Chapter XI
18. Thus we find that learning those things whose images we do not take in by our senses, but which we intuit within ourselves without images and as they actually are, is nothing else except the gathering together of those same things which the memory already contains--but in an indiscriminate and confused manner- -and putting them together by careful observation as they are at hand in the memory; so that whereas they formerly lay hidden, scattered, or neglected, they now come easily to present themselves to the mind which is now familiar with them. And how many things of this sort my memory has stored up, which have already been discovered and, as I said, laid up for ready reference. These are the things we may be said to have learned and to know. Yet, if I cease to recall them even for short intervals of time, they are again so submerged--and slide back, as it were, into the further reaches of the memory--that they must be drawn out again as if new from the same place (for there is nowhere else for them to have gone) and must be collected [cogenda] so that they can become known. In other words, they must be gathered up [colligenda] from their dispersion. This is where we get the word cogitate [cogitare]. For cogo [collect] and cogito [to go on collecting] have the same relation to each other as ago [do] and agito [do frequently], and facio [make] and factito [make frequently]. But the mind has properly laid claim to this word [cogitate] so that not everything that is gathered together anywhere, but only what is collected and gathered together in the mind, is properly said to be "cogitated."
CHAPTER XII
19. The memory also contains the principles and the unnumbered laws of numbers and dimensions. None of these has been impressed on the memory by a physical sense, because they have neither color nor sound, nor taste, nor sense of touch. I have heard the sound of the words by which these things are signified when they are discussed: but the sounds are one thing, the things another. For the sounds are one thing in Greek, another in Latin; but the things themselves are neither Greek nor Latin nor any other language. I have seen the lines of the craftsmen, the finest of which are like a spider's web, but mathematical lines are different. They are not the images of such things as the eye of my body has showed me. The man who knows them does so without any cogitation of physical objects whatever, but intuits them within himself. I have perceived with all the senses of my body the numbers we use in counting; but the numbers by which we count are far different from these. They are not the images of these; they simply are. Let the man who does
not see these things mock me for saying them; and I will pity him while he laughs at me.