,an ,essay ,towards a ,new ,theory of ,vision by ,george ,berkeley 7#afhe-agec7 ,,contents ,sect4 #a ,design #b ,distance of itself invisible #c ,remote distance perceived rather by experience than by sense #d ,near distance thought to be perceived by the ,,angle of the ,,optic ,,axes #e ,difference between this and the former manner of perceiving distance #f ,also by diverging rays #g ,this depends not on experience #h ,these the common accounts1 but not satisfactory #i ,some ,,ideas perceived by the mediation of others #aj ,no ,,idea which is not itself perceived1 can be the means of perceiving another #aa ,distance perceived by means of some other ,,idea #ab ,those lines and angles mentioned in optics1 are not themselves perceived #ac ,hence the mind does not perceive distance by lines and angles #ad ,also because they have no real existence #ae ,and because they are insufficient to explain the phenomena #af ,the ,,ideas that suggest distance are1 #ast1 the sensation arising from the turn of the eyes #ag ,betwixt which and distance there is no necessary connection #ah ,scarce room for mistake in this matter #ai ,no regard had to the angle of the ,,optic ,,axes #bj ,judgment of distance made with both eyes1 the result of ,,experience #ba #bndly1 ,confusedness of appearance #bb ,this the occasion of those judgments attributed to diverging rays #bc ,objection answered #bd ,what deceives the writers of optics in this matter #be ,the cause why one ,,idea may suggest another #bf ,this applied to confusion and distance #bg ,thirrdly1 the straining of the eye #bh ,the occasions which suggest distance have in their own nature no relation to it #bi ,a difficult case proposed by ,dr4 ,barrow as repugnant to all the known theories #cj ,this case contradicts a received principle in catoptrics #ca ,it is shown to agree with the principles we have laid down #cb ,this phenomenon illustrated #cc ,it confirms the truth of the principle whereby it is explained #cd ,vision when distinct1 and when confused #ce ,the different effects of parallel diverging and converging rays #cf ,how converging and diverging rays come to suggest the same distance #cg ,a person extreme purblind would judge aright in the forementioned case #ch ,lines and angles1 why useful in optics #ci ,the not understanding this1 a cause of mistake #dj ,a query proposed1 by ,mr4 ,molyneux in his ,,dioptrics1 considered #da ,one born blind would not at first have any ,,idea of distance by sight #db ,this not agreeable to the common principles #dc ,the proper objects of sight1 not without the mind1 nor the images of any thing without the mind #dd ,this more fully explained #de ,in what sense we must be understood to see distance and external things #df ,distance1 and things placed at a distance1 not otherwise perceived by the eye than by the ear #dg ,the ,,ideas of sight more apt to be confounded with the ,,ideas of touch than those of hearing are #dh ,how this comes to pass #di ,strictly speaking1 we never see and feel the same thing #ej ,objects of ,,sight twofold1 mediate and immediate #ea ,these hard to separate in our thoughts #eb ,the received accounts of our perceiving magnitude by sight1 false #ec ,magnitude perceived as immediately as distance #ed ,two kinds of sensible extension1 neither of which is infinitely divisible #ee ,the tangible magnitude of an ,,object steady1 the visible not #ef ,by what means tangible magnitude is perceived by sight #eg ,this further enlarged on #eh ,no necessary connection between confusion or faintness of appearance1 and small or great magnitude #ei ,the tangible magnitude of an ,,object more heeded than the visible1 and why #fj ,an instance of this #fa ,men do not measure by visible feet or inches #fb ,no necessary connection between visible and tangible extension #fc ,greater visible magnitude might signify lesser tangible magnitude #fd ,the judgments we make of magnitude depend altogether on experience #fe ,distance and magnitude seen as shame or anger #ff ,but we are prone to think otherwise1 and why #fg ,the moon seems greater in the horizon than in the meridian #fh ,the cause of this phenomenon assigned #fi ,the horizontal moon1 why greater at one time than another4 #gj ,the account we have given proved to be true #ga ,and confirmed by the moon's appearing greater in a mist #gb ,objection answered #gc ,the way wherein faintness suggests greater magnitude illustrated #gd ,appearance of the horizontal moon1 why thought difficult to explain #ge ,attempts towards the solution of it made by several1 but in vain #gf ,the opinion of ,dr4 ,wallis #gg ,it is shown to be unsatisfactory #gh ,how lines and angles may be of use in computing apparent magnitudes #gi ,one born blind1 being made to see1 what judgment he would make of magnitude #hj ,the ,,minimum ,,visible the same to all creatures #ha ,objection answered #hb ,the eye at all times perceives the same number of visible points #hc ,two imperfections in the ,,visive ,,faculty #hd ,answering to which1 we may conceive two perfections #he ,in neither of these two ways do microscopes improve the sight #hf ,the case of microscopical eyes1 considered #hg ,the sight1 admirably adapted to the ends of seeing #hh ,difficulty concerning erect vision #hi ,the common way of explaining it #ij ,the same shown to be false #ia ,not distinguishing between ,,ideas of sight and touch1 cause of mistake in this matter #ib ,the case of one born blind1 proper to be considered #ic ,such a one might by touch attain to have ,,ideas of ,,upper and ,,lower #id ,which modes of situation he would attribute only to things tangible #ie ,he would not at first sight think anything he saw1 high or low1 erect or inverted #if ,this illustrated by an example #ig ,by what means he would come to denominate visible ,,objects1 high or low1 etc4 #ih ,why he should think those ,,objects highest1 which are painted on the lowest part of his eye1 and ,,vice ,,versa #ii ,how he would perceive by sight1 the situation of external objects #ajj ,our propension to think the contrary1 no argument against what has been said #aja ,objection #ajb ,answer #ajc ,an object could not be known at first sight by the colour #ajd ,nor by the magnitude thereof #aje ,nor by the figure #ajf ,in the first act of vision1 no tangible thing would be suggested by sight #ajg ,difficulty proposed concerning number #ajh ,number of things visible1 would not at first sight suggest the like number of things tangible #aji ,number the creature of the mind #aaj ,one born blind would not at first sight number visible things as others do #aaa ,the situation of any object determined with respect only to objects of the same sense #aab ,no distance1 great or small1 between a visible and tangible thing #aac ,the not observing this1 cause of difficulty in erect vision #aad ,which otherwise includes nothing unaccountable #aae ,what is meant by the picture being inverted #aaf ,cause of mistake in this matter #aag ,images in the eye1 not pictures of external objects #aah ,in what sense they are pictures #aai ,in this affair we must carefully distinguish between ideas of sight and touch #abj ,difficult to explain by words the true ,theory of ,vision #aba ,the question1 whether there is any ,,idea common to sight and touch1 stated #abb ,abstract extension inquired into #abc ,it is incomprehensible #abd ,abstract extension not the ,,object of geometry #abe ,the general ,,idea of a triangle1 considered #abf ,vacuum1 or pure space1 not common to sight and touch #abg ,there is no idea1 or kind of idea1 common to both senses #abh ,first argument in proof hereof #abi ,second argument #acj ,visible figure and extension1 not distinct ,,ideas from colour #aca ,third argument #acb ,confirmation drawn from ,mr4 ,molyneux's problem of a sphere and a cube1 published by ,mr4 ,locke #acc ,which is falsely solved1 if the common supposition be true #acd ,more might be said in proof of our tenet1 but this suffices #ace ,further reflection on the foregoing problem #acf ,the same thing doth not affect both sight and touch #acg ,the same idea of motion not common to sight and touch #ach ,the way wherein we apprehend motion by sight1 easily collected from what hath been said #aci ,,qu4 ,how visible and tangible ,,ideas came to have the same name if not of the same kind #adj ,this accounted for without supposing them of the same kind #ada ,,obj4 ,that a tangible square is liker to a visible square than to a visible circle #adb ,,ans4 ,that a visible square is fitter than a visible circle1 to represent a tangible square #adc ,but it doth not hence follow1 that a visible square is like a tangible square #add ,why we are more apt to confound visible with tangible ,,ideas1 than other signs with the things signified #ade ,several other reasons hereof1 assigned #adf ,reluctancy in rejecting any opinion1 no argument of its truth #adg ,proper objects of vision the language of nature #adh ,in it there is much admirable1 and deserving our attention #adi ,question proposed1 concerning the object of geometry #aej ,at first view we are apt to think visible extension the object of geometry #aea ,visible extension shown not to be the object of geometry #aeb ,words may as well be thought the object of geometry1 as visible extension #aec ,it is proposed to inquire1 what progress an intelligence that could see1 but not feel1 might make in geometry #aed ,he cannot understand those parts which relate to solids1 and their surfaces1 and lines generated by their section #aee ,nor even the elements of plane geometry #aef ,the proper objects of sight incapable of being managed as geometrical figures #aeg ,the opinion of those who hold plane figures to be the immediate objects of sight1 considered #aeh ,planes no more the immediate objects of sight1 than solids #aei ,difficult to enter precisely into the thoughts of the above-mentioned intelligence #afj ,the object of geometry1 its not being sufficiently understood1 cause of difficulty1 and useless labour in that science ,,an ,,essay ,,towards ,a ,,new ,,theory ,,of ,,vision #a4 ,my design is to show the manner wherein we perceive by sight the distance1 magnitude1 and situation of ,,objects4 ,also to consider the difference there is betwixt the ,,ideas of sight and touch1 and whether there be any ,,idea common to both senses4 #b4 ,it is1 ,i think1 agreed by all that ,,distance1 of itself and immediately1 cannot be seen4 ,for ,,distance being a ,line directed end-wise to the eye1 it projects only one point in the fund of the eye1 which point remains invariably the same1 whether the distance be longer or shorter4 #c4 ,i find it also acknowledged that the estimate we make of the distance of ,,objects considerably remote is rather an act of judgment grounded on ,,experience than of ,,sense4 ,for example1 when ,i perceive a great number of intermediate ,,objects1 such as houses1 fields1 rivers1 and the like1 which ,i have experienced to take up a considerable space1 ,i thence form a judgment or conclusion that the ,,object ,i see beyond them is at a great distance4 ,again1 when an ,,object appears faint and small1 which at a near distance ,i have experienced to make a vigorous and large appearance1 ,i instantly conclude it to be far off3 ,and this1 it is evident1 is the result of ,,experience2 without which1 from the faintness and littleness ,i should not have inferred anything concerning the distance of ,,objects4 #d4 ,but when an ,,object is placed at so near a distance as that the interval between the eyes bears any sensible proportion to it1 the opinion of speculative men is that the two ,,optic ,,axes 7the fancy that we see only with one eye at once being exploded7 concurring at the ,,object do there make an ,,angle1 by means of which1 according as it is greater or lesser1 the ,,object is perceived to be nearer or farther off4 #e4 ,betwixt which and the foregoing manner of estimating distance there is this remarkable difference3 that whereas there was no apparent1 necessary connection between small distance and a large and strong appearance1 or between great distance and a little and faint appearance1 there appears a very necessary connection between an obtuse angle and near distance1 and an acute angle and farther distance4 ,it does not in the least depend upon experience1 but may be evidently known by anyone before he had experienced it1 that the nearer the concurrence of the ,,optic ,,axes1 the greater the ,,angle1 and the remoter their concurrence is1 the lesser will be the ,,angle comprehended by them4 #f4 ,there is another way mentioned by optic writers1 whereby they will have us judge of those distances1 in respect of which the breadth of the ,,pupil hath any sensible bigness3 ,and that is the greater or lesser divergency of the rays1 which issuing from the visible point do fall on the ,,pupil1 that point being judged nearest which is seen by most diverging rays1 and that remoter which is seen by less diverging rays3 and so on1 the apparent distance still increasing1 as the divergency of the rays decreases1 till at length it becomes infinite1 when the rays that fall on the ,,pupil are to sense parallel4 ,and after this manner it is said we perceive distance when we look only with one eye4 #g4 ,in this case also it is plain we are not beholding to experience3 it being a certain1 necessary truth that the nearer the direct rays falling on the eye approach to a ,,parallelism1 the farther off is the point of their intersection1 or the visible point from whence they flow4 #h4 ,i have here set down the common1 current accounts that are given of our perceiving near distances by sight1 which1 though they are unquestionably received for true by ,,mathematicians1 and accordingly made use of by them in determining the apparent places of ,,objects1 do1 nevertheless seem to me very unsatisfactory3 and that for these following reasons3-- #i4 ,,first1 ,it is evident that when the mind perceives any ,,idea1 not immediately and of itself1 it must be by the means of some other ,,idea4 ,thus1 for instance1 the passions which are in the mind of another are of themselves to me invisible4 ,i may nevertheless perceive them by sight1 though not immediately1 yet by means of the colours they produce in the countenance4 ,we often see shame or fear in the looks of a man1 by perceiving the changes of his countenance to red or pale4 #aj4 ,moreover it is evident that no ,,idea which is not itself perceived can be the means of perceiving any other ,,idea4 ,if ,i do not perceive the redness or paleness of a man's face themselves1 it is impossible ,i should perceive by them the passions which are in his mind4 #aa4 ,now from sect4 #b it is plain that distance is in its own nature imperceptible1 and yet it is perceived by sight4 ,it remains1 therefore1 that it be brought into view by means of some other ,,idea that is itself immediately perceived in the act of ,,vision4 #ab4 ,but those ,,lines and ,,angles1 by means whereof some ,,mathematicians pretend to explain the perception of distance1 are themselves not at all perceived1 nor are they in truth ever thought of by those unskilful in optics4 ,i appeal to anyone's experience whether upon sight of an ,,object he computes its distance by the bigness of the ,,angle made by the meeting of the two ,,optic ,,axes8 ,or whether he ever thinks of the greater or lesser divergency of the rays1 which arrive from any point to his ,,pupil8 ,everyone is himself the best judge of what he perceives1 and what not4 ,in vain shall all the ,,mathematicians in the world tell me1 that ,i perceive certain ,,lines and ,,angles which introduce into my mind the various ,,ideas of ,,distance1 so long as ,i myself am conscious of no such thing4 #ac4 ,since1 therefore1 those ,,angles and ,,lines are not themselves perceived by sight1 it follows from sect4 #aj that the mind doth not by them judge of the distance of ,,objects4 #ad4 ,secondly1 the truth of this assertion will be yet farther evident to anyone that considers those ,,lines and ,,angles have no real existence in nature1 being only an ,,hypothesis framed by the ,,mathematicians1 and by them introduced into ,,optics1 that they might treat of that science in a ,,geometrical way4 #ae4 ,the third and last reason ,i shall give for rejecting that doctrine is1 that though we should grant the real existence of those ,,optic ,,angles1 etc41 and that it was possible for the mind to perceive them1 yet these principles would not be found sufficient to explain the ,,phenomena of ,,distance1 as shall be shown hereafter4 #af4 ,now1 it being already shown that distance is suggested to the mind by the mediation of some other ,,idea which is itself perceived in the act of seeing1 it remains that we inquire what ,,ideas or ,,sensations there be that attend ,,vision1 unto which we may suppose the ,,ideas of distance are connected1 and by which they are introduced into the mind4 ,and ,,first1 it is certain by experience that when we look at a near ,,object with both eyes1 according as it approaches or recedes from us1 we alter the disposition of our eyes1 by lessening or widening the interval between the ,,pupils4 ,this disposition or turn of the eyes is attended with a sensation1 which seems to me to be that which in this case brings the ,,idea of greater or lesser distance into the mind4 #ag4 ,not that there is any natural or necessary connection between the sensation we perceive by the turn of the eyes and greater or lesser distance1 but because the mind has by constant ,,experience found the different sensations corresponding to the different dispositions of the eyes to be attended each with a different degree of distance in the ,,object3 there has grown an habitual or customary connection between those two sorts of ,,ideas1 so that the mind no sooner perceives the sensation arising from the different turn it gives the eyes1 ,in order to bring the ,,pupils nearer or farther asunder1 but it withal perceives the different ,,idea of distance which was wont to be connected with that sensation2 just as upon hearing a certain sound1 the ,,idea is immediately suggested to the understanding which custom had united with it4 #ah ,nor do ,i see how ,i can easily be mistaken in this matter4 ,i know evidently that distance is not perceived of itself4 ,that by consequence it must be perceived by means of some other ,,idea which is immediately perceived1 and varies with the different degrees of distance4 ,i know also that the sensation arising from the turn of the eyes is of itself immediately perceived1 and various degrees thereof are connected with different distances1 which never fail to accompany them into my mind1 when ,i view an ,,object distinctly with both eyes1 whose distance is so small that in respect of it the interval between the eyes has any considerable magnitude4 #ai4 ,i know it is a received opinion that by altering the disposition of the eyes the mind perceives whether the angle of the ,,optic ,,axes is made greater or lesser4 ,and that accordingly by a kind of ,,natural ,,geometry it judges the point of their intersection to be nearer or farther off4 ,but that this is not true ,i am convinced by my own experience1 since ,i am not conscious that ,i make any such use of the perception ,i have by the turn of my eyes4 ,and for me to make those judgments1 and draw those conclusions from it1 without knowing that ,i do so1 seems altogether incomprehensible4 #bj4 ,from all which it follows that the judgment we make of the distance of an ,,object1 viewed with both eyes1 is entirely the ,,result ,,of ,,experience4 ,if we had not constantly found certain sensations arising from the various disposition of the eyes1 attended with certain degrees of distance1 we should never make those sudden judgments from them concerning the distance of ,,objects2 no more than we would pretend to judge a man's thoughts by his pronouncing words we had never heard before4 #ba4 ,secondly1 an ,,object placed at a certain distance from the eye1 to which the breadth of the ,,pupil bears a considerable proportion1 being made to approach1 is seen more confusedly3 and the nearer it is brought the more confused appearance it makes4 ,and this being found constantly to be so1 there ariseth in the mind an habitual ,,connection between the several degrees of confusion and distance2 the greater confusion still implying the lesser distance1 and the lesser confusion the greater distance of the ,,object4 #bb4 ,this confused appearance of the ,,object doth therefore seem to be the ,,medium whereby the mind judgeth of distance in those cases wherein the most approved writers of optics will have it judge by the different divergency with which the rays flowing from the radiating point fall on the ,,pupil4 ,no man1 ,i believe1 will pretend to see or feel those imaginary angles that the rays are supposed to form according to their various inclinations on his eye4 ,but he cannot choose seeing whether the ,,object appear more or less confused4 ,it is therefore a manifest consequence from what bath been demonstrated1 that instead of the greater or lesser divergency of the rays1 the mind makes use of the greater or lesser confusedness of the appearance1 thereby to determine the apparent place of an ,,object4 #bc ,nor doth it avail to say there is not any necessary connection between confused ,,vision and distance1 great or small4 ,for ,i ask any man what necessary connection he sees between the redness of a blush and shame8 ,and yet no sooner shall he behold that colour to arise in the face of another1 but it brings into his and the ,,idea of that passion which hath been observed to accompany it4 #bd4 ,what seems to have misled the writers of optics in this matter is that they imagine men judge of distance as they do of a conclusion in mathematics1 betwixt which and the premises it is indeed absolutely requisite there be an apparent1 necessary connection3 but it is far otherwise in the sudden judgments men make of distance4 ,we are not to think that brutes and children1 or even grown reasonable men1 whenever they perceive an ,,object to approach1 or depart from them1 do it by virtue of ,,geometry and ,,demonstration4 #be4 ,that one ,,idea may suggest another to the mind it will suffice that they have been observed to go together1 without any demonstration of the necessity of their coexistence1 or without so much as knowing what it is that makes them so to coexist4 ,of this there are innumerable instances of which no one can be ignorant4 #bf4 ,thus1 greater confusion having been constantly attended with nearer distance1 no sooner is the former ,,idea perceived1 but it suggests the latter to our thoughts4 ,and if it had been the ordinary course of ,nature that the farther off an ,,object were placed1 the more confused it should appear1 it is certain the very same perception that now makes us think an ,,object approaches would then have made us to imagine it went farther off4 ,that perception1 abstracting from ,,custom and ,,experience1 being equally fitted to produce the ,,idea of great distance1 or small distance1 or no distance at all4 #bg4 ,thirdly1 an ,,object being placed at the distance above specified1 and brought nearer to the eye1 we may nevertheless prevent1 at least for some time1 the appearances growing more confused1 by straining the eye4 ,in which case that sensation supplies the place of confused ,,vision in aiding the mind to judge of the distance of the ,,object2 it being esteemed so much the nearer by how much the effort or straining of the eye in order to distinct ,,vision is greater4 #bh4 ,i have here set down those sensations or ,,ideas that seem to be the constant and general occasions of introducing into the mind the different ,,ideas of near distance4 ,it is true in most cases that divers other circumstances contribute to frame our ,,idea of distance1 to wit1 the particular number1 size1 kind1 etc41 of the things seen4 ,concerning which1 as well as all other the forementioned occasions which suggest distance1 ,i shall only observe they have none of them1 in their own nature1 any relation or connection with it3 nor is it possible they should ever signify the various degrees thereof1 otherwise than as by ,,experience they have been found to be connected with them4 #bi4 ,i shall proceed upon these principles to account for a phenomenon which has hitherto strangely puzzled the writers of optics1 and is so far from being accounted for by any of their ,,theories ,,of ,,vision that it is1 by their own confession1 plainly repugnant to them2 and of consequence1 if nothing else could be objected1 were alone sufficient to bring their credit in question4 ,the whole difficulty ,i shall lay before you in the words of the learned ,dr4 ,barrow1 with which he concludes his optic lectures3-- ',i have here delivered what my thoughts have suggested to me concerning that part of optics which is more properly mathematical4 ,as for the other parts of that science 7which being rather physical1 do consequently abound with plausible conjectures instead of certain principles71 there has in them scarce anything occurred to my observation different from what has been already said by ,kepler1 ,scheinerus1 ,descartes1 and others4 ,and methinks1 ,i had better say nothing at all1 than repeat that which has been so often said by others4 ,i think it therefore high time to take my leave of this subject3 but before ,i quit it for good and all1 the fair and ingenuous dealing that ,i owe both to you and to truth obligeth me to acquaint you with a certain untoward difficulty1 which seems directly opposite to the doctrine ,i have been hitherto inculcating1 at least1 admits of no solution from it4 ,in short it is this4 ,before the double convex glass or concave speculum ,,ebf1 let the point ,a be placed at such a distance that the rays proceeding from ,a1 after refraction or reflection1 be brought to unite somewhere in the ,ax,a,b4 ,and suppose the point of union 7i4e4 the image of the point ,a1 as hath been already set forth7 to be ,z2 between which and ,b1 the vertex of the glass or speculum1 conceive the eye to be anywhere placed4 ,the question now is1 where the point ,a ought to appear8 ,experience shows that it does not appear behind at the point ,z1 and it were contrary to nature that it should1 since all the impression which affects the sense comes from towards ,a4 ,but from our tenets it should seem to follow that it would appear before the eye at a vast distance off1 so great as should in some sort surpass all sensible distance4 ,for since if we exclude all anticipations and prejudices1 every ,,object appears by so much the farther off1 by how much the rays it sends to the eye are less diverging4 ,and that ,,object is thought to be most remote from which parallel rays proceed unto the eye4 ,reason would make one think that ,,object should appear at yet a greater distance which is seen by converging rays4 ,moreover it may in general be asked concerning this case what it is that determines the apparent place of the point ,a1 and maketh it to appear after a constant manner sometimes nearer1 at other times farther off8 ,to which doubt ,i see nothing that can be answered agreeable to the principles we have laid down except only that the point ,a ought always to appear extremely remote4 ,but on the contrary we are assured by experience that the point ,a appears variously distant1 according to the different situations of the eye between the points ,b and ,z4 ,and that it doth never 7if at all7 seem farther off1 than it would if it were beheld by the naked eye1 but on the contrary it doth sometimes appear much nearer4 ,nay1 it is even certain that by how much the rays falling on the eye do more converge by so much the nearer doth the ,,object seem to approach4 ,for the eye being placed close to the point ,b1 the ,,object ,a appears nearly in its own natural place1 if the point ,b is taken in the glass1 or at the same distance1 if in the speculum4 ,the eye being brought back to ,o1 the ,,object seems to draw near3 and being come to ,p it beholds it still nearer4 ,and so on little and little1 till at length the eye being placed somewhere1 suppose at ,q1 the ,,object appearing extremely near1 begins to vanish into mere confusion4 ,all which doth seem repugnant to our principles1 at least not rightly to agree with them4 ,nor is our tenet alone struck at by this experiment1 but likewise all others that ever came to my knowledge are1 every whit as much1 endangered by it4 ,the ancient one especially 7which is most commonly received1 and comes nearest to mine7 seems to be so effectually overthrown thereby that the most learned ,tacquet has been forced to reject that principle1 as false and uncertain1 on which alone he had built almost his whole ,,catoptrics2 and consequently by taking away the foundation1 hath himself pulled down the superstructure he had raised on it4 ,which1 nevertheless1 ,i do not believe he would have done had he but considered the whole matter more thoroughly1 and examined the difficulty to the bottom4 ,but as for me1 neither this nor any other difficulty shall have so great an influence on me as to make me renounce that which ,i know to be manifestly agreeable to reason3 especially when1 as it here falls out1 the difficulty is founded in the peculiar nature of a certain odd and particular case4 ,for in the present case something peculiar lies hid1 which being involved in the subtilty of nature will1 perhaps1 hardly be discovered till such time as the manner of vision is more perfectly made known4 ,concerning which1 ,i must own1 ,i have hitherto been able to find out nothing that has the least show of ,,probability1 not to mention ,,certainty4 ,i shall1 therefore1 leave this knot to be untied by you1 wishing you may have better success in it than ,i have had4' #cj4 ,the ancient and received principle1 which ,dr4 ,barrow here mentions as the main foundation of ,tacquet's ,,catoptrics1 is that3 'every visible point seen by reflection from a speculum shall appear placed at the intersection of the reflected ray1 and the perpendicular of incidence3' which intersection in the present case1 happening to be behind the eye1 it greatly shakes the authority of that principle1 whereon the aforementioned author proceeds throughout his whole ,,catoptrics in determining the apparent place of ,,objects seen by reflection from any kind of speculum4 #ca4 ,let us now see how this phenomenon agrees with our tenets4 ,the eye the nearer it is placed to the point ,b in the foregoing figures1 the more distinct is the appearance of the ,,object2 but as it recedes to ,o the appearance grows more confused2 and at ,p it sees the ,,object yet more confused2 and so on till the eye being brought back to ,z sees the ,,object in the greatest confusion of all4 ,wherefore by sect4 #ba the ,,object should seem to approach the eye gradually as it recedes from the point ,b1 that is1 at ,o it should 7in consequence of the principle ,i have laid down in the aforesaid section7 seem nearer than it did at ,b1 and at ,p nearer than at ,o1 and at ,q nearer than at ,p2 and so on1 till it quite vanishes at ,z4 ,which is the very matter of fact1 as anyone that pleases may easily satisfy himself by experiment4 #cb4 ,this case is much the same as if we should suppose an ,englishman to meet a foreigner who used the same words with the ,english1 but in a direct contrary signification4 ,the ,englishman would not fail to make a wrong judgment of the ,,ideas annexed to those sounds in the mind of him that used them4 ,just so1 in the present case the ,,object speaks 7if ,i may so say7 with words that the eye is well acquainted with1 that is1 confusions of appearance2 but whereas heretofore the greater confusions were always wont to signify nearer distances1 they have in this case a direct1 contrary signification1 being connected with the greater distances4 ,whence it follows that the eye must unavoidably be mistaken1 since it will take the confusions in the sense it has been used to1 which is directly opposed to the true4 #cc4 ,this phenomenon as it entirely subverts the opinion of those who will have us judge of distance by lines and angles1 on which supposition it is altogether inexplicable1 so it seems to me no small confirmation of the truth of that principle whereby it is explained4 ,but in order co a more full explication of this point1 and to show how far the hypothesis of the mind's judging by the various divergency of rays may be of use in determining the apparent place of an ,,object1 it will be necessary to premise some few things1 which are already well known to those who have any skill in dioptrics4 #cd4 ,,first1 any radiating point is then distinctly seen when the rays proceeding from it are1 by the refractive power of the crystalline1 accurately reunited in the retina or fund of the eye3 but if they are reunited1 either before they arrive at the retina1 or after they have passed it1 then there is confused vision4 #ce4 ,,secondly1 suppose in the adjacent figures ,,np represent an eye duly framed and retaining its natural figure4 ,in ,fig4 #a the rays falling nearly parallel on the eye1 are by the crystalline ,,ab refracted1 so as their focus or point of union ,f falls exactly on the retina3 but if the rays fall sensibly diverging on the eye1 as in ,fig4 #b1 then their focus falls beyond the retina3 or if the rays are made to converge by the lens ,,qs before they come at the eye1 as in ,fig4 #c1 their focus ,f will fall before the retina4 ,in which two last cases it is evident from the foregoing section that the appearance of the point ,z is confused4 ,and by how much the greater is the convergency1 or divergency1 of the rays falling on the pupil1 by so much the farther will the point of their reunion be from the retina1 either before or behind it1 and consequently the point ,z will appear by so much the more confused4 ,and this1 by the bye1 may show us the difference between confused and faint vision4 ,confused vision is when the rays proceedings from each distinct point of the ,,object are not accurately recollected in one corresponding point on the retina1 but take up some space thereon1 so that rays from different points become mixed and confused together4 ,this is opposed to a distinct vision1 and attends near objects4 ,faint vision is when by reason of the distance of the object or grossness of the interjacent medium few rays arrive from the object to the eye4 ,this is opposed to vigorous or clear vision1 and attends remote objects4 ,but to return4 #cf4 ,the eye1 or 7to speak truly7 the mind1 perceiving only the confusion itself1 without ever considering the cause from which it proceeds1 doth constantly annex the same degree of distance to the same degree of confusion4 ,whether that confusion be occasioned by converging or by diverging rays1 it matters not4 ,whence it follows that the eye viewing the object ,z through the glass ,,qs 7which by refraction causeth the rays ,,zq1 ,,zs1 etc41 to converge7 should judge it to be at such a nearness at which if it were placed it would radiate on the eye with rays diverging to that degree as would produce the same confusion which is now produced by converging rays1 i4e4 would cover a portion of the retina equal to ,,dc 7,,vid4 ,fig4 #c supra74 ,but then this must be understood 7to use ,dr4 ,barrow's phrase7 ,,seclusis ,,praenotionibus ,,et ,,praejudiciis1 in case we abstract from all other circumstances of vision1 such as the figure1 size1 faintness1 etc4 of the visible objects2 all which do ordinarily concur to form our idea of distance1 the mind having by frequent experience observed their several sorts or degrees to be connected with various distances4 #cg4 ,it plainly follows from what hath been said that a person perfectly purblind 7i4e4 that could not see an object distinctly but when placed close to his eye7 would not make the same wrong judgment that others do in the forementioned case4 ,for to him greater confusions constantly suggesting greater distances1 he must1 as he recedes from the glass and the object grows more confused1 judge it to be at a farther distance1 contrary to what they do who have had the perception of the objects growing more confused connected with the idea of approach4 #ch4 ,hence also it doth appear there may be good use of computation by lines and angles in optics2 not that the mind judgeth of distance immediately by them1 but because it judgeth by somewhat which is connected with them1 and to the determination whereof they may be subservient4 ,thus the mind judging of the distance of an object by the confusedness of its appearance1 and this confusedness being greater or lesser to the naked eye1 according as the object is seen by rays more or less diverging1 it follows that a man may make use of the divergency of the rays in computing the apparent distance1 though not for its own sake1 yet on account of the confusion with which it is connected4 ,but1 so it is1 the confusion itself is entirely neglected by mathematicians as having no necessary relation with distance1 such as the greater or lesser angles of divergency are conceived to have4 ,and these 7especially for that they fall under mathematical computation7 are alone regarded in determining the apparent places of objects1 as though they were the sole and immediate cause of the judgments the mind makes of distance4 ,whereas1 in truth1 they should not at all be regarded in themselves1 or any otherwise1 than as they are supposed to be the cause of confused vision4 #ci4 ,the not considering of this has been a fundamental and perplexing oversight4 ,for proof whereof we need go no farther than the case before us4 ,it having been observed that the most diverging rays brought into the mind the idea of nearest distance1 and that still1 as the divergency decreased1 the distance increased3 and it being thought the connexion between the various degrees of divergency and distance was immediate2 this naturally leads one to conclude1 from an ill-grounded analogy1 that converging rays shall make an object appear at an immense distance3 and that1 as the convergency increases1 the distance 7if it were possible7 should do so likewise4 ,that this was the cause of ,dr4 ,barrow's mistake is evident from his own words which we have quoted4 ,whereas had the learned doctor observed that diverging and converging rays1 how opposite soever they may seem1 do nevertheless agree in producing the same effect1 to wit1 confusedness of vision1 greater degrees whereof are produced indifferently1 either as the divergency or convergency and the rays increaseth4 ,and that it is by this effect1 which is the same in both1 that either the divergency or convergency is perceived by the eye2 ,i say1 had he but considered this1 it is certain he would have made a quite contrary judgment1 and rightly concluded that those rays which fall on the eye with greater degrees of convergency should make the object from whence they proceed appear by so much the nearer4 ,but it is plain it was impossible for any man to attain to a right notion of this matter so long as he had regard only to lines and angles1 and did not apprehend the true nature of vision1 and how far it was of mathematical consideration4 #dj4 ,before we dismiss this subject1 it is fit we take notice of a query relating thereto1 proposed by the ingenious ,mr4 ,molyneux1 is his ,,treatise ,,of ,,dioptrics1,par4 ,i4 ,prop4 #ca1 ,sect4 #i4 where speaking of this difficulty1 he has these words3 ',and so he 7i4e4 ,dr4 ,barrow7 leaves this difficulty to the solution of others1 which ,i 7after so great an example7 shall do likewise2 but with the resolution of the same admirable author of not quitting the evident doarine which we have before laid down1 for determining the ,,locus ,,objecti1 on account of being pressed by one difficulty