157.  I must confess men are tempted to think that flat or plane figures are immediate objects of sight, though they acknowledge solids are not.  And this opinion is grounded on what is observed in painting, wherein (it seems) the ideas immediately imprinted on the mind are only of planes variously coloured, which by a sudden act of the judgment are changed into solids.  But with a little attention we shall find the planes here mentioned as the immediate objects of sight are not visible but tangible planes.  For when we say that pictures are planes, we mean thereby that they appear to the touch smooth and uniform.  But then this smoothness and uniformity, or, in other words, this planeness of the picture, is not perceived immediately by vision:  for it appeareth to the eye various and multiform.

158.  From all which we may conclude that planes are no more the immediate object of sight than solids.  What we strictly see are not solids, nor yet planes variously coloured:  they are only diversity of colours.  And some of these suggest to the mind solids, and other plane figures, just as they have been experienced to be connected with the one or the other:  so that we see planes in the same way that we see solids, both being equally suggested by the immediate objects of sight, which accordingly are themselves denominated planes and solids.  But though they are called by the same names with the things marked by them, they are nevertheless of a nature entirely different, as hath been demonstrated.

159.  What hath been said is, if I mistake not, sufficient to decide the question we proposed to examine, concerning the ability of a pure spirit, such as we have described, to know geometry.  It is, indeed, no easy matter for us to enter precisely into the thoughts of such an intelligence, because we cannot without great pains cleverly separate and disentangle in our thoughts the proper objects of sight from those of touch which are connected with them.  This, indeed, in a complete degree seems scarce possible to be performed:  which will not seem strange to us if we consider how hard it is for anyone to hear the words of his native language pronounced in his ears without understanding them.  Though he endeavour to disunite the meaning from the sound, it will nevertheless intrude into his thoughts, and he shall find it extreme difficult, if not impossible, to put himself exactly in the posture of a foreigner that never learned the language, so as to be affected barely with the sounds themselves, and not perceive the signification annexed to them.

160.  By this time, I suppose, it is clear that neither abstract nor visible extension makes the object of geometry; the not discerning of which may perhaps have created some difficulty and useless labour in mathematics.  Sure I am, that somewhat relating thereto has occurred to my thoughts, which, though after the most anxious and repeated examination I am forced to think it true, doth, nevertheless, seem