Great Kabbalistic Art — Hartmann Schopper, 1564-1569

be 300, and the number of the fourth line, which must multiply it, is 0, which does not change it; wherefore 300 will remain as it is. Then the quantity of the last line of the pyramid corresponding to it is likewise 300, from which when the sum is subtracted, 0 remains. Wherefore for the Root you will establish 30, which is the divisor of this sum, as I taught above to be done.

But here two things seem to be noted: First, if after the subtraction is made (which in such a case, as has been said, will retain no remainder, but will see only a Zero) it should happen that the divisor was likewise 0; then observe whether the sum of the word, which when multiplied equals the quantity of the last line of the pyramid, has for its multiplying number likewise 0 or 1. For if matters stand thus, then you will write 0 for the Root. If, however, that sum of words, from any other number besides 0 or 1 multiplying it, has obtained that quantity equal to the last pyramidal line, and its quotient divisor, as we said, was 0; then having cast away the multiplication, you will take the sum as it is, and you will subtract it from the number or quantity of the last pyramidal line, and you will put the remainder for the Root marked with ±, as being not direct. For instance, let the sum of some word be 234 and its multiplying number be 2 or 3, which likewise will generate that same 234. Then let the quantity of the last pyramidal line be 234, and the divisor already placed in the first line is likewise 0. Then because from the subtraction there remains likewise 0, and similarly the sum of the word to be multiplied has for its multiplier number 2 or 1: then you will keep the Divisor, which is 0, for the Root. But if the sum of the word to be multiplied had been 39, and on account of that multiplying number, which was 6, it soon obtained the origin of the said sum 234; then having taken that sum of the word to be multiplied, namely 39, you subtract it from the 234 quantity of the last line of the pyramid, and the Remainder which would be 195 you will note for the Root to be marked with ±. Second, in the same case, if nothing remained from their subtraction, as has been said, it might happen that the