(18) In all questions, then, there is something which is previously known, - that which being self-evident is believed without demonstration; which must be made the starting point in their investigation, and the criterion of apparent results.

(7) Now, either all things require demonstration, or some of them are self-evident. But if the first, by demanding the demonstration of each demonstration we shall go on ad infinitum; and so demonstration is subverted.

(5) Another marked case is that of Zerah Colburn, the mathematical prodigy, whose feats attracted the attention of the scientific world during the last century. In this case, the child under eight years of age, without any previous knowledge of even the common rules of arithmetic, or even of the use and powers of the Arabic numerals, solved a great variety of arithmetical problems by a simple operation of the mind, and without the use of any visible symbols or contrivances. He could answer readily a question involving the statement of the exact number of minutes or seconds in any given period of time. He could also state with equal facility the exact product of the multiplication of any number containing two, three, or four figures by another number consisting of a like number of figures. He could state almost instantly all the factors composing a number of six or seven places of figures. He could likewise determine instantly questions concerning the extraction of the square and cube roots of any number proposed, and likewise whether it was a prime number incapable of division by any other number, for which there is no known general rule among mathematicians. Asked such questions in the midst of his ordinary childish play, he would answer them almost instantly and then proceed with his play.

(103) Of which much were to be written, but [in the present book] you will find it more apprehensibly at the place concerning the creation: For there are to be found living testimonies enough, so that none need doubt whether the things be so or no.

(101) Concerning this, much higher things are to be written, which you will find concerning the creation of this world: This is only brought in for a similitude, and described in the briefest manner.

(6) This child once undertook and completely succeeded in raising the number 8 progressively up to the sixteenth power—in naming the result, 281,474,976,710,656 he was absolutely correct in every figure. He could raise any given number progressively up to the 10th power, with so much speed that the person putting down the figures on paper would frequently request him to manifest less speed. He gave instantly the square root of 106,929, and the cube root of 268,336,125. He could give the prime factors of very large numbers, and could detect large prime numbers instantly. Once asked how many minutes there were in forty-eight years, and before the question could be written down he answered "25,228,800", adding "and the number of seconds in such period is 1,513,728,000." The child, when questioned concerning his ability to give such answers, and to solve such difficult problems, was unable to give such information. He could say that he did not know how the answer came into his mind, but it was evident from watching him that some actual process was under way in his mind, and that there was no question of mere trick of memory in his feats. Moreover, it is important to note that he was totally ignorant of even the common rules of arithmetic, and could not "figure" on slate or paper even the simplest sum in addition or multiplication. It is interesting to note the sequel to this case, i.e., the fact that when a few years later the child was sent to the common schools and was there instructed in the art of written arithmetic, his power began to vanish, and eventually it left him altogether, and he became no more than any other child of his age. It seemed as if some door of his soul had been closed, while before it had stood ajar.

(2) We saw we saw we saw what really preexists, that it really is and is the first eternal one.

(5) And Râ said: “A mystery, a mystery, in the Net.”

(95) This I set down here only for a manuduction; you will find it demonstrated more at large concerning the creation of this world.

(2) Accordingly, by investigation, the point proposed for inquiry and answer knocks at the door of truth, according to what appears. And on an opening being made through the obstacle in the process of investigation, there results scientific contemplation. To those who thus knock, according to my view, the subject under investigation is opened.

(11) It will also turn out that there are other starting points for demonstrations, after the source which takes its rise in faith, - the things which appear clearly to sensation and understanding. For the phenomena of sensation are simple, and incapable of being decompounded; but those of understanding are simple, rational, and primary. But those produced from them are compound, but no less clear and reliable, and having more to do with the reasoning faculty than the first. For therefore the peculiar native power of reason, which we all have by nature, deals with agreement and disagreement. If, then, any argument be found to be of such a kind, as from points already believed to be capable of producing belief in what is not yet believed, we shall aver that this is the very essence of demonstration.

(2) Philosophers, in fact, present demonstration as having a substantial existence, one in one way, another in another. Therefore, if one would treat aright of each question, he cannot carry back the discourse to another more generally admitted fundamental principle than what is admitted to be signified by the term by all of the same nation and language.

(12) Now it is affirmed that the nature of demonstration, as that of belief, is twofold: that which produces in the souls of the hearers persuasion merely, and that which produces knowledge.

(47) I here set down this description of the birth or geniture of man's life, to the end that the original of the stars and planets may be the better conceived. In the description of the creation of man thou wilt find all, more fundamentally and deeply, what the beginning of man is. Now observe:

(8) But as there are two methods, one by question and answer, and the other the method of exposition, if he decline the former, let him listen to us, while we expound all that bears on the problem. Then when we have done, he may treat of each point in turn. But if he attempt to interrupt the investigation by putting questions, he plainly does not want to hear.

(2) Now, not only demonstration and belief and knowledge, but foreknowledge also, are used in a twofold manner. There is that which is scientific and certain, and that which is merely based on hope.

(7) The ancient teachings, which were later embodied in the early Rosicrucian teachings, held that in order that there might be Becoming, Change, or Creation, there must be Re-action following Action—the play of one force on another. And the best teachings of the ancients were that these two opposing forces in Nature were Masculine, and Feminine, respectively—dual aspects of the Universal Being. And Modern Science is fast coming to recognize and teach the same great truth.

(36) And said to him: "How many are the aeons of the immortals, starting from the infinities?"

(5) For He indeed showed the mode of combination of the letters, each with each, Aleph with all, and all with Aleph. Thus in combining all together in pairs are produced these two hundred and thirty-one gates of knowledge. And from Nothingness did He make something, and all forms of speech and every created thing, and from the empty void He made the solid earth, and from the non-existent He brought forth Life.

(42) For the earthly and corrupt nature has continually laboured from the beginning of its creation to this day to bring forth heavenly forms or shapes in the earth, as also in man and beasts; as men very well see that every year new arts are invented and brought to light, which has been constantly so from the beginning to this time.