[_This Appendix is contained only in the second edition._]
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 is 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, &c., and then it is 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 Des Cartes(460):--
"Distantiam præterea discimus, per mutuam quandam conspirationem oculorum. Ut enim cæcus noster duo bacilla tenens, _A E_ et _C E_, de quorum longitudine incertus, solumque intervallum manuum _A_ et _C_, cum magnitudine angulorum _A C E_, et _C A E_ exploratum habens, inde, ut ex Geometria quadam omnibus innata, scire potest ubi sit punctum _E_. Sic quum nostri oculi _R S T_ et _r s t_ ambo, vertuntur ad _X_, magnitudo lineæ _S s_, et angulorum _X S s_ et _X s S_, certos nos reddunt ubi sit punctum _X_. Et idem opera alterutrius possumus indagare, loco illum movendo, ut si versus _X_ illum semper dirigentes, prime sistamus in puncto _S_, et statim post in puncto _s_, hoc sufficiet ut magnitudo lineæ _S s_, et duorum angulorum _X S s_ et _X s S_ nostræ imaginationi simul occurrant, et distantiam puncti _X_ nos edoceant: idque per actionem mentis, quæ licet simplex judicium esse videatur, ratiocinationem tamen quandam involutam habet, similem illi, qua Geometræ per duas stationes diversas, loca inaccessa dimetiuntur."