which seems inexplicable till a more intimate knowledge of the visive faculty be obtained by mortals4 ,in the meantime1 ,i propose it to the consideration of the ingenious1 whether the ,,locus ,,apparens of an object placed as in this #ith section be not as much before the eye as the distinct base is behind the eye6' ,to which query we may venture to answer in the negative4 ,for in the present case the rule for determining the distance of the distinct base1 or respective focus from the glass1 is this3 as the difference between the distance of the object and focus is to the focus or focal length1 so the distance of the object from the glass is to the distance of the respective focus or distinct base from the glass4 ,molyneux ,dioptr41 ,par4 ,i4 ,prop4 #e4 ,let us now suppose the object to be placed at the distance of the focal length1 and one half of the focal length from the glass1 and the eye close to the glass1 hence it will follow by the rule that the distance of the distinct base behind the eye is double the true distance of the object before the eye4 ,if therefore ,mr4 ,molyneux's conjecture held good1 it would follow that the eye should see the object twice as far off as it really is2 and in other cases at three or four times its due distance1 or more4 ,but this manifestly contradicts experience1 the object never appearing1 at farthest1 beyond its due distance4 ,whatever1 therefore1 is built on this supposition 7,,vid4 ,,corol4 ,i4 ,,prop4 #eg1 ,,ibid47 comes to the ground along with it4 #da4 ,from what hath been premised it is a manifest consequence that a man born blind1 being made to see1 would1 at first1 have no idea of distance by sight2 the sun and stars1 the remotest objects as well as the nearer1 would all seem to be in his eye1 or rather in his mind4 ,the objects intromitted by sight would seem to him 7as in truth they are7 no other than a new set of thoughts or sensations1 each whereof is as near to him as the perceptions of pain or pleasure1 or the most inward passions of his soul4 ,for our judging objects provided by sight to be at any distance1 or without the mind1 is 7,,vid4 sect4 #bh7 entirely the effect of experience1 which one in those circumstances could not yet have attained to4 #db4 ,it is indeed otherwise upon the common supposition that men judge of distance by the angle of the optic axes1 just as one in the dark1 or a blind-man by the angle comprehended by two sticks1 one whereof he held in each hand4 ,for if this were true1 it would follow that one blind from his birth being made to see1 should stand in need of no new experience in order to perceive distance by sight4 ,but that this is false has1 ,i think1 been sufficiently demonstrated4 #dc4 ,and perhaps upon a strict inquiry we shall not find that even those who from their birth have grown up in a continued habit of seeing are irrecoverably prejudiced on the other side1 to wit1 in thinking what they see to be at a distance from them4 ,for at this time it seems agreed on all hands1 by those who have had any thoughts of that matter1 that colours1 which are the proper and immediate object of sight1 are not without the mind4 ,but then it will be said1 by sight we have also the ideas of extension1 and figure1 and motion2 all which may well be thought without1 and at some distance from the mind1 though colour should not4 ,in answer to this ,i appeal to any man's experience1 whether the visible extension of any object doth not appear as near to him as the colour of that object2 nay1 whether they do not both seem to be in the very same place4 ,is not the extension we see coloured1 and is it possible for us1 so much as in thought1 to separate and abstract colour from extension8 ,now1 where the extension is there surely is the figure1 and there the motion too4 ,i speak of those which are perceived by sight4 #dd4 ,but for a fuller explication of this point1 and to show that the immediate objects of sight are not so much as the ideas or resemblances of things placed at a distance1 it is requisite that we look nearer into the matter and carefully observe what is meant in common discourse1 when one says that which he sees is at a distance from him4 ,suppose1 for example1 that looking at the moon ,i should say it were fifty or sixty semidiameters of the earth distant from me4 ,let us see what moon this is spoken of3 it is plain it cannot be the visible moon1 or anything like the visible moon1 or that which ,i see1 which is only a round1 luminous plane of about thirty visible points in diameter4 ,for in case ,i am carried from the place where ,i stand directly towards the moon1 it is manifest the object varies1 still as ,i go on2 and by the time that ,i am advanced fifty or sixty semidiameters of the earth1 ,i shall be so far from being near a small1 round1 luminous flat that ,i shall perceive nothing like it2 this object having long since disappeared1 and if ,i would recover it1 it must be by going back to the earth from whence ,i set out4 ,again1 suppose ,i perceive by sight the faint and obscure idea of something which ,i doubt whether it be a man1 or a tree1 or a tower1 but judge it to be at the distance of about a mile4 ,it is plain ,i cannot mean that what ,i see is a mile off1 or that it is the image or likeness of anything which is a mile off1 since that every step ,i take towards it the appearance alters1 and from being obscure1 small1 and faint1 grows clear1 large1 and vigorous4 ,and when ,i come to the mile's end1 that which ,i saw first is quite lost1 neither do ,i find anything in the likeness of it4 #de4 ,in these and the like instances the truth of the matter stands thus3 having of a long time experienced certain ideas1 perceivable by touch1 as distance1 tangible figure1 and solidity1 to have been connected with certain ideas of sight1 ,i do upon perceiving these ideas of sight forthwith conclude what tangible ideas are1 by the wonted ordinary course of ,nature like to follow4 ,looking at an object ,i perceive a certain visible figure and colour1 with some degree of faintness and other circumstances1 which from what ,i have formerly observed1 determine me to think that if ,i advance forward so many paces or miles1 ,i shall be affected with such and such ideas of touch3 so that in truth and strictness of speech ,i neither see distance itself1 nor anything that ,i take to be at a distance4 ,i say1 neither distance nor things placed at a distance are themselves1 or their ideas1 truly perceived by sight4 ,this ,i am persuaded of1 as to what concerns myself3 and ,i believe whoever will look narrowly into his own thoughts and examine what he means by saying he sees this or that thing at a distance1 will agree with me that what he sees only suggests to his understanding that after having passed a certain distance1 to be measured by the motion of his body1 which is perceivable by touch1 he shall come to perceive such and such tangible ideas which have been usually connected with such and such visible ideas4 ,but that one might be deceived by these suggestions of sense1 and that there is no necessary connexion between visible and tangible ideas suggested by them1 we need go no farther than the next looking-glass or pictures to be convinced4 ,note that when ,i speak of tangible ideas1 ,i take the word idea for any the immediate object of sense or understanding1 in which large signification it is commonly used by the moderns4 #df4 ,from what we have shown it is a manifest consequence that the ideas of space1 outness1 and things placed at a distance are not1 strictly speaking1 the object of sight2 they are not otherwise perceived by the eye than by the ear4 ,sitting in my study ,i hear a coach drive along the street2 ,i look through the casement and see it2 ,i walk out and enter into it2 thus1 common speech would incline one to think ,i heard1 saw1 and touched the same thing1 to wit1 the coach4 ,it is nevertheless certain1 the ideas intromitted by each sense are widely different and distinct from each other2 but having been observed constantly to go together1 they are spoken of as one and the same thing4 ,by the variation of the noise ,i perceive the different distances of the coach1 and know that it approaches before ,i look out4 ,thus by the ear ,i perceive distance1 just after the same manner as ,i do by the eye4 #dg4 ,i do not nevertheless say ,i hear distance in like manner as ,i say that ,i see it1 the ideas perceived by hearing not being so apt to be confounded with the ideas of touch as those of sight are4 ,so likewise a man is easily convinced that bodies and external things are not properly the object of hearing2 but only sounds1 by the mediation whereof the idea of this or that body or distance is suggested to his thoughts4 ,but then one is with more difficulty brought to discern the difference there is betwixt the ideas of sight and touch3 though it be certain a man no more sees and feels the same thing than he hears and feels the same thing4 #dh4 ,one reason of which seems to be this4 ,it is thought a great absurdity to imagine that one and the same thing should have any more than one extension1 and one figure4 ,but the extension and figure of a body1 being let into the mind two ways1 and that indifferently either by sight or touch1 it seems to follow that we see the same extension and the same figure which we feel4 #di4 ,but if we take a close and accurate view of things1 it must be acknowledged that we never see and feel one and the same object4 ,that which is seen is one thing1 and that which is felt is another4 ,if the visible figure and extension be not the same with the tangible figure and extension1 we are not to infer that one and the same thing has divers extensions4 ,the true consequence is that the objects of sight and touch are two distinct things4 ,it may perhaps require some thought rightly to conceive this distinction4 ,and the difficulty seems not a little increased1 because the combination of visible ideas hath constantly the same name as the combination of tangible ideas wherewith it is connected3 which doth of necessity arise from the use and end of language4 #ej4 ,in order therefore to treat accurately and unconfusedly of vision1 we must bear in mind that there are two sorts of objects apprehended by the eye1 the one primarily and immediately1 the other secondarily and by intervention of the former4 ,those of the first sort neither are1 nor appear to be1 without the mind1 or at any distance off2 they may indeed grow greater or smaller1 more confused1 or more clear1 or more faint1 but they do not1 cannot approach or recede from us4 ,whenever we say an object is at a distance1 whenever we say it draws near1 or goes farther off1 we must always mean it of the latter sort1 which properly belong to the touch1 and are not so truly perceived as suggested by the eye in like manner as thoughts by the ear4 #ea4 ,no sooner do we hear the words of a familiar language pronounced in our ears1 but the ideas corresponding thereto present themselves to our minds3 in the very same instant the sound and the meaning enter the understanding3 so closely are they united that it is not in our power to keep out the one1 except we exclude the other also4 ,we even act in all respects as if we heard the very thoughts themselves4 ,so likewise the secondary objects1 or those which are only suggested by sight1 do often more strongly affect us1 and are more regarded than the proper objects of that sense2 along with which they enter into the mind1 and with which they have a far more strict connexion1 than ideas have with words4 ,hence it is we find it so difficult to discriminate between the immediate and mediate objects of sight1 and are so prone to attribute to the former what belongs only to the latter4 ,they are1 as it were1 most closely twisted1 blended1 and incorporated together4 ,and the prejudice is confirmed and riveted in our thoughts by a long tract of time1 by the use of language1 and want of reflexion4 ,however1 ,i believe anyone that shall attentively consider what we have already said1 and shall say1 upon this subject before we have done 7especially if he pursue it in his own thoughts7 may be able to deliver himself from that prejudice4 ,sure ,i am it is worth some attention1 to whoever would understand the true nature of vision4 #eb4 ,i have now done with distance1 and proceed to show how it is that we perceive by sight the magnitude of objects4 ,it is the opinion of some that we do it by angles1 or by angles in conjunction with distance3 but neither angles nor distance being perceivable by sight1 and the things we see being in truth at no distance from us1 it follows that as we have shown lines and angles not to be the medium the mind makes use of in apprehending the apparent place1 so neither are they the medium whereby it apprehends the apparent magnitude of objects4 #ec4 ,it is well known that the same extension at a near distance shall subtend a greater angle1 and at a farther distance a lesser angle4 ,and by this principle 7we are told7 the mind estimates the magnitude of an object1 comparing the angle under which it is seen with its distance1 and thence inferring the magnitude thereof4 ,what inclines men to this mistake 7beside the humour of making one see by geometry7 is that the same perceptions or ideas which suggest distance do also suggest magnitude4 ,but if we examine it we shall find they suggest the latter as immediately as the former4 ,i say1 they do not first suggest distance1 and then leave it to the judgment to use that as a medium whereby to collect the magnitude2 but they have as close and immediate a connexion with the magnitude as with the distance2 and suggest magnitude as independently of distance as they do distance independently of magnitude4 ,all which will be evident to whoever considers what hath been already said1 and what follows4 #ed4 ,it hath been shown there are two sorts of objects apprehended by sight2 each whereof hath its distinct magnitude1 or extension4 ,the one1 properly tangible1 i4e4 to be perceived and measured by touch1 and not immediately falling under the sense of seeing3 the other1 properly and immediately visible1 by mediation of which the former is brought in view4 ,each of these magnitudes are greater or lesser1 according as they contain in them more or fewer points1 they being made up of points or minimums4 ,for1 whatever may be said of extension in abstract1 it is certain sensible extension is not infinitely divisible4 ,there is a ,,minimum ,,tangibile and a ,,minimum ,,visibile1 beyond which sense cannot perceive4 ,this everyone's experience will inform him4 #ee4 ,the magnitude of the object which exists without the mind1 and is at a distance1 continues always invariably the same3 but the visible object still changing as you approach to1 or recede from1 the tangible object1 it hath no fixed and determinate greatness4 ,whenever1 therefore1 we speak of the magnitude of anything1 for instance a tree or a house1 we must mean the tangible magnitude1 otherwise there can be nothing steady and free from ambiguity spoken of it4 ,but though the tangible and visible magnitude in truth belong to two distinct objects3 ,i shall nevertheless 7especially since those objects are called by the same name1 and are observed to coexist71 to avoid tediousness and singularity of speech1 sometimes speak of them as belonging to one and the same thing4 #ef4 ,now in order to discover by what means the magnitude of tangible objects is perceived by sight4 ,i need only reflect on what passes in my own mind1 and observe what those things be which introduce the ideas of greater or lesser into my thoughts1 when ,i look on any object4 ,and these ,i find to be1 ,,first1 the magnitude or extension of the visible object1 which being immediately perceived by sight1 is connected with that other which is tangible and placed at a distance4 ,,secondly1 the confusion or distinctness4 ,and thirdly1 the vigorousness or faintness of the aforesaid visible appearance4 ,,ceteris ,,paribus1 by how much the greater or lesser the visible object is1 by so much the greater or lesser do ,i conclude the tangible object to be4 ,but1 be the idea immediately perceived by sight never so large1 yet if it be withal confused1 ,i judge the magnitude of the thing to be but small4 ,if it be distinct and clear1 ,i judge it greater4 ,and if it be faint1 ,i apprehend it to be yet greater4 ,what is here meant by confusion and faintness hath been explained in sect4 #ce4 #eg4 ,moreover the judgments we make of greatness do1 in like manner as those of distance1 depend on the disposition of the eye1 also on the figure1 number1 and situation of objects and other circumstances that have been observed to attend great or small tangible magnitudes4 ,thus1 for instance1 the very same quantity of visible extension1 which in the figure of a tower doth suggest the idea of great magnitude1 shall in the figure of a man suggest the idea of much smaller magnitude4 ,that this is owing to the experience we have had of the usual bigness of a tower and a man no one1 ,i suppose1 need be told4 #eh4 ,it is also evident that confusion or faintness have no more a necessary connexion with little or great magnitude than they have with little or great distance4 ,as they suggest the latter1 so they suggest the former to our minds4 ,and by consequence1 if it were not for experience1 we should no more judge a faint or confused appearance to be connected with great or little magnitude1 than we should that it was connected with great or little distance4 #ei4 ,nor will it be found that great or small visible magnitude hath any necessary relation to great or small tangible magnitude3 so that the one may certainly be inferred from the other4 ,but before we come to the proof of this1 it is fit we consider the difference there is betwixt the extension and figure which is the proper object of touch1 and that other which is termed visible2 and how the former is principally1 though not immediately taken notice of1 when we look at any object4 ,this has been before mentioned1 but we shall here inquire into the cause thereof4 ,we regard the objects that environ us in proportion as they are adapted to benefit or injure our own bodies1 and thereby produce in our minds the sensation of pleasure or pain4 ,now bodies operating on our organs1 by an immediate application1 and the hurt or advantage arising therefrom1 depending altogether on the tangible1 and not at all on the visible1 qualities of any object3 this is a plain reason why those should be regarded by us much more than these3 and for this end the visive sense seems to have been bestowed on animals1 to wit1 that by the perception of visible ideas 7which in themselves are not capable of affecting or any wise altering the frame of their bodies7 they may be able to foresee 7from the experience they have had what tangible ideas are connected with such and such visible ideas7 and damage or benefit which is like to ensue1 upon the application of their own bodies to this or that body which is at a distance4 ,which foresight1 how necessary it is to the preservation of an animal1 everyone's experience can inform him4 ,hence it is that when we look at an object1 the tangible figure and extension thereof are principally attended to2 whilst there is small heed taken of the visible figure and magnitude1 which1 though more immediately perceived1 do less concern us1 and are not fitted to produce any alteration in our bodies4 #fj4 ,that the matter of fact is true will be evident to anyone who considers that a man placed at ten foot distance is thought as great as if he were placed at a distance only of five foot3 which is true not with relation to the visible1 but tangible greatness of the object3 the visible magnitude being far greater at one station3 than it is at the other4 #fa4 ,inches1 feet1 etc41 are settled stated lengths whereby we measure objects and estimate