y
purblind (i.e. that could not see an object distinctly but when placed
close to his eye) would not make the same wrong judgment that others do
in the forementioned case. For to him greater confusions constantly
suggesting greater distances, he must, as he recedes from the glass and
the object grows more confused, judge it to be at a farther distance,
contrary to what they do who have had the perception of the objects
growing more confused connected with the idea of approach.

38. Hence also it doth appear there may be good use of computation by
lines and angles in optics; not that the mind judgeth of distance
immediately by them, but because it judgeth by somewhat which is
connected with them, and to the determination whereof they may be
subservient. Thus the mind judging of the distance of an object by the
confusedness of its appearance, and this confusedness being greater or
lesser to the naked eye, according as the object is seen by rays more or
less diverging, it follows that a man may make use of the divergency of
the rays in computing the apparent distance, though not for its own sake,
yet on account of the confusion with which it is connected. But, so it
is, the confusion itself is entirely neglected by mathematicians as
having no necessary relation with distance, such as the greater or lesser
angles of divergency are conceived to have. And these (especially for
that they fall under mathematical computation) are alone regarded in
determining the apparent places of objects, as though they were the sole
and immediate cause of the judgments the mind makes of distance. Whereas,
in truth, they should not at all be regarded in themselves, or any
otherwise, than as they are supposed to be the cause of confused vision.

39. The not considering of this has been a fundamental and perplexing
oversight. For proof whereof we need go no farther than the case before
us. It having been observed that the most diverging rays brought into the
mind the idea of nearest distance, and that still, as the divergency
decreased, the distance increased: and it being thought the connexion
between the various degrees of divergency and distance was immediate;
this naturally leads one to conclude, from an ill-grounded analogy, that
converging rays shall make an object appear at an immense distance: and
that, as the convergency increases, the distance (if it were possible)
should do so likewise. That this was the cause of Dr. Barrow's mistake