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. 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. Appendix

The censures which, I am informed, have been made on the foregoing essay inclined me to think I had not been clear and express enough in some points, and to prevent being misunderstood for the future, I was willing to make any necessary alterations or additions in what I had written. But that was impracticable, the present edition having been almost finished before I received this information. Wherefore I think it proper to consider in this place the principal objections that are come to my notice.

In the first place it's objected that in the beginning of the essay I argue either against all use of lines and angles in optics, and then what I say is false; or against those writers only who will have it that we can perceive by sense the optic axes, angles, etc., and then it's insignificant, this being an absurdity which no one ever held. To which I answer that I argue only against those who are of opinion that we perceive the distance of objects by lines and angles or, as they term it, by a kind of innate geometry. And to shew that this is not fighting with my own shadow, I shall here set down a passage from the celebrated Descartes.

Distantiam praeterea discimus, per mutuam quandam conspirationem oculorum. Ut enim caecus noster duo bacilla tenens AE et CE, de quorum longitudine incercus, solumque intervallum manuum A et C, cum magnitudine angulorum ACE, et CAE exploratum habens, inde, ut ex geometria quadam omnibus innata, scire potest ubi sit punctum E. Sic quum nostri oculi RST et rst ambo, vertuntur ad X, magnitudo lineae S s , et angulorum XS s et X s S, certos nos redunt ubi sit punctum X. Et idem opera alterutrius possumus indagare, loco illum movendo, ut si versus X illum semper dirigentes, primo sistamus in puncto S, et statim post in puncto s, hoc sufficiet ut magnitudo lineae S s , et duorum angulorum XS s et X s Snostrae imaginationi simul occurrant, et distantiam puncti X nos edoceant;idque per actionem mentis, quae licet simplex judicium esse videatur, ratiocinationem tamen quandam involutam habet, similem illi, qua geometrae per duas stationes diversas, loca inaccessa dimetiuntur.I might amass together citations from several authors to the same purpose, but this being so clear in the point, and from an author of so great note, I shall not trouble the reader with any more. What I have said on this head was not for the sake of finding fault with other men, but because I judged it necessary to demonstrate in the first place that we neither see distance immediately, nor yet perceive it by the mediation of anything that hath (as lines and angles) a necessary connexion with it. For on the demonstration of this point the whole theory depends.