their magnitude3 we say1 for example1 an object appears to be six inches or six foot long4 ,now1 that this cannot be meant of visible inches1 etc41 is evident1 because a visible inch is itself no constant1 determinate magnitude1 and cannot therefore serve to mark out and determine the magnitude of any other thing4 ,take an inch marked upon a ruler3 view it1 successively1 at the distance of half a foot1 a foot1 a foot and a half1 etc41 from the eye3 at each of which1 and at all the intermediate distances1 the inch shall have a different visible extension1 i4e4 there shall be more or fewer points discerned in it4 ,now ,i ask which of all these various extensions is that stated1 determinate one that is agreed on for a common measure of other magnitudes8 ,no reason can be assigned why we should pitch on one more than another3 and except there be some invariable1 determinate extension fixed on to be marked to the word inch1 it is plain it can be used to little purpose2 and to say a thing contains this or that number of inches shall imply no more than that it is extended1 without bringing any particular idea of that extension into the mind4 ,farther1 an inch and a foot1 from different distances1 shall both exhibit the same visible magnitude1 and yet at the same time you shall say that one seems several times greater than the other4 ,from all which it is manifest that the judgments we make of the magnitude of objects by sight are altogether in reference to their tangible extension4 ,whenever we say an object is great1 or small1 of this or that determinate measure1 ,i say it must be meant of the tangible1 and not the visible extension1 which1 though immediately perceived1 is nevertheless little taken notice of4 #fb4 ,now1 that there is no necessary connexion between these two distinct extensions is evident from hence3 because our eyes might have been framed in such a manner as to be able to see nothing but what were less than the ,,minimum ,,tangibile4 ,in which case it is not impossible we might have perceived all the immediate objects of sight1 the very same that we do now3 but unto those visible appearances there would not be connected those different tangible magnitudes that are now4 ,which shows the judgments we make of the magnitude of things placed at a distance from the various greatness of the immediate objects of sight do not arise from any essential or necessary but only a customary tie1 which has been observed between them4 #fc4 ,moreover1 it is not only certain that any idea of sight might not have been connected with this or that idea of touch1 which we now observe to accompany it3 but also that the greater visible magnitudes might have been connected with1 and introduced into our minds lesser tangible magnitudes and the lesser visible magnitudes greater tangible magnitudes4 ,nay1 that it actually is so we have daily experience2 that object which makes a strong and large appearance1 not seeming near so great as another1 the visible magnitude whereof is much less1 but more faint1 and the appearance upper1 or which is the same thing painted lower on the ,,retina1 which faintness and situation suggest both greater magnitude and greater distance4 #fd4 ,from which1 and from sect4 #eg and #eh1 it is manifest that as we do not perceive the magnitudes of objects immediately by sight1 so neither do we perceive them by the mediation of anything which has a necessary connexion with them4 ,those ideas that now suggest unto us the various magnitudes of external objects before we touch them1 might possibly have suggested no such thing3 or they might have signified them in a direct contrary manner3 so that the very same ideas1 on the perception whereof we judge an object to be small1 might as well have served to make us conclude it great4 ,those ideas being in their own nature equally fitted to bring into our minds the idea of small or great1 or no size at all of outward objects2 just as the words of any language are in their own nature indifferent to signify this or that thing or nothing at all4 #fe4 ,as we see distance1 so we see magnitude4 ,and we see both in the same way that we see shame or anger in the looks of a man4 ,those passions are themselves invisible1 they are nevertheless let in by the eye along with colours and alterations of countenance1 which are the immediate object of vision3 and which signify them for no other reason than barely because they have been observed to accompany them4 ,without which experience we should no more have taken blushing for a sign of shame than of gladness4 #ff4 ,we are nevertheless exceeding prone to imagine those things which are perceived only by the mediation of others to be themselves the immediate objects of sight2 or1 at least1 to have in their own nature a fitness to be suggested by them1 before ever they had been experienced to coexist with them4 ,from which prejudice everyone1 perhaps1 will not find it easy to emancipate himself1 by any but the clearest convictions of reason4 ,and there are some grounds to think that if there was one only invariable and universal languages in the world1 and that men were born with the faculty of speaking it1 it would be the opinion of many that the ideas of other men's minds were properly perceived by the ear1 or had at least a necessary and inseparable tie with the sounds that were affixed to them4 ,all which seems to arise from want of a due application of our discerning faculty1 thereby to discriminate between the ideas that are in our understandings1 and consider them apart from each other2 which would preserve us from confounding those that are different1 and make us see what ideas do1 and what do not include or imply this or that other idea4 #fg4 ,there is a celebrated phenomenon1 the solution whereof ,i shall attempt to give by the principles that have been laid down1 in reference to the manner wherein we apprehend by sight the magnitude of objects4 ,the apparent magnitude of the moon when placed in the horizon is much greater than when it is in the meridian1 though the angle under which the diameter of the moon is seen be not observed greater in the former case than in the latter3 and the horizontal moon doth not constantly appear of the same bigness1 but at some times seemeth far greater than at others4 #fh4 ,now in order to explain the reason of the moon's appearing greater than ordinary in the horizon1 it must be observed that the particles which compose our atmosphere intercept the rays of light proceeding from any object to the eye2 and by how much the greater is the portion of atmosphere interjacent between the object and the eye1 by so much the more are the rays intercepted2 and by consequence the appearance of the object rendered more faint1 every object appearing more vigorous or more faint in proportion as it sendeth more or fewer rays into the eye4 ,now between the eye and the moon1 when situated in the horizon1 there lies a far greater quantity of atmosphere than there does when the moon is in the meridian4 ,whence it comes to pass that the appearance of the horizontal moon is fainter1 and therefore by sect4 #ef it should be thought bigger in that situation than in the meridian1 or in any other elevation above the horizon4 #fi4 ,farther1 the air being variously impregnated1 sometimes more and sometimes less1 with vapours and exhalations fitted to retund and intercept the rays of light1 it follows that the appearance of the horizontal moon hath not always an equal faintness1 and by consequence that luminary1 though in the very same situation1 is at one time judged greater than at another4 #gj4 ,that we have here given the true account of the phenomena of the horizontal moon will1 ,i suppose1 be farther evident to anyone from the following considerations4 ,,first1 it is plain that which in this case suggests the idea of greater magnitude must be something which is itself perceived2 for that which is unperceived cannot suggest to our perception any other thing4 ,,secondly1 it must be something that does not constantly remain the same1 but is subject to some change or variation1 since the appearance of the horizontal moon varies1 being at one time greater than at another4 ,and yet1 ,,thirdly1 it cannot be the visible figure or magnitude1 since that remains the same1 or is rather lesser1 by how much the moon is nearer to the horizon4 ,it remains therefore that the true cause is that affection or alteration of the visible appearance which proceeds from the greater paucity of rays arriving at the eye1 and which ,i term ,,faintness3 since this answers all the forementioned conditions1 and ,i am not conscious of any other perception that doth4 #ga4 ,add to this that in misty weather it is a common observation that the appearance of the horizontal moon is far larger than usual1 which greatly conspires with and strengthens our opinion4 ,neither would it prove in the least irreconcilable with what we have said1 if the horizontal moon should chance sometimes to seem enlarged beyond its usual extent1 even in more serene weather4 ,for we must not only have regard to the mist which happens to be in the place where we stand2 we ought also to take into our thoughts the whole sum of vapours and exhalations which lie betwixt the eye and the moon3 all which cooperating to render the appearance of the moon more faint1 and thereby increase its magnitude1 it may chance to appear greater than it usually does1 even in the horizontal position1 at a time when1 though there be no extraordinary fog or haziness1 just in the place where we stand1 yet the air between the eye and the moon1 taken all together1 may be loaded with a greater quantity of interspersed vapours and exhalations than at other times4 #gb4 ,it may be objected that in consequence of our principles the interposition of a body in some degree opaque1 which may intercept a great part of the rays of light1 should render the appearance of the moon in the meridian as large as when it is viewed in the horizon4 ,to which ,i answer1 it is not faintness anyhow applied that suggests greater magnitude1 there being no necessary but only an experimental connexion between those two things4 ,it follows that the faintness which enlarges the appearance must be applied in such sort1 and with such circumstances1 as have been observed to attend the vision of great magnitudes4 ,when from a distance we behold great objects1 the particles of the intermediate air and vapours1 which are themselves unperceivable1 do interrupt the rays of light1 and thereby render the appearance less strong and vivid3 now1 faintness of appearance caused in this sort hath been experienced to coexist with great magnitude4 ,but when it is caused by the interposition of an opaque sensible body1 this circumstance alters the case1 so that a faint appearance this way caused doth not suggest greater magnitude1 because it hath not been experienced to coexist with it4 #gc4 ,faintness1 as well as all other ideas or perceptions which suggest magnitude or distance1 doth it in the same way that words suggest the notions to which they are annexed4 ,now1 it is known a word pronounced with certain circumstances1 or in a certain context with other words1 hath not always the same import and signification that it hath when pronounced in some other circumstances or different context of words4 ,the very same visible appearance as to faintness and all other respects1 if placed on high1 shall not suggest the same magnitude that it would if it were seen at an equal distance on a level with the eye4 ,the reason whereof is that we are rarely accustomed to view objects at a great height2 our concerns lie among things situated rather before than above us1 and accordingly our eyes are not placed on the top of our heads1 but in such a position as is most convenient for us to see distant objects standing in our way4 ,and this situation of them being a circumstance which usually attends the vision of distant objects1 we may from hence account for 7what is commonly observed7 an object's appearing of different magnitude1 even with respect to its horizontal extension1 on the top of a steeple1 for example1 an hundred feet high to one standing below1 from what it would if placed at an hundred feet distance on a level with his eye4 ,for it hath been shown that the judgment we make on the magnitude of a thing depends not on the visible appearance alone1 but also on divers other circumstances1 any one of which being omitted or varied may suffice to make some alteration in our judgment4 ,hence1 the circumstances of viewing a distant object in such a situation as is usual1 and suits with the ordinary posture of the head and eyes being omitted1 and instead thereof a different situation of the object1 which requires a different posture of the head taking place1 it is not to be wondered at if the magnitude be judged different3 but it will be demanded why an high object should constantly appear less than an equidistant low object of the same dimensions1 for so it is observed to be3 it may indeed be granted that the variation of some circumstances may vary the judgment made on the magnitude of high objects1 which we are less used to look at3 but it does not hence appear why they should be judged less rather than greater8 ,i answer that in case the magnitude of distant objects was suggested by the extent of their visible appearance alone1 and thought proportional thereto1 it is certain they would then be judged much less than now they seem to be 7,,vide sect4 #gi74 ,but several circumstances concurring to form the judgment we make on the magnitude of distant objects1 by means of which they appear far larger than others1 whose visible appearance hath an equal or even greater extension2 it follows that upon the change or omission of any of those circumstances which are wont to attend the vision of distant objects1 and so come to influence the judgments made on their magnitude1 they shall proportionably appear less than otherwise they would4 ,for any of those things that caused an object to be thought greater than in proportion to its visible extension being either omitted or applied without the usual circumstances1 the judgment depends more entirely on the visible extension1 and consequently the object must be judged less4 ,thus in the present case the situation of the thing seen being different from what it usually is in those objects we have occasion to view1 and whose magnitude we observe1 it follows that the very same object1 being an hundred feet high1 should seem less than if it was an hundred feet off on 7or nearly on7 a level with the eye4 ,what has been here set forth seems to me to have no small share in contributing to magnify the appearance of the horizontal moon1 and deserves not to be passed over in the explication of it4 #gd4 ,if we attentively consider the phenomenon before us1 we shall find the not discerning between the mediate and immediate objects of sight to be the chief cause of the difficulty that occurs in the explication of it4 ,the magnitude of the visible moon1 or that which is the proper and immediate object of vision1 is not greater when the moon is in the horizon than when it is in the meridian4 ,how comes it1 therefore1 to seem greater in one situation than the other8 ,what is it can put this cheat on the understanding8 ,it has no other perception of the moon than what it gets by sight3 and that which is seen is of the same extent1 ,i say1 the visible appearance hath the same1 or rather a less1 magnitude when the moon is viewed in the horizontal than when in the meridional position3 and yet it is esteemed greater in the former than in the latter4 ,herein consists the difficulty1 which doth vanish and admit of a most easy solution1 if we consider that as the visible moon is not greater in the horizon than in the meridian1 so neither is it thought to be so4 ,it hath been already shown that in any act of vision the visible object absolutely1 or in itself1 is little taken notice of1 the mind still carrying its view from that to some tangible ideas which have been observed to be connected with it1 and by that means come to be suggested by it4 ,so that when a thing is said to appear great or small1 or whatever estimate be made of the magnitude of any thing1 this is meant not of the visible but of the tangible object4 ,this duly considered1 it will be no hard matter to reconcile the seeming contradiction there is1 that the moon should appear of a different bigness1 the visible magnitude thereof remaining still the same4 ,for by sect4 #ef the very same visible extension1 with a different faintness1 shall suggest a different tangible extension4 ,when therefore the horizontal moon is said to appear greater than the meridional moon1 this must be understood not of a greater visible extension1 but a of greater tangible or real extension1 which by reason of the more than ordinary faintness of the visible appearance1 is suggested to the mind along with it4 #ge4 ,many attempts have been made by learned men to account for this appearance4 ,gassendus1 ,descartes1 ,hobbes1 and several others have employed their thoughts on that subject2 but how fruitless and unsatisfactory their endeavours have been is sufficiently shown in ,,the ,,transactions1,phil4 ,trans4 ,num4 #ahg4 p4 #cad where you may see their several opinions at large set forth and confuted1 not without some surprize at the gross blunders that ingenious men have been forced into by endeavouring to reconcile this appearance with the ordinary ,principles of optics4 ,since the writing of which there hath been published in the ,,transactions ,numb4 #ahg4 ,p4 #cbc another paper relating to the same affair by the celebrated ,dr4 ,wallis1 wherein he attempts to account for that phenomenon which1 though it seems not to contain anything new or different from what had been said before by others1 ,i shall nevertheless consider in this place4 #gf4 ,his opinion1 in short1 is this2 we judge not of the magnitude of an object by the visual angle alone1 but by the visual angle in conjunction with the distance4 ,hence1 though the angle remain the same1 or even become less1 yet if withal the distance seem to have been increased1 the object shall appear greater4 ,now1 one way whereby we estimate the distance of anything is by the number and extent of the intermediate objects3 when therefore the moon is seen in the horizon1 the variety of fields1 houses1 etc41 together with the large prospect of the wide extended land or sea that lies between the eye and the utmost limb of the horizon1 suggest unto the mind the idea of greater distance1 and consequently magnify the appearance4 ,and this1 according to ,dr4 ,wallis1 is the true account of the extraordinary largeness attributed by the mind to the horizontal moon at a time when the angle subtended by its diameter is not one jot greater than it used to be4 #gg4 ,with reference to this opinion1 not to repeat what hath been already said concerning distance1 ,i shall only observe1 ,,first1 that if the prospect of interjacent objects be that which suggests the idea of farther distance1 and this idea of farther distance be the cause that brings into the mind the idea of greater magnitude1 it should hence follow that if one looked at the horizontal moon from behind a wall1 it would appear no bigger than ordinary4 ,for in that case the wall interposing cuts off all that prospect of sea and land1 etc4 which might otherwise increase the apparent distance1 and thereby the apparent magnitude of the moon4 ,nor will it suffice to say the memory doth even then suggest all that extent of land1 etc41 which lies within the horizon2 which suggestion occasions a sudden judgment of sense that the moon is farther off and larger than usual4 ,for ask any man who1 from such a station beholding the horizontal moon1 shall think her greater than usual1 whether he hath at that time in his mind any idea of the intermediate