Make of the man and woman a Circle, of that a Quadrangle, of this a Triangle, of the same a Circle
and you will have the Stone of the Philosophers.
Plato that most Excellent Philosopher was of the Opinion that those notions or Ideas which are the Foundations of Arts and Sciences are as it were actually engraved and imprinted upon the mind of Man, and that by the Repetition and remembrance of them he can apprehend and know all manner of learning. To prove this he introduced a young Lad, rude and uninstructed, and asked him such Geometricall Questions that the Youth might be perceived to answer right whether he will or no, and although before he understood nothing of the matter, yet by these answers seemed to have penetrated into the Depths of so abstruse a Science. From whence he concluded that in children all Discipline and Doctrine is not at first taken in and learnt, but called to mind and brought by the memory, alluding by this to his Annus Magnus or Great Year, of which he says that forty eight thousand solar Years agoe, before the Revolution of the Heaven, the same persons, thinges and actions were then in being which are at the present time, whensoever that is. But every person may perceive that these thinges have no more foundations of truth in them than mere dreams. We do not deny that there are some sparks of notions and mere powers imprinted in us, which must be reduced into act by institution, but we utterly deny that they are such or so great as to be the Summaries of Arts and Sciences without any precedent instruction.
It will then be asked from whence Arts and Sciences have proceeded if men have not invented them, or whether they were not at first delivered from Heaven by the God of the Nations. I answer by saying that burning Coals may lye hid under Ashes in so great a quantity that if the Ashes were but removed they would be sufficient for the dressing of meat or warming oneself; but this is a different thinge from affirming that only some small spark lyes there, which before it can be of use and administer a sufficient heat must be cherished and nourished with fresh fewell by human Act, Care and Industry, or otherwise it would be easily extinguished. The Aristotelicks assert the latter as the Platonicks do the former. Reason and Experience seem to agree with this latter, whereas the first depends only upon Imagination and Phansy. Here it may be asked why Plato wrote over the Door of his school that no one ignorant of Geometry was there to be admitted, seeing he affirmed that little boys did actually know it. Are men more unlearned than boys? Or when they grow up, do they forget what they knew when children? That cannot be supposed, for we see that Brutes do by the instinct of Nature as soon as they are brought forth abhor and avoid the danger of Fire, Water, Precipices and the like. Yet an infant neither knows nor shuns such thinges. Why do not the Bee, Fly and Gnatt precipitate themselves into the Fire, seeing that they cannot know by experience that danger will arise from it? Because nature has taught them, but she has not done so by man when he is newly born. If Geometry is so easy and naturall to children, how comes it to passe that Plato did not know the Quadrature of a Circle, so that Aristotle who was his schollar affirms that it might be known but was not yet known?
But that this was not unknown to the Philosophers of Nature is apparent from this: That they command a Circle to be turned into a Quadrangle, and this by a Triangle to be reduced again to a Circle. By a circle they understand the most simple body without angles, as by the Quadrangle they do the four Elements. It is as if they should say: The most simple corporeal Figure that can be found is to be taken and divided into four Elementall Colours, becoming an Equilaterall Quadrangle. Now every man understands that this Quadration is Physicall and agreeable to Nature, by which far more benefit accrues to the Publick, and more light appears to the mind of Man, than by any meere Theory of Mathematicks when abstracted from Matter. To learn this perfectly a Geometrician acting upon solid bodyes must enquire what is the depth of solid Figures, as for example the Profundity of Sphere and Cube must be knowne and transferred to manuall use and practice. If the Capacity or Circumference of the sphere be 32 foot, how much will one of the sides of the Cube be to Equalize the Capacity of this Sphere? On the contrary, one might look back from the Measures which the Cube contains to the feet of each Circumference.
In like manner the Philosophers would have the Quadrangle reduced into a Triangle, that is, into a Body, Spirit and Soul, which three appear in the three previous colours before Rednesse: that is, the Body or earth in the Blacknesse of Saturn, the Spirit in the Lunar whitenesse as water, and the Soul or air in the Solar Citrinity. Then the Triangle will be perfect, but this again must be changed into a Circle; that is, into an invariable rednesse, by which operation the woman is converted into the man and made one with him, and six the first of the perfect numbers is absolved by one, two having returned again to an unity in which there is Rest and eternall peace.