52.  I have now done with distance, and proceed to show how it is that we perceive by sight the magnitude of objects.  It is the opinion of some that we do it by angles, or by angles in conjunction with distance:  but neither angles nor distance being perceivable by sight, and the things we see being in truth at no distance from us, it follows that as we have shown lines and angles not to be the medium the mind makes use of in apprehending the apparent place, so neither are they the medium whereby it apprehends the apparent magnitude of objects.

53.  It is well known that the same extension at a near distance shall subtend a greater angle, and at a farther distance a lesser angle.  And by this principle (we are told) the mind estimates the magnitude of an object, comparing the angle under which it is seen with its distance, and thence inferring the magnitude thereof.  What inclines men to this mistake (beside the humour of making one see by geometry)is that the same perceptions or ideas which suggest distance do also suggest magnitude.  But if we examine it we shall find they suggest the latter as immediately as the former.  I say, they do not first suggest distance, and then leave it to the judgment to use that as a medium whereby to collect the magnitude; but they have as close and immediate a connexion with the magnitude as with the distance; and suggest magnitude as independently of distance as they do distance independently of magnitude.  All which will be evident to whoever considers what hath been already said, and what follows.

54.  It hath been shown there are two sorts of objects apprehended by sight; each whereof hath its distinct magnitude, or extension.  The one, properly tangible, i.e. to be perceived and measured by touch, and not immediately falling under the sense of seeing:  the other, properly and immediately visible, by mediation of which the former is brought in view.  Each of these magnitudes are greater or lesser, according as they contain in them more or fewer points, they being made up of points or minimums.  For, whatever may be said of extension in abtract, it is certain sensible extension is not infinitely divisible.  There is a Minimum TANGIBILE and a Minimum VISIBILE, beyond which sense cannot perceive.  This everyone’s experience will inform him.

55.  The magnitude of the object which exists without the mind, and is at a distance, continues always invariably the same:  but the visible object still changing as you approach to, or recede from, the tangible object, it hath no fixed and determinate greatness.  Whenever, therefore, we speak of the magnitude of anything, for instance a tree or a house, we must mean the tangible magnitude, otherwise there can be nothing steady and free from ambiguity spoken of it.  But though the tangible and visible magnitude in truth belong to two distinct objects:  I shall nevertheless (especially since those objects are called by the same name, and are observed to coexist), to avoid tediousness and singularity of speech, sometimes speak of them as belonging to one and the same thing.