objects1 or long tract of land that lies between his eye and the extreme edge of the horizon8 ,and whether it be that idea which is the cause of his making the aforementioned judgment8 ,he will1 ,i suppose1 reply in the negative1 and declare the horizontal moon shall appear greater than the meridional1 though he never thinks of all or any of those things that lie between him and it4 ,,secondly1 it seems impossible by this hypothesis to account for the moon's appearing in the very same situation at one time greater than at another2 which nevertheless has been shown to be very agreeable to the principles we have laid down1 and receives a most easy and natural explication from them4 ,for the further clearing' up of this point it is to be observed that what we immediately and properly see are only lights and colours in sundry situations and shades and degrees of faintness and clearness1 confusion and distinctness4 ,all which visible objects are only in the mind1 nor do they suggest ought external1 whether distance or magnitude1 otherwise than by habitual connexion as words do things4 ,we are also to remark that1 beside the straining of the eyes1 and beside the vivid and faint1 the distinct and confused appearances 7which1 bearing some proportion to lines and angles1 have been substituted instead of them in the foregoing part of this treatise71 there are other means which suggest both distance and magnitude2 particularly the situation of visible points of objects1 as upper or lower2 the one suggesting a farther distance and greater magnitude1 the other a nearer distance and lesser magnitude3 all which is an effect only of custom and experience2 there being really nothing intermediate in the line of distance between the uppermost and lowermost1 which are both equidistant1 or rather at no distance from the eye1 as there is also nothing in upper or lower1 which by necessary connexion should suggest greater or lesser magnitude4 ,now1 as these customary1 experimental means of suggesting distance do likewise suggest magnitude1 so they suggest the one as immediately as the other4 ,i say they do not 7,,vide sect4 #ec7 first suggest distance1 and then leave the mind from thence to infer or compute magnitude1 jut suggest magnitude as immediately and directly as they suggest distance4 #gh4 ,this phenomenon of the horizontal moon is a clear instance of the insufficiency of lines and angles for explaining the way wherein the mind perceives and estimates the magnitude of outward objects4 ,there is nevertheless a use of computation by them in order to determine the apparent magnitude of things1 so far as they have a connexion with1 and are proportional to1 those other ideas or perceptions which are the true and immediate occasions that suggest to the mind the apparent magnitude of things4 ,but this in general may1 ,i think1 be observed concerning mathematical computation in optics3 that it can never be very precise and exact since the judgments we make of the magnitude of external things do often depend on several circumstances1 which are not proportionable to1 or capable of being defined by1 lines and angles4 #gi4 ,from what has been said we may safely deduce this consequence2 to wit1 that a man born blind and made to see would1 at first opening of his eyes1 make a very different judgment of the magnitude of objects intromitted by them from what others do4 ,he would not consider the ideas of sight with reference to1 or as having any connexion with1 the ideas of touch3 his view of them being entirely terminated within themselves1 he can no otherwise judge them great or small than as they contain a greater or lesser number of visible points4 ,now1 it being certain that any visible point can cover or exclude from view only one other visible point1 it follows that whatever object intercepts the view of another hath an equal number of visible points with it2 and consequently they shall both be thought by him to have the same magnitude4 ,hence it is evident one in those circumstances would judge his thumb1 with which he might hide a tower or hinder its being seen1 equal to that tower1 or his hand1 the interposition whereof might conceal experimental means the firmament from his view1 equal to the firmament3 how great an inequality soever there may in our apprehensions seem to be betwixt those two things1 because of the customary and close connexion that has grown up in our minds between the objects of sight and touch2 whereby the very different and distinct ideas of those two senses are so blended and confounded together as to be mistaken for one and the same thing2 out of which prejudice we cannot easily extricate ourselves4 #hj4 ,for the better explaining the nature of vision1 and setting the manner wherein we perceive magnitudes in a due light1 ,i shall proceed to make some observations concerning matters relating thereto1 whereof the want of reflexion1 and duly separating between tangible and visible ideas1 is apt to create in us mistaken and confused notions4 ,and ,,first1 ,i shall observe that the ,,minimum ,,visibile is exactly equal in all beings whatsoever that are endowed with the visive faculty4 ,no exquisite formation of the eye1 no peculiar sharpness of sight1 can make it less in one creature than in another2 for it not being distinguishable into parts1 nor in any wise a consisting of them1 it must necessarily be the same to all4 ,for suppose it otherwise1 and that the ,,minimum ,,visibile of a mite1 for instance1 be less than the ,,minimum ,,visibile of a man3 the latter therefore may by detraction of some part be made equal to the former3 it doth therefore consist of parts1 which is inconsistent with the notion of a ,,minimum ,,visibile or point4 #ha4 ,it will perhaps be objected that the ,,minimum ,,visibile of a man doth really and in itself contain parts whereby it surpasses that of a mite1 though they are not perceivable by the man4 ,to which ,i answer1 the ,,minimum ,,visibile having 7in like manner as all other the proper and immediate objects of sight7 been shown not to have any existence without the mind of him who sees it1 it follows there cannot be any pan of it that is not actually perceived1 and therefore visible4 ,now for any object to contain distinct visible parts1 and at the same time to be a ,,minimum ,,visibile1 is a manifest contradiction4 #hb4 ,of these visible points we see at all times an equal number4 ,it is every whit as great when our view is contracted and bounded by near objects as when it is extended to larger and remoter4 ,for it being impossible that one ,,minimum ,,visibile should obscure or keep out of sight mote than one other1 it is a plain consequence that when my view is on all sides bounded by the walls of my study see just as many visible points as ,i could1 in case that by the removal of the study-walls and all other obstructions1 ,i had a full prospect of the circumjacent fields1 mountains1 sea1 and open firmament3 for so long as ,i am shut up within the walls1 by their interposition every point of the external objects is covered from my view3 but each point that is seen being able to cover or exclude from sight one only other corresponding point1 it follows that whilst my sight is confined to those narrow walls ,i see as many points1 or ,,minima ,,visibilia1 as ,i should were those walls away1 by looking on all the external objects whose prospect is intercepted by them4 ,whenever therefore we are said to have a greater prospect at one time than another1 this must be understood with relation1 not to the proper and immediate1 but the secondary and mediate objects of vision1 which1 as hath been shown1 properly belong to the touch4 #hc4 ,the visive faculty considered with reference to its immediate objects may be found to labour of two defects4 ,,first1 in respect of the extent or number of visible points that are at once perceivable by it1 which is narrow and limited to a certain degree4 ,it can take in at one view but a certain determinate number of ,,minima ,,visibilia1 beyond which it cannot extend its prospect4 ,secondly1 our sight is defective in that its view is not only narrow1 but also for the most part confused3 of those things that we take in at one prospect we can see but a few at once clearly and unconfusedly3 and the more we fix our sight on any one object1 by so much the darker and more indistinct shall the rest appear4 #hd4 ,corresponding to these two defects of sight1 we may imagine as many perfections1 to wit1 #a,,st1 that of comprehending in one view a greater number of visible points4 #b;,,dly1 of being able to view them all equally and at once with the utmost clearness and distinction4 ,that those perfections are not actually in some intelligences of a different order and capacity from ours it is impossible for us to know4 #he4 ,in neither of those two ways do microscopes contribute to the improvement of sight2 for when we look through a microscope we neither see more visible points1 nor are the collateral points more distinct than when we look with the naked eye at objects placed in a due distance4 ,a microscope brings us1 as it were1 into a new world3 it presents us with a new scene of visible objects quite different from what we behold with the naked eye4 ,but herein consists the most remarkable difference1 to wit1 that whereas the objects perceived by the eye alone have a certain connexion with tangible objects1 whereby we are taught to foresee what will ensue upon the approach or application of distant objects to the parts of our own body1 which much conduceth to its preservation1 there is not the like connexion between things tangible and those visible objects that are perceived by help of a fine microscope4 #hf4 ,hence it is evident that were our eyes turned into the nature of microscopes1 we should not be much benefited by the change2 we should be deprived of the forementioned advantage we at present receive by the visive faculty1 and have left us only the empty amusement of seeing1 without any other benefit arising from it4 ,but in that case1 it will perhaps be said1 our sight would be endued with a far greater sharpness and penetration than it now hath4 ,but it is certain from what we have already shown that the ,,minimum ,,visibile is never greater or lesser1 but in all cases constantly the same3 and in the case of microscopical eyes ,i see only this difference1 to wit1 that upon the ceasing of a certain observable connexion betwixt the divers perceptions of sight and touch1 which before enabled us to regulate our actions by the eye1 it would now be rendered utterly unserviceable to that purpose4 #hg4 ,upon the whole it seems that if we consider the use and end of sight1 together with the present state and circumstances of our being1 we shall not find any great cause to complain of any defect or imperfection in it1 or easily conceive how it could be mended4 ,with such admirable wisdom is that faculty contrived1 both for the pleasure and convenience of life4 #hh4 ,having finished what ,i intended to say concerning the distance and magnitude of objects1 ,i come now to treat of the manner wherein the mind perceives by sight their situation4 ,among the discoveries of the last age1 it is reputed none of the least that the manner of vision hath been more clearly explained than ever it had been before4 ,there is at this day no one ignorant that the pictures of external objects are painted on the ,,retina1 or fund of the eye3 that we can see nothing which is not so painted3 and that1 according as the picture is more distinct or confused1 so also is the perception we have of the object3 but then in this explication of vision there occurs one mighty difficulty4 ,the objects are painted in an inverted order on the bottom of the eye3 the upper part of any object being painted on the lower part of the eye1 and the lower part of the object on the upper part of the eye3 and so also as to right and left4 ,since therefore the pictures are thus inverted1 it is demanded how it comes to pass that we see the objects erect and in their natural posture8 #hi4 ,in answer to this difficulty we are told that the mind1 perceiving an impulse of a ray of light on the upper part of the eye1 considers this ray as coming in a direct line from the lower part of the object2 and in like manner tracing the ray that strikes on the lower part of the eye1 it is directed to the upper part of the object4 ,thus in the adjacent figure1 ,c1 the lower point of the object ,,abc1 is projected on ,c the upper part of the eye4 ,so likewise the highest point ,a is projected on ,a the lowest part of the eye1 which makes the representation ,,cba inverted3 but the mind considering the stroke that is made on ,c as coming in the straight line ,,cc from the lower end of the object2 and the stroke or impulse on a as coming in the line ,,aa from the upper end of the object1 is directed to make a right judgment of the situation of the object ,,abc1 notwithstanding the picture of it is inverted4 ,this is illustrated by conceiving a blind man who1 holding in his hands two sticks that cross each other1 doth with them touch the extremities of an object1 placed in a perpendicular situation4 ,it is certain this man will judge that to be the upper part of the object which he touches with the stick held in the undermost hand1 and that to be the lower part of the object which he touches with the stick in his uppermost hand4 ,this is the common explication of the erect appearance of objects1 which is generally received and acquiesced in1 being 7as ,mr4 ,molyneux tells us ,diopt4 par4 #b4 c4 #g4 ,p4 #bhi47 'allowed by all men as satisfactory'4 #ij4 ,but this account to me does not seem in any degree true4 ,did ,i perceive those impulses1 decussations1 and directions of the rays of light in like manner as hath been set forth1 then indeed it would not be altogether void of probability4 ,and there might be some pretence for the comparison of the blind man and his cross sticks4 ,but the case is far otherwise4 ,i know very well that ,i perceive no such thing4 ,and of consequence ,i cannot thereby make an estimate of the situation of objects4 ,i appeal to anyone's experience1 whether he be conscious to himself that he thinks on the intersection made by the radious ,,sic pencils1 or pursues the impulses they give in right lines1 whenever he perceives by sight the position of any object8 ,to me it seems evident that crossing and tracing of the rays is never thought on by children1 idiots1 or in truth by any other1 save only those who have applied themselves to the study of optics4 ,and for the mind to judge of the situation of objects by those things without perceiving them1 or to perceive them without knowing it1 is equally beyond my comprehension4 ,add to this that the explaining the manner of vision by the example of cross sticks and hunting for the object along the axes of the radious pencils1 doth suppose the proper objects of sight to be perceived at a distance from us1 contrary to what hath been demonstrated4 #ia4 ,it remains1 therefore1 that we look for some other explication of this difficulty3 and ,i believe it not impossible to find one1 provided we examine it to the bottom1 and carefully distinguish between the ideas of sight and touch2 which cannot be too oft inculcated in treating of vision3 but more especially throughout the consideration of this affair we ought to carry that distinction in our thoughts3 for that from want of a right understanding thereof the difficulty of explaining erect vision seems chiefly to arise4 #ib4 ,in order to disentangle our minds from whatever prejudices we may entertain with relation to the subject in hand1 nothing seems more apposite than the taking into our thoughts the case of one born blind1 and afterwards1 when grown up1 made to see4 ,and though1 perhaps1 it may not be an easy task to divest ourselves entirely of the experience received from sight1 so as to be able to put our thoughts exactly in the posture of such a one's1 we must1 nevertheless1 as far as possible1 endeavour to frame true conceptions of what might reasonably be supposed to pass in his mind4 #ic4 ,it is certain that a man actually blind1 and who had continued so from his birth1 would by the sense of feeling attain to have ideas of upper and lower4 ,by the motion of his hand he might discern the situation of any tangible object placed within his ,,fi reach4 ,that part on which he felt himself supported1 or towards which he perceived his body to gravitate1 he would term lower1 and the contrary to this upper2 and accordingly denominate whatsoever objects he touched4 #id4 ,but then1 whatever judgments he makes concerning the situation of objects are confined to those only that are perceivable by touch4 ,all those things that are intangible and of a spiritual nature1 his thoughts and desires1 his passions1 and in general all the modifications of the soul1 to these he would never apply the terms ,,upper and ,,lower1 except only in a metaphorical sense4 ,he may1 perhaps1 by way of allusion1 speak of high or low thoughts3 but those terms in their proper signification would never be applied to anything that was not conceived to exist without the mind4 ,for a man born blind1 and remaining in the same state1 could mean nothing else by the words ,,higher and ,,lower than a greater or lesser distance from the earth2 which distance he would measure by the motion or application of his hand or some other part of his body4 ,it is therefore evident that all those things which1 in respect of each other1 would by him be thought higher or lower1 must be such as were conceived to exist without his mind1 in the ambient space4 #ie4 ,whence it plainly follows that such a one1 if we suppose him made to see1 would not at first sight think anything he saw was high or low1 erect or inverted2 for it hath been already demonstrated in sect4 #da that he would not think the things he perceived by sight to be at any distance from him1 or without his mind4 ,the objects to which he had hitherto been used to apply the terms ,,up and ,,down1 ,,high and ,,low1 were such only as affected or were some way perceived by his couch3 but the proper objects of vision make a new set of ideas1 perfectly distinct and different from the former1 and which can in no sort make themselves perceived by touch4 ,there is1 therefore1 nothing at all that could induce him to think those terms applicable to them3 nor would he ever think it till such time as he had observed their connexion with tangible objects1 and the same prejudice began to insinuate itself into his understanding1 which from their infancy had grown up in the understandings of other men4 #if4 ,to set this matter in a clearer light ,i shall make use of an example4 ,suppose the above-mentioned blind person by his touch perceives a man to stand erect4 ,let us inquire into the manner of this4 ,by the application of his hand to the several parts of a human body he had perceived different tangible ideas1 which being collected into sundry complex ones1 have distinct names annexed to them4 ,thus one combination of a certain tangible figure1 bulk1 and consistency of parts is called the head1 another the hand1 a third the foot1 and so of the rest3 all which complex ideas could1 in his understanding1 be made up only of ideas perceivable by touch4 ,he had also by his touch obtained an idea of earth or ground1 towards which he perceives the parts of his body to have a natural tendency4 ,now1 by ,,erect nothing more being meant than that perpendicular position of a man wherein his feet are nearest to the earth1 if the blind person by moving his hand over the parts of the man who stands before him perceives the tangible ideas that compose the head to be farthest from1 and those that compose the feet to be nearest to1 that other combination of tangible ideas which he calls earth1 he will denominate that man erect4 ,but if we suppose him on a