when a manufcript on optics, profeiling to be the 
work of Ptolemy, and to be tranflated from the Arabic, 
was found in the king’s library at Paris. The moft va¬ 
luable part of this work is that which relates to refraCtion ; 
from whence it appears, that many experiments had been 
made on that fubjeCt, and the angles of incidence and re- 
fraCtiqn, for different tranfparent fubftances, obferved 
with fo much accuracy, that the fame ratio very nearly of 
the fines of thefe angles, from air into water, or intoglafs, 
is obtained from Ptolemy's numbers, which the repeated 
experiments of later times have fnown to be true. The 
work, however, in the date in which it now appears, is 
very obfcure, the reafoning often deficient in accuracy, 
and the mathematical part much lefs perfeCt than might 
have been expected. Modern writers, prefuming partly 
on the reputation of Ptolemy, and partly guided by the 
authority of Roger Bacon, had afc'ribed to this treatife 
more merit than it appears to poflels ; and, of confe- 
quence, had allowed lefs to the Arabian author Alhazen, 
■who comes next in the order of time, than of right be¬ 
longs to him. Montucla, on the authority of Bacon, 
lays, that Ptolemy afcribed the increafe of the apparent 
magnitude of the heavenly bodies near the horizon, to 
the greater diftance at which they are fuppofed to be, on 
account of the number of intervening objeCts acrofs 
which they are feen. Ptolemy’s explanation, however, as 
ftated by Delambre, from the manufcript juft mentioned, 
is quite different from this, and amounts to no more than 
the vague and unfatisfaftory remark, that an obferver 
looks at the bodies near the zenith in a constrained pof- 
ture, and in the fituation to which the eye is not accuf- 
tomed. Theformerexplanation, therefore, given by Al¬ 
hazen, but fuppofed to have been borrowed from Ptolemy, 
muft now be returned to its right owner. It is the beft 
explanation yet known. The glimpfes of truth, not def- 
tined to be fully difcovered till many ages afterwards, 
which are found in the writings of the ancients, are al¬ 
ways interefting. Ptolemy diftinguiflies what has fince 
I C S. 
been called the virtual focus, which takes place in certain 
cafes of reflection from fpherical fpecula. He remarks, 
that colours are confounded by the rapidity of motion ; 
and gives the inftance of a wheel painted with different 
colours, and turned quickly round. 
Another Greek treatife on optics, that of Pleliodorus of 
Lariffa, has been preferved, and was firft publifhed by 
Erafmus Bartholinus at Paris, in 1657. It isa fuperficial 
work, which, to a good deal of obfcure and unfound 
metaphyfics, adds the demonftration of a few very-obvious 
truths. The author holds the Platonic opinion, that 
vifion is performed by the emiffion of fomething from the 
eyes; and the reafon which he affigns is, that the eyes 
are convex, and more adapted to emit than to receive. 
His metaphyfics may be judged of from this fpecimen. 
He has not been made mention of by any ancient author, 
and the time when he wrote is unknown. As he quotes, 
however, the writings of Ptolemy and Hero, he muft have 
been later than the firft century. 
After Ptolemy, there occurs agreatchafm in the hiftory 
of optics, as well as other branches of mathematics and 
philofophy, which were cultivated chiefly by the Arabs 
during the dark ages of Europe. An interval of nearly 
athoufand years divided Ptolemy homAikazen, who, in the 
hiPeory of optical difcovery, appears as his immediate 
fucceffor. This ingenious Arabian lived in the eleventh 
century, and his merit can be more fairly, and will be 
more highly, appreciated, now that the work of his pre- 
deceffor has become known. The merit of his book on 
optics was always admitted ; but he was fuppofed to have 
borrowed much from Ptolemy, without acknowledging 
it; and the prejudices entertained in favour of a Greek 
author, efpecially of one who had been for fo many years 
a legiflator in fcience, gave a falfe impreflion, both of the 
genius and integrity of his modern rival. The work of 
Alhazen is, neverthelefs, in many refpects, fuperior to 
that of Ptolemy, and in nothing more than in the geome¬ 
try which it employs. The problem known by his name, 
to find the point in a fpherical fpecuium, at which a ray 
coming from one given point lhall be reflected to another 
given point, is very well refolved in his book; though a 
problem of fo much difficulty, that Montucla hazards 
the opinion, that no Arabian geometer was ever equal 
to the folution of it. It is now certain, however, that 
the foiution, from whatever quarter it came, was not bor¬ 
rowed from Ptolemy, in whofe work no mention is made 
of any fuch queftion ; and it may very well be doubted, 
whether, had this problem been propofed to him, the 
Greek geometer would have appeared to as much advan¬ 
tage as the Arabian. 
Alhazen gives a tolerable defcription of the eye; and 
difcourfes largely concerning the nature of vifion, main¬ 
taining, that the cryftalline humour of the eye is of prin¬ 
cipal ufe for this purpofe, without confidering it as a 
lens; and aJferting, that vifion is not completed till the 
ideas of external objeCts are conveyed by the optic nerves 
to the brain. He accounts for Angle vifion by two eyes, 
by fuppofing that, when two correfponding parts of the 
retina are aft'eCted, the mind perceives but one image : 
and he treats much at large of optical deceptions, both in 
direCt vifion, and alio in vifion by reflected and refraCted 
light. Alhazen alfo inquired concerning the nature of 
refra£tion more than any of the ancient writers ; and, 
from aftronomical obfervations, he deduced feveral pro¬ 
perties of atmofpherical refraction : firft of all advancing, 
that the ftars are lometimes feen above the horizon by 
means of refraCtion, when they are really below it. He 
alfo obferved, that refraction contracts the diameters and 
distances of tire heavenly bodies, and that it is the caufe 
of the twinkling of the ltars. 
Prolixity and want of method are the faults of Alha¬ 
zen. Vitello, or Vitellio, a learned Pole, commented on 
his works, and has very much improved their method and 
arrangement in a treatife publifhed in 1270. He has alfo 
treated more fully of the fubjeCt of refraCtion, and re- 
i duced 