sudden to receive his sight1 and that he behold a man standing before him1 it is evident in that case he would neither judge the man he sees to be erect nor inverted2 for he never having known those terms applied to any other save tangible things1 or which existed in the space without him1 and what he sees neither being tangible nor perceived as existing without1 he could not know that in propriety of language they were applicable to it4 #ig4 ,afterwards1 when upon turning his head or eyes up and down to the right and left he shall observe the visible objects to change1 and shall also attain to know that they are called by the same names1 and connected with the objects perceived by touch2 then indeed he will come to speak of them and their situation1 in the same terms that he has been used to apply to tangible things2 and those that he perceives by turning up his eyes he will call upper1 and those that by turning down his eyes he will call lower4 #ih4 ,and this seems to me the true reason why he should think those objects uppermost that are painted on the lower part of his eye3 for by turning the eye up they shall be distinctly seen2 as likewise those that are painted on the highest part of the eye shall be distinctly seen by turning the eye down1 and are for that reason esteemed lowest2 for we have shown that to the immediate objects of sight considered in themselves1 he would not attribute the terms ,,high and ,,low4 ,it must therefore be on account of some circumstances which are observed to attend them3 and these1 it is plain1 are the actions of turning the eye up and down1 which suggest a very obvious reason why the mind should denominate the objects of sight accordingly high or low4 ,and without this motion of the eye1 this turning it up and down in order to discern different objects1 doubtless ,,erect1 ,,inverse1 and other the like terms relating to the position of tangible objects1 would never have been transferred1 or in any degree apprehended to belong to the ideas of sight3 the mere act of seeing including nothing in it to that purpose2 whereas the different situations of the eye naturally direct the mind to make a suitable judgment of the situation of objects intromitted by it4 #ii4 ,farther1 when he has by experience learned the connexion there is between the several ideas of sight and touch1 he will be able1 by the perception he has of the situation of visible things in respect of one another1 to make a sudden and true estimate of the situation of outward1 tangible things corresponding to them4 ,and thus it is he shall perceive by sight the situation of external objects which do not properly fall under that sense4 #ajj4 ,i know we are very prone to think that1 if just made to see1 we should judge of the situation of visible things as we do now3 but we are also as prone to think that1 at first sight1 we should in the same way apprehend the distance and magnitude of objects as we do now3 which hath been shown to be a false and groundless persuasion4 ,and for the like reasons the same censure may be passed on the positive assurance that most men1 before they have thought sufficiently of the matter1 might have of their being able to determine by the eye at first view1 whether objects were erect or inverse4 #aja4 ,it will1 perhaps1 be objected co our opinion that a man1 for instance1 being thought erect when his feet are next the earth1 and inverted when his head is next the earth1 it doth hence follow that by the mere act of vision1 without any experience or altering the situation of the eye1 we should have determined whether he were erect or inverted3 for both the earth itself1 and the limbs of the man who stands thereon1 being equally perceived by sight1 one cannot choose seeing what part of the man is nearest the earth1 and what part farthest from it1 i4e4 whether he be erect or inverted4 #ajb4 ,to which ,i answer1 the ideas which constitute the tangible earth and man are entirely different from those which constitute the visible earth and man4 ,nor was it possible1 by virtue of the visive faculty alone1 without superadding any experience of touch1 or altering the position of the eye1 ever to have known1 or so much as suspected1 there had been any relation or connexion between them4 ,hence a man at first view would not denominate anything he saw earth1 or head1 or foot2 and consequently he could not tell by the mere act of vision whether the head or feet were nearest the earth3 nor1 indeed1 would we have thereby any thought of earth or man1 erect or inverse1 at all3 which will be made yet more evident if we nicely observe1 and make a particular comparison between1 the ideas of both senses4 #ajc4 ,that which ,i see is only variety of light and colours4 ,that which ,i feel is hard or soft1 hot or cold1 rough or smooth4 ,what similitude1 what connexion have those ideas with these8 ,or how is it possible that anyone should see reason to give one and the same name to combinations of ideas so very different before he had experienced their coexistence8 ,we do not find there is any necessary connexion betwixt this or that tangible quality and any colour whatsoever4 ,and we may sometimes perceive colours where there is nothing to be felt4 ,all which doth make it manifest that no man1 at first receiving of his sight1 would know there was any agreement between this or that particular object of his sight and any object of touch he had been already acquainted with3 the colours1 therefore1 of the head would to him no more suggest the idea of head than they would the idea of foot4 #ajd4 ,farther1 we have at large shown 7,,vid4 sect4 #fc and #fd7 there is no discoverable necessary connexion between any given visible magnitude and any one particular tangible magnitude2 but that it is entirely the result of custom and experience1 and depends on foreign and accidental circumstances that we can by the perception of visible extension inform ourselves what may be the extension of any tangible object connected with it4 ,hence it is certain that neither the visible magnitude of head or foot would bring along with them into the mind1 at first opening of the eyes1 the respective tangible magnitudes of those parts4 #aje4 ,by the foregoing section it is plain the visible figure of any part of the body hath no necessary connexion with the tangible figure thereof1 so as at first sight to suggest it to the mind4 ,for figure is the termination of magnitude2 whence it follows that no visible magnitude having in its own nature an aptness to suggest any one particular tangible magnitude1 so neither can any visible figure be inseparably connected with its corresponding tangible figure3 so as of itself and in a way prior to experience1 it might suggest it to the understanding4 ,this will be farther evident if we consider that what seems smooth and round to the touch may to sight1 if viewed through a microscope1 seem quite otherwise4 #ajf4 ,from all which laid together and duly considered1 we may clearly deduce this inference4 ,in the first act of vision no idea entering by the eye would have a perceivable connexion with the ideas to which the names ,,earth1 ,,man1 ,,head1 ,,foot1 etc41 were annexed in the understanding of a person blind from his birth2 so as in any sort to introduce them into his mind1 or make themselves be called by the same names1 and reputed the same things with them1 as afterwards they come to be4 #ajg4 ,there doth1 nevertheless1 remain one difficulty1 which perhaps may seem to press hard on our opinion1 and deserve not to be passed over3 for though it be granted that neither the colour1 size1 nor figure of the visible feet have any necessary connexion with the ideas that compose the tangible feet1 so as to bring them at first sight into my mind1 or make me in danger of confounding them before ,i had been used to1 and for some time experienced their connexion3 yet thus much seems undeniable1 namely1 that the number of the visible feet being the same with that of the tangible feet1 ,i may from hence without any experience of sight reasonably conclude that they represent or are connected with the feet rather than the head4 ,i say1 it seems the idea of two visible feet will sooner suggest to the mind the idea of two tangible feet than of one head2 so that the blind man upon first reception of the visive faculty might know which were the feet or two1 and which the head or one4 #ajh4 ,in order to get clear of this seeming difficulty we need only observe that diversity of visible objects doth not necessarily infer diversity of tangible objects corresponding to them4 ,a picture painted with great variety of colours affects the touch in one uniform manner2 it is therefore evident that ,i do not by any necessary consecution1 independent of experience1 judge of the number of things tangible from the number of things visible4 ,i should not1 therefore1 at first opening my eyes conclude that because ,i see two ,i shall feel two4 ,how1 therefore1 can ,i1 before experience teaches me1 know that the visible legs1 because two1 are connected with the tangible legs1 or the visible head1 because one1 is connected with the tangible head8 ,the truth is1 the things ,i see are so very different and heterogeneous from the things ,i feel that the perception of the one would never have suggested the other to my thoughts1 or enabled me to pass the least judgment thereon1 until ,i had experienced their connexion4 #aji4 ,but for a fuller illustration of this matter it ought to be considered that number 7however some may reckon it amongst the primary qualities7 is nothing fixed and settled1 really existing in things themselves4 ,it is entirely the creature of the mind1 considering either an idea by itself1 or any combination of ideas to which it gives one name1 and so makes it pass for an unit4 ,according as the mind variously combines its ideas the unit varies3 and as the unit1 so the number1 which is only a collection of units1 doth also vary4 ,we call a window one1 a chimney one1 and yet a house in which there are many windows and many chimneys hath an equal right to be called one1 and many houses go to the making of the city4 ,in these and the like1 instances it is evident the unit constantly relates to the particular draughts the mind makes of its ideas1 to which it affixes names1 and wherein it includes more or less as best suits its own ends and purposes4 ,whatever1 therefore1 the mind considers as one1 that is an unit4 ,every combination of ideas is considered as one thing by the mind1 and in token thereof is marked by one name4 ,now1 this naming and combining together of ideas is perfectly arbitrary1 and done by the mind in such sort as experience shows it to be most convenient3 without which our ideas had never been collected into such sundry distinct combinations as they now are4 #aaj4 ,hence it follows that a man born blind and afterwards1 when grown up1 made to see1 would not in the first act of vision parcel out the ideas of sight into the same distinct collections that others do1 who have experienced which do regularly coexist and are proper to be bundled up together under one name4 ,he would not1 for example1 make into one complex idea1 and thereby esteem an unit1 all those particular ideas which constitute the visible head or foot4 ,for there can be no reason assigned why he should do so1 barely upon his seeing a man stand upright before him4 ,there crowd into his mind the ideas which compose the visible man1 in company with all the other ideas of sight perceived at the same time3 but all these ideas offered at once to his view1 he would not distribute into sundry distinct combinations till such time as by observing the motion of the parts of the man and other experiences he comes to know which are to be separated and which to be collected together4 #aaa4 ,from what hath been premised it is plain the objects of sight and touch make1 if ,i may so say1 two sets of ideas which are widely different from each other4 ,to objects of either kind we indifferently attribute the terms high and low1 right and left1 and suchlike1 denoting the position or situation of things3 but then we must well observe that the position of any object is determined with respect only to objects of the same sense4 ,we say any object of touch is high or low1 according as it is more or less distant from the tangible earth3 and in like manner we denominate any object of sight high or low in proportion as it is more or less distant from the visible earth3 but to define the situation of visible things with relation to the distance they bear from any tangible thing1 or ,,vice ,,versa1 this were absurd and perfectly unintelligible4 ,for all visible things are equally in the mind1 and take up no part of the external space3 and consequently are equidistant from any tangible thing which exists without the mind4 #aab4 ,or rather1 to speak truly1 the proper objects of sight are at no distance1 neither near nor far1 from any tangible thing4 ,for if we inquire narrowly into the matter we shall find that those things only are compared together in respect of distance which exist after the same manner1 or appertain unto the same sense4 ,for by the distance between any two points nothing more is meant than the number of intermediate points3 if the given points are visible the distance between them is marked out by the number of the interjacent visible points3 if they are tangible1 the distance between them is a line consisting of tangible points2 but if they are one tangible and the other visible1 the distance between them doth neither consist of points perceivable by sight nor by touch1 i4e4 it is utterly inconceivable4 ,this1 perhaps1 will not find an easy admission into all men's understanding3 however1 ,i should gladly be informed whether it be not true by anyone who will be at the pains to reflect a little and apply it home to his thoughts4 #aac4 ,the not observing what has been delivered in the two last sections seems to have occasioned no small part of the difficulty that occurs in the business of erect appearances4 ,the head1 which is painted nearest the earth1 seems to be farthest from it3 and on the other hand the feet1 which are painted farthest from the earth1 are thought nearest to it4 ,herein lies the difficulty1 which vanishes if we express the thing more clearly and free from ambiguity1 thus3 how comes it that to the eye the visible head which is nearest the tangible earth seems farthest from the earth1 and the visible feet1 which are farthest from the tangible earth seem nearest the earth8 ,the question being thus proposed1 who sees not the difficulty is founded on a supposition that the eye1 or visive faculty1 or rather the soul by means thereof1 should judge of the situation of visible objects with reference to their distance from the tangible earth8 ,whereas it is evident the tangible earth is not perceived by sight3 and it hath been shown in the two last preceding sections that the location of visible objects is determined only by the distance they bear from one another2 and that it is nonsense to talk of distance1 far or near1 between a visible and tangible thing4 #aad4 ,if we confine our thoughts to the proper objects of sight1 the whole is plain and easy4 ,the head is painted farthest from1 and the feet nearest to1 the visible earth2 and so they appear to be4 ,what is there strange or unaccountable in this8 ,let us suppose the pictures in the fund of the eye to be the immediate objects of the sight4 ,the consequence is that things should appear in the same posture they are painted in2 and is it not so8 ,the head which is seen seems farthest from the earth which is seen2 and the feet which are seen seem nearest to the earth1 which is seen2 and just so they are painted4 #aae4 ,but1 say you1 the picture of the man is inverted1 and yet the appearance is erect3 ,i ask1 what mean you by the picture of the man1 or1 which is the same thing1 the visible man's being inverted8 ,you tell me it is inverted1 because the heels are uppermost and the head undermost8 ,explain me this4 ,you say that by the head's being undermost you mean that it is nearest to the earth2 and by the heels being uppermost that they are farthest from the earth4 ,i ask again what earth you mean8 ,you cannot mean the earth that is painted on the eye1 or the visible earth3 for the picture of the head is farthest from the picture of the earth1 and the picture of the feet nearest to the picture of the earth2 and accordingly the visible head is farthest from the visible earth1 and the visible feet nearest to it4 ,it remains1 therefore1 that you mean the tangible earth1 and so determine the situation of visible things with respect to tangible things2 contrary to what hath been demonstrated in sect4 #aaa and #aab4 ,the two distinct provinces of sight and touch should be considered apart1 and as if their objects had no intercourse1 no manner of relation one to another1 in point of distance or position4 #aaf4 ,farther1 what greatly contributes to make us mistake in this matter is that when we think of the pictures in the fund of the eye1 we imagine ourselves looking on the fund of another's eye1 or another looking on the fund of our own eye1 and beholding the pictures painted thereon4 ,suppose two eyes ,a and ,b3 ,a from some distance looking on the pictures in ,b sees them inverted1 and for that reason concludes they are inverted in ,b3 but this is wrong4 ,there are projected in little on the bottom of ,a the images of the pictures of1 suppose1 man1 earth1 etc41 which are painted on ,b4 ,and besides these the eye ,b itself1 and the objects which environ it1 together with another earth1 are projected in a larger size on ,a4 ,now1 by the eye ,a these larger images are deemed the true objects1 and the lesser only pictures in miniature4 ,and it is with respect to those greater images that it determines the situation of the smaller images3 so that comparing the little man with the great earth1 ,a judges him inverted1 or that the feet are farthest from and the head nearest to the great earth4 ,whereas1 if ,a compare the little man with the little earth1 then he will appear erect1 i4e4 his head shall seem farthest from1 and his feet nearest to1 the little earth4 ,but we must consider that ,b does not see two earths as ,a does3 it sees only what is represented by the little pictures in ,a1 and consequently shall judge the man erect4 ,for1 in truth1 the man in ,b is not inverted1 for there the feet are next the earth2 but it is the representation of it in ,a which is inverted1 for there the head of the representation of the picture of the man in ,b is next the earth1 and the feet farthest from the earth1 meaning the earth which is without the representation of the pictures in ,b4 ,for if you take the little images of the pictures in ,b1 and consider them by themselves1 and with respect only to one another1 they are all erect and in their natural posture4 #aag4 ,farther1 there lies a mistake in our imagining that the pictures of external objects are painted on the bottom of the eye4 ,it hath been shown there is no resemblance ,,between the ideas of sight and things tangible4 ,it hath likewise been demonstrated that the proper objects of sight do not exist without the mind4 ,whence it clearly follows that the pictures painted on the bottom of the eye are not the pictures of external objects4 ,let anyone consult his own thoughts1 and then say what affinity1 what likeness there is between that certain variety and disposition of colours which constitute the visible man1 or picture of a man1 and that other combination of far different ideas1 sensible by touch1 which compose the tangible man4 ,but if this be the case1 how come they to be accounted pictures or images1 since that supposes them to copy or represent some originals or other8 #aah4 ,to which ,i answer3 in the forementioned instance the eye ,a takes the little images1 included within the representation of the other eye ,b1 to be pictures or copies1 whereof the archetypes are not things existing without1 but the larger pictures projected on its own fund3 and which by ,a are not thought pictures1 but the originals1 or true things themselves4 ,though if we suppose a third eye ,c from a due distance to behold the fund of ,a1 then indeed the things projected thereon shall1 to ,c1 seem pictures or images in the same sense that those projected on ,b do to ,a4 #aai4 ,rightly to conceive this point we must carefully distinguish between the ideas of sight and touch1 between the visible and tangible eye2 for certainly on the tangible eye nothing either is or seems to be painted4 ,again1 the visible eye1 as well as all other visible objects1 hath been shown to exist only in the mind1 which perceiving its own ideas1 and comparing them together1 calls some ,,pictures in respect of others4 ,what hath been said1 being rightly comprehended and laid together1 doth1 ,i think1 afford a full and genuine explication of the erect appearance of objects2 which phenomenon1 ,i must confess1 ,i do not see how it can be explained by any theories of vision hitherto made public4 #abj4 ,in treating of these things the use of language is apt to occasion some obscurity and confusion1 and create in us wrong ideas2 for language being accommodated to the common notions and prejudices of men1 it is scarce possible to deliver the naked and precise truth without great circumlocution1 impropriety1 and 7to an unwary reader7 seeming contradictions2 ,i do therefore once for all desire whoever shall think it worth his while to understand what ,i have written concerning vision1 that he would not stick in this or that phrase1 or manner of expression1 but candidly collect my meaning from the whole sum and tenor of my discourse1 and laying aside the words as much as possible1 consider the bare notions themselves1 and then judge whether they are agreeable to truth and his own experience1 or no4 #aba4 ,we have shown the way wherein the mind by mediation of visible ideas doth perceive or apprehend the distance1 magnitude and situation of tangible objects4 ,we come now to inquire more particularly concerning the difference between the ideas of sight and touch1 which are called by the same names1 and see whether there be any idea common to both senses4 ,from what we have at large set forth and demonstrated in the foregoing parts of this treatise1 it is plain there is no one selfsame numerical extension perceived both by sight and touch2 but that the particular figures and extensions perceived by sight1 however they may be called by the same names and reputed the same things with those perceived by touch1 are nevertheless different1 and have an existence distinct and separate from them3 so that the question is not now concerning the same numerical ideas1 but whether there be any one and the same sort of species of ideas equally perceivable to both senses2 or1 in other words1 whether extension1 figure1 and motion perceived by sight are not specifically distinct from extension1 figure1 and motion perceived by touch4 #abb4 ,but before ,i come more particularly to discuss this matter1 ,i find it proper to consider extension in abstract3 for of this there is much talk1 and ,i am apt to think that when men speak of extension as being an idea common to two senses1 it is with a secret supposition that we can single out extension from all other tangible and visible qualities1 and form thereof an abstract idea1 which idea they will have common both to sight and touch4 ,we are therefore to understand by extension in abstract an idea of extension1 for instance1 a line or surface entirely stripped of all other sensible qualities and circumstances that might determine it to any particular existence2 it is neither black nor white1 nor red1 nor hath it any colour at all1 or any tangible quality whatsoever and consequently it is of no finite determinate magnitude3 for that which bounds or distinguishes one extension from another is some quality or circumstance wherein they disagree4 #abc4 ,now ,i do not find that ,i can perceive1 imagine1 or any wise frame in my mind such an abstract idea as is here spoken of4 ,a line or surface which is neither black1 nor white1 nor blue1 nor yellow1 etc41 nor long1 nor short1 nor rough1 nor smooth1 nor square1 nor round1 etc41 is perfectly incomprehensible4 ,this ,i am sure of as to myself3 how far the faculties of other men may reach they best can tell4 #abd4 ,it is commonly said that the object of geometry is abstract extension3 but geometry contemplates figures3 now1 figure is the termination of magnitude3 but we have shown that extension in abstract hath no finite determinate magnitude4 ,whence it clearly follows that it can have no figure1 and consequently is not the object of geometry4 ,it is indeed a tenet as well of the modern as of the ancient philosophers that all general truths are concerning universal abstract ideas2 without which1 we are told1 there could be no science1 no demonstration of any general proposition in geometry4 ,but it were no hard matter1 did ,i think it necessary to my present purpose1 to show that propositions and demonstrations in geometry might be universal1 though they who make them never think of abstract general ideas of triangles or circles4 #abe4 ,after reiterated endeavours to apprehend the general idea a triangle1 ,i have found it altogether incomprehensible4 ,and surely if anyone were able to introduce that idea into my mind1 it must be the author of the ,,essay ,,concerning ,,human ,,understanding2 he who has so far distinguished himself from the generality of writers by the clearness and significancy of what he says4 ,let us therefore see how this celebrated author describes the general or abstract idea of a triangle4 ',it must be 7says he7 neither oblique nor rectangular1 neither equilateral1 equicrural1 nor scalenum2 but all and none of these at once4 ,in effect1 it is somewhat imperfect that cannot exist2 an idea1 wherein some parts of several different and inconsistent ideas are put together' ,,essay ,,on ,,hum4 ,,understand4 ,b4 iv4 ,c4 #g4 ,s4#i4 ,this is the idea which he thinks needful for the enlargement of knowledge1 which is the subject of mathematical demonstration1 and without which we could never come to know any general proposition concerning triangles4 ,that author acknowledges it doth 'require some pains and skill to form this general idea of a triangle4' ,,ibid4 ,but had he called to mind what he says in another place1 to wit1 ',that ideas of mixed modes wherein any inconsistent ideas are put together cannot so much as exist in the mind1 i4e4 be conceived4' ,,vid4 ,b4 iii4 ,c4 #aj4 ,s4 #cc4 ,,ibid4 ,i say1 had this occurred to his thoughts1 it is not improbable he would have owned it above all the pains and skill he was master of to form the above-mentioned idea of a triangle1 which is made up of manifest1 staring contradictions4 ,that a man who laid so great a stress on clear and determinate ideas should nevertheless talk at this rate seems very surprising4 ,but the wonder will lessen if it be considered that the source whence this opinion flows is the prolific womb which has brought forth innumerable errors and difficulties in all parts of philosophy and in all the sciences3 but this matter1 taken in its full extent1 were a subject too comprehensive to be insisted on in this place4 ,and so much for extension in abstract4 #abf4 ,some1 perhaps1 may think pure space1 ,,vacuum1 or trine dimension to be equally the object of sight and touch3 but though we have a very great propension to think the ideas of outness and space to be the immediate object of sight1 yet1 if ,i mistake not1 in the foregoing parts of this essay that hath been clearly demonstrated to be a mere delusion1 arising from the quick and sudden suggestion of fancy1 which so closely connects the idea of distance with those of sight1 that we are apt to think it is itself a proper and immediate object of that sense till reason corrects the mistake4 #abg4 ,it having been shown that there are no abstract ideas of figure1 and that it is impossible for us by any precision of thought to frame an idea of extension separate from all other visible and tangible qualities which shall be common both to sight and touch3 the question now remaining is1 whether the particular extensions1 figures1 and motions perceived by sight be of the same kind with the particular extensions1 figures1 and motions perceived by touch8 ,in answer to which ,i shall venture to lay down the following proposition3 ,,the ,,extension1 ,,figures1 ,,and ,,motions ,,perceived ,,by ,,sight ,,are ,,specifically ,,distinct ,,from ,,the ,,ideas ,,of ,,touch ,,called ,,by ,,the ,,same ,,names1 ,,nor is ,,there ,,any ,,such ,,thing as ,,one ,,idea ,,or ,,kind ,,of ,,idea ,,common ,,to ,,both ,,senses4 ,this proposition may without much difficulty be collected from what hath been said in several places of this essay4 ,but because it seems so remote from1 and contrary to1 the received notions and settled opinion of mankind1 ,i shall attempt to demonstrate it more particularly and at large by the following arguments4 #abh4 ,when upon perception of an idea ,i range it under this or that sort1 it is because it is perceived after the same manner1 or because it has a likeness or conformity with1 or affects me in the same way as1 the ideas of the sort ,i rank it under4 ,in short1 it must not be entirely new1 but have something in it old and already perceived by me4 ,it must1 ,i say1 have so much at least in common with the ideas ,i have before known and named as to make me give it the same name with them4 ,but it has been1 if ,i mistake not1 clearly made out that a man born blind would not at first reception of his sight think the things he saw were of the same nature with the objects of touch1 or had anything in common with them2 but that they were a new set of ideas1 perceived in a new manner1 and entirely different from all he had ever perceived before3 so that he would not call them by the same name1 nor repute them to be of the same sort with anything he had hitherto known4 #abi4 ,,secondly1 light and colours are allowed by all to constitute a son or species entirely different from the ideas of touch3 nor will any man1 ,i presume1 say they can make themselves perceived by that sense3 but there is no other immediate object of sight besides light and colours4 ,it is therefore a direct consequence that there is no idea common to both senses4 #acj4 ,it is a prevailing opinion1 even amongst those who have thought and writ most accurately concerning our ideas and the ways whereby they enter into the understanding1 that something more is perceived by sight than barely light and colours with their variations4 ,mr4 ,locke termeth sight1 ',the most comprehensive of all our senses1 conveying to our minds the ideas of light and colours1 which are peculiar only to that sense2 and also the far different ideas of space1 figure1 and motion4 ,,essay ,,on ,,human ,,understand4 ,b4 ii4 ,c4 #i4 ,s4 #i4 ,space or distance1 we have shown1 is not otherwise the object of sight than of hearing4 ,,vid4 sect4 #df4 ,and as for figure and extension1 ,i leave it to anyone that shall calmly attend to his own clear and distinct ideas to decide whether he had any idea intromitted immediately and properly by sight save only light and colours3 or whether it ,de possible for him to frame in his mind a distinct abstract idea of visible extension or figure exclusive of all colour3 and on the other hand1 whether he can conceive colour without visible extension8 ,for my own part1 ,i must confess ,i am not able to attain so great a nicety of abstraction3 in a strict sense1 ,i see nothing but light and colours1 with their several shades and variations4 ,he who beside these doth also perceive by sight ideas far different and distinct from them hath that faculty in a degree more perfect and comprehensive than ,i can pretend to4 ,it must be owned that by the mediation of light and colours other far different ideas are suggested to my mind3 but so they are by hearing1 which beside sounds which are peculiar to that sense1 doth by their mediation suggest not only space1 figure1 and motion1 but also all other ideas whatsoever that can be signified by words4 #aca4 ,,thirdly1 it is1 ,i think1 an axiom universally received that quantities of the same kind may be added together and make one entire sum4 ,mathematicians add lines together3 but they do not add a line to a solid1 or conceive it as making one sum with a surface3 these three kinds of quantity being thought incapable of any such mutual addition1 and consequently of being compared together in the several ways of proportion1 are by then esteemed entirely disparate and heterogeneous4 ,now let anyone try in his thoughts to add a visible line or surface to a tangible line or surface1 so as to conceive them making one continued sum or whole4 ,he that can do this may think them homogeneous3 but he that cannot1 must by the foregoing axiom think them heterogeneous4 ,a blue and a red line ,i can conceive added together into one sum and making one continued line3 but to make in my thoughts one continued line of a visible and tangible line added together is1 ,i find1 a task far more difficult1 and even insurmountable3 and ,i leave it to the reflexion and experience of every particular person to determine for himself4 #acb4 ,a farther confirmation of our tenet may be drawn from the solution of ,mr4 ,molyneux's problem1 published by ,mr4 ,locke in his ,,essay3 which ,i shall set down as it there lies1 together with ,mr4 ,locke's opinion of it1 ',suppose a man born blind1 and now adult1 and taught by his touch to distinguish between a cube and a sphere of the same metal1 and nighly ,,sic of the same bigness1 so as to tell1 when he felt one and t'other1 which is the cube and which the sphere4 ,suppose then the cube and sphere placed on a table1 and the blind man to be made to see3 ,,quaere1 whether by his sight1 before he touched them1 he could now distinguish and tell which is the globe1 which the cube8 ,to which the acute and judicious proposer answers3 ,not4 ,for though he has obtained the experience of how a globe1 how a cube1 affects his touch1 yet he has not yet attained the experience that what affects his touch so or so must affect his sight so or so3 or that a protuberant angle in the cube that pressed his hand unequally shall appear to his eye as it doth in the cube4 ,i agree with this thinking gentleman1 whom ,i am proud to call my friend1 in his answer to this his problem2 and am of opinion that the blind man at first sight would not be able with certainty to say which was the globe1 which the cube1 whilst he only saw them4' 7,,essay ,,on ,,human ,,understanding1 ,b4 ii4 ,c4 #i4 ,s4 #h47 #acc4 ,now1 if a square surface perceived by touch be of the same sort with a square surface perceived by sight1 it is certain the blind man here mentioned might know a square surface as soon as he saw it3 it is no more but introducing into his mind by a new inlet an idea he has been already well acquainted with4 ,since1 therefore1 he is supposed to have known by his touch that a cube is a body terminated by square surfaces1 and that a sphere is not terminated by square surfaces3 upon the supposition that a visible and tangible square differ only ,,in ,,numero it follows that he might know1 by the unerring mark of the square surfaces1 which was the cube1 and which not1 while he only saw them4 ,we must therefore allow either that visible extension and figures are specifically distinct from tangible extension and figures1 or else that the solution of this problem given by those two thoughtful and ingenious men is wrong4 #acd4 ,much more might be laid together in proof of the proposition ,i have advanced3 but what has been said is1 if ,i mistake not1 sufficient to convince anyone that shall yield a reasonable attention3 and as for those that will not be at the pains of a little thought1 no multiplication of words will ever suffice to make them understand the truth1 or rightly conceive my meaning4 #ace4 ,i cannot let go the above-mentioned problem without some reflexion on it4 ,it hath been evident that a man blind from his birth would not1 at first sight1 denominate anything he saw by the names he had been used to appropriate to ideas of touch1 ,,vid4 sect4 #ajf4 ,cube1 sphere1 table are words he has known applied to things perceivable by touch1 but to things perfectly intangible he never knew them applied4 ,those words in their wonted application always marked out to his mind bodies or solid things which were perceived by the resistance they gave3 but there is no solidity1 no resistance or protrusion1 perceived by sight4 ,in short1 the ideas of sight are all new perceptions1 to which there be no names annexed in his mind3 he cannot therefore understand what is said to him concerning them3 and to ask of the two bodies he saw placed on the table1 which was the sphere1 which the cube8 were to him a question downright bantering and unintelligible2 nothing he sees being able to suggest to his thoughts the idea of body1 distance1 or in general of anything he had already known4 #acf4 ,it is a mistake to think the same thing affects both sight and touch4 ,if the same angle or square which is the object of touch be also the object of vision1 what should hinder the blind man at first sight from knowing it8 ,for though the manner wherein it affects the sight be different from that wherein it affected his touch1 yet1 there being beside his manner or circumstance1 which is new and unknown1 the angle or figure1 which is old and known1 he cannot choose but discern it4 #acg4 ,visible figure and extension having been demonstrated to be of a nature entirely different and heterogeneous from tangible figure and extension1 it remains that we inquire concerning4 ,now that visible motion is not of the same sort with tangible motion seems to need no farther proof1 it being an evident corollary from what we have shown concerning the difference there is between visible and tangible extension3 but for a more full and express proof hereof we need only observe that one who had not yet experienced vision would not at first sight know motion4 ,whence it clearly follows that motion perceivable by sight is of a sort distinct from motion perceivable by touch4 ,the antecedent ,i prove thus3 by touch he could not perceive any motion but what was up or down1 to the right or left1 nearer or farther from him2 besides these and their several varieties or complications1 it is impossible he should have any idea of motion4 ,he would not therefore think anything to be motion1 or give the name motion to any idea which he could not range under some or other of those particular kinds thereof4 ,but from sect4 #ie it is plain that by the mere act of vision he could not know motion upwards or downwards1 to the right or left1 or in any other possible direction4 ,from which ,i conclude he would not know motion at all at first sight4 ,as for the idea of motion in abstract1 ,i shall not waste paper about it1 but leave it to my reader to make the best he can of it4 ,to me it is perfectly unintelligible4 #ach4 ,the consideration of motion may furnish a new field for inquiry3 but since the manner wherein the mind apprehends by sight the motion of tangible objects1 with the various degrees thereof1 may be easily collected from what hath been said concerning the manner wherein that sense doth suggest their various distances1 magnitudes1 and situations1 ,i shall not enlarge any farther on this subject1 but proceed to consider what may be alleged1 with greatest appearance of reason1 against the proposition we have shown to be true4 ,for where there is so much prejudice to be encountered1 a bare and naked demonstration of the truth will scarce suffice4 ,we must also satisfy the scruples that men may raise in favour of their preconceived notions1 show whence the mistake arises1 how it came to spread1 and carefully disclose and root out those false persuasions that an early prejudice might have implanted in the mind4 #aci4 ,,first1 therefore1 it will be demanded how visible extension and figures come to be called by the same name with tangible extension and figures1 if they are not of the same kind with them8 ,it must be something more than humour or accident that could occasion a custom so constant and universal as this1 which has obtained in all ages and nations of the world1 and amongst all ranks of men1 the learned as well as the illiterate4 #adj4 ,to which ,i answer1 we can no more argue a visible and tangible square to be of the same species from their being called by the same name1 than we can that a tangible square and the monosyllable consisting of six letters whereby it is marked are of the same species because they are both called by the same name4 ,it is customary to call written words and the things they signify by the same name3 for words not being regarded in their own nature1 or otherwise than as they are marks of things1 it had been superfluous1 and beside the design of language1 to have given them names distinct from those of the things marked by them4 ,the same reason holds here also4 ,visible figures are the marks of tangible figures1 and from sect4 #ei it is plain that in themselves they are little regarded1 or upon any other score than for their connexion with tangible figures1 which by nature they are ordained to signify4 ,and because this language of nature doth not vary in different ages or nations1 hence it is that in all times and places visible figures are called by the same names as the respective tangible figures suggested by them1 and not because they are alike or of the same sort with them4 #ada4 ,but1 say you1 surely a tangible square is liker to a visible square than to a visible circle3 it has four angles and as many sides3 so also has the visible square3 but the visible circle has no such thing1 being bounded by one uniform curve without right lines or angles1 which makes it unfit to represent the tangible square but very fit to represent the tangible circle4 ,whence it clearly follows that visible figures are patterns of1 or of the same species with1 the respective tangible figures represented by them3 that they are like unto them1 and of their own nature fitted to represent them1 as being of the same sort3 and that they are in no respect arbitrary signs1 as words4 #adb4 ,i answer1 it must be acknowledged the visible square is fitter than the visible circle to represent the tangible square1 but then it is not because it is liker1 or more of a species with it1 but because the visible square contains in it several distinct parts1 whereby to mark the several distinct corresponding parts of a tangible square1 whereas the visible circle doth not4 ,the square perceived by touch hath four distinct1 equal sides1 so also hath it four distinct equal angles4 ,it is therefore necessary that the visible figure which shall be most proper to mark it contain four distinct equal parts corresponding to the four sides of the tangible square1 as likewise four other distinct and equal parts whereby to denote the four equal angles of the tangible square4 ,and accordingly we see the visible figures contain in them distinct visible parts1 answering to the distinct tangible parts of the figures signified or suggested by them4 #adc4 ,but it will not hence follow that any visible figure is like unto1 or of the same species with1 its corresponding tangible figure1 unless it be also shown that not only the number but also the kind of the parts be the same in both4 ,to illustrate this1 ,i observe that visible figures represent tangible figures much after the same manner that written words do sounds4 ,now1 in this respect words are not arbitrary1 it not being indifferent what written word stands for any sound3 but it is requisite that each word contain in it so many distinct characters as there are variations in the sound it stands for4 ,thus the single letter ,a is proper to mark one simple uniform sound2 and the word ,,adultery is accommodated to represent the sound annexed to it1 in the formation whereof there being eight different collisions or modifications of the air by the organs of speech1 each of which produces a difference of sound1 it was fit the word representing it should consist of as many distinct characters1 thereby to mark each particular difference or part of the whole sound4 ,and yet nobody1 ,i presume1 will say the single letter a1 or the word ,,adultery1 are like unto1 or of the same species with1 the respective sounds by them represented4 ,it is indeed arbitrary that1 in general1 letters of any language represent sounds at all3 but when that is once agreed1 it is not arbitrary what combination of letters shall represent this or that particular sound4 ,i leave this with the reader to pursue1 and apply it in his own thoughts4 #add4 ,it must be confessed that we are not so apt to confound other signs with the things signified1 or to think them of the same species1 as we are visible and tangible ideas4 ,but a little consideration will show us how this may be without our supposing them of a like nature4 ,these signs are constant and universal1 their connexion with tangible ideas has been learnt at our first entrance into the world2 and ever since1 almost every moment of our lives1 it has been occurring to our thoughts1 and fastening and striking deeper on our minds4 ,when we observe that signs are variable1 and of human institution2 when we remember there was a time they were not connected in our minds with those things they now so readily suggest2 but that their signification was learned by the slow steps of experience3 this preserves us from confounding them4 ,but when we find the same signs suggest the same things all over the world2 when we know they are not of human institution1 and cannot remember that we ever learned their signification1 but think that at first sight they would have suggested to us the same things they do now3 all this persuades us they are of the same species as the things respectively represented by them1 and that it is by a natural resemblance they suggest them to our minds4 #ade4 ,add to this that whenever we make a nice survey of any object1 successively directing the optic axis to each point thereof1 there are certain lines and figures described by the motion of the head or eye1 which being in truth perceived by feeling1 do nevertheless so mix themselves1 as it were1 with the ideas of sight1 that we can scarce think but they appertain to that sense4 ,again1 the ideas of sight enter into the mind several at once1 more distinct and unmingled than is usual in the other senses beside the touch4 ,sounds1 for example1 perceived at the same instant1 are apt to coalesce1 if ,i may so say1 into one sound3 but we can perceive at the same time great variety of visible objects1 very separate and distinct from each other4 ,now tangible extension being made up of several distinct coexistent parts1 we may hence gather another reason that may dispose us to imagine a likeness or an analogy between the immediate objects of sight and touch4 ,but nothing1 certainly1 doth more contribute to blend and confound them together than the strict and close connexion they have with each other4 ,we cannot open our eyes but the ideas of distance1 bodies1 and tangible figures are suggested by them4 ,so swift and sudden and unperceived is the transition from visible to tangible ideas that we can scarce forbear thinking them equally the immediate object of vision4 #adf4 ,the prejudice which is grounded on these1 and whatever other causes may be assigned thereof1 sticks so fast that it is impossible without obstinate striving and labour of the mind to get entirely clear of it4 ,but then the reluctancy we find in rejecting any opinion can be no argument of its truth to whoever considers what has been already shown with regard to the prejudices we entertain concerning the distance1 magnitude1 and situation of objects2 prejudices so familiar to our minds1 so confirmed and inveterate1 as they will hardly give way to the clearest demonstration4 #adg4 ,upon the whole1 ,i think we may fairly conclude that the proper objects of vision constitute an universal language of the ,author of ,nature1 whereby we are instructed how to regulate our actions in order to attain those things that are necessary to the preservation and well-being of our bodies1 as also to avoid whatever may be hurtful and destructive of them4 ,it is by their information that we are principally guided in all the transactions and concerns of life4 ,and the manner wherein they signify and mark unto us the objects which are at a distance is the same with that of languages and signs of human appointment1 which do not suggest the things signified by any likeness or identity of nature1 but only by an habitual connexion that experience has made us to observe between them4 #adh4 ,suppose one who had always continued blind be told by his guide that after he has advanced so many steps he shall come to the brink of a precipice1 or be stopped by a wall2 must not this to him seem very admirable and surprizing8 ,he cannot conceive how it is possible for mortals to frame such predictions as these1 which to him would seem as strange and unaccountable as prophesy doth to others4 ,even they who are blessed with the visive faculty may 7though familiarity make it less observed7 find therein sufficient cause of admiration4 ,the wonderful art and contrivance wherewith it is adjusted to those ends and purposes for which it was apparently designed1 the vast extent1 number1 and variety of objects that are at once with so much ease and quickness and pleasure suggested by it3 all these afford subject for much and pleasing speculation1 and may1 if anything1 give us some glimmering analogous prenotion of things which are placed beyond the certain discovery and comprehension of our present state4 #adi4 ,i do not design to trouble myself with drawing corollaries from the doctrine ,i have hitherto laid down4 ,if it bears the test others may1 so far as they shall think convenient1 employ their thoughts in extending it farther1 and applying it to whatever purposes it may be subservient to3 only1 ,i cannot forbear making some inquiry concerning the object of geometry1 which the subject we have been upon doth naturally lead one to4 ,we have shown there is no such idea as that of extension in abstract1 and that there are two kinds of sensible extension and figures which are entirely distinct and heterogeneous from each other4 ,now1 it is natural to inquire which of these is the object of geometry4 #aej4 ,some things there are which at first sight incline one to think geometry conversant about visible extension4 ,the constant use of the eyes1 both in the practical and speculative parts of that science1 doth very much induce us thereto4 ,it would1 without doubt1 seem odd to a mathematician to go about to convince him the diagrams he saw upon paper were not the figures1 or even the likeness of the figures1 which make the subject of the demonstration4 ,the contrary being held an unquestionable truth1 not only by mathematicians1 but also by those who apply themselves more particularly to the study of logic2 ,i mean1 who consider the nature of science1 certainty1 and demonstration3 it being by them assigned as one reason of the extraordinary clearness and evidence of geometry that in this science the reasonings are free from those inconveniences which attend the use of arbitrary signs1 the very ideas themselves being copied out and exposed to view upon paper4 ,but1 by the bye1 how well this agrees with what they likewise assert of abstract ideas being the object of geometrical demonstration ,i leave to be considered4 #aea4 ,to come to a resolution in this point we need only observe what hath been said in sect4 #ei1 #fj1 #fa1 where it is shown that visible extensions in themselves are little regarded1 and have no settled determinable greatness1 and that men measure altogether1 by the application of tangible extension to tangible extension4 ,all which makes it evident that visible extension and figures are not the object of geometry4 #aeb4 ,it is therefore plain that visible figure are of the same use in geometry that words are3 and the one may as well be accounted the object of that science as the other1 neither of them being otherwise concerned therein than as they represent or suggest to the mind the particular tangible figures connected with them4 ,there is indeed this difference between the signification of tangible figures by visible figures1 and of ideas by words3 that whereas the latter is variable and uncertain1 depending altogether on the arbitrary appointment of men1 the former is fixed and immutably the same in all times and places4 ,a visible square1 for instance1 suggests to the mind the same tangible figure in ,europe that it doth in ,america4 ,hence it is that the voice of the ,author of' ,nature which speaks to our eyes1 is not liable to that misinterpretation and ambiguity that languages of human contrivance are unavoidably subject to4 #aec4 ,though what has been said may suffice to show what ought to be determined with relation to the object of geometry1 ,i shall nevertheless1 for the fuller illustration thereof1 consider the case of an intelligence1 or unbodied spirit1 which is supposed to see perfectly well1 i4e4 to have a clear perception of the proper and immediate objects of sight1 but to have no sense of touch4 ,whether there be any such being in ,nature or no is beside my purpose to inquire4 ,it sufficeth that the supposition contains no contradiction in it4 ,let us now examine what proficiency such a one may be able to make in geometry4 ,which speculation will lead us more clearly to see whether the ideas of sight can possibly be the object of that science4 #aed4 ,,first1 then1 it is certain the aforesaid intelligence could have no idea of a solid1 or quantity of three dimensions1 which followeth from its not having any idea of distance4 ,we indeed are prone to think that we have by sight the ideas of space and solids1 which ariseth from our imagining that we do1 strictly speaking1 see distance and some parts of an object at a greater distance than others2 which hath been demonstrated to be the effect of the experience we have had1 what ideas of touch are connected with such and such ideas attending vision3 but the intelligence here spoken of is supposed to have no experience of touch4 ,he would not1 therefore1 judge as we do1 nor have any idea of distance1 outness1 or profundity1 nor consequently of space or body1 either immediately or by suggestion4 ,whence it is plain he can have no notion of those parts of geometry which relate to the mensuration of solids and their convex or concave surfaces1 and contemplate the properties of lines generated by the section of a solid4 ,the conceiving of any part whereof is beyond the reach of his faculties4 #aee4 ,farther1 he cannot comprehend the manner wherein geometers describe a right line or circle2 the rule and compass with their use being things of which it is impossible he should have any notion3 nor is it an easier matter for him to conceive the placing of one plane or angle on another1 in order to prove their equality3 since that supposeth some idea of distance or external space4 ,all which makes it evident our pure intelligence could never attain to know so much as the first elements of plane geometry4 ,and perhaps upon a nice inquiry it will be found he cannot even have an idea of plane figures any more than he can of solids2 since some idea of distance is necessary to form the idea of a geometrical plane1 as will appear to whoever shall reflect a little on it4 #aef4 ,all that is properly perceived by the visive faculty amounts to no more than colours1 with their variations and different proportions of light and shade4 ,but the perpetual mutability and fleetingness of those immediate objects of sight render them incapable of being managed after the manner of geometrical figures2 nor is it in any degree useful that they should4 ,it is true there are divers of them perceived at once1 and more of some and less of others3 but accurately to compute their magnitude and assign precise determinate proportions between things so variable and inconstant1 if we suppose it possible to be done1 must yet be a very trifling and insignificant labour4 #aeg4 ,i must confess men are tempted to think that flat or plane figures are immediate objects of sight1 though they acknowledge solids are not4 ,and this opinion is grounded on what is observed in painting1 wherein 7it seems7 the ideas immediately imprinted on the mind are only of planes variously coloured1 which by a sudden act of the judgment are changed into solids4 ,but with a little attention we shall find the planes here mentioned as the immediate objects of sight are not visible but tangible planes4 ,for when we say that pictures are planes1 we mean thereby that they appear to the touch smooth and uniform4 ,but then this smoothness and uniformity1 or1 in other words1 this planeness of the picture1 is not perceived immediately by vision3 for it appeareth to the eye various and multiform4 #aeh4 ,from all which we may conclude that planes are no more the immediate object of sight than solids4 ,what we strictly see are not solids1 nor yet planes variously coloured3 they are only diversity of colours4 ,and some of these suggest to the mind solids1 and other plane figures1 just as they have been experienced to be connected with the one or the other3 so that we see planes in the same way that we see solids1 both being equally suggested by the immediate objects of sight1 which accordingly are themselves denominated planes and solids4 ,but though they are called by the same names with the things marked by them1 they are nevertheless of a nature entirely different1 as hath been demonstrated4 #aei4 ,what hath been said is1 if ,i mistake not1 sufficient to decide the question we proposed to examine1 concerning the ability of a pure spirit1 such as we have described1 to know ,,geometry4 ,it is1 indeed1 no easy matter for us to enter precisely into the thoughts of such an intelligence1 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 them4 ,this1 indeed1 in a complete degree seems scarce possible to be performed3 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 them4 ,though he endeavour to disunite the meaning from the sound1 it will nevertheless intrude into his thoughts1 and he shall find it extreme difficult1 if not impossible1 to put himself exactly in the posture of a foreigner that never learned the language1 so as to be affected barely with the sounds themselves1 and not perceive the signification annexed to them4 #afj4 ,by this time1 ,i suppose1 it is clear that neither abstract nor visible extension makes the object of geometry2 the not discerning of which may perhaps have created some difficulty and useless labour in mathematics4 ,sure ,i am1 that somewhat relating thereto has occurred to my thoughts1 which1 though after the most anxious and repeated examination ,i am forced to think it true1 doth1 nevertheless1 seem so far out of the common road of geometry1 that ,i know not whether it may not be thought presumption1 if ,i should make it public in an age1 wherein that science hath received such mighty improvements by new methods2 great part whereof1 as well as of the ancient discoveries1 may perhaps lose their reputation1 and much of that ardour with which men study the abstruse and fine geometry be abated1 if what to me1 and those few to whom ,i have imparted it1 seems evidently true1 should really prove to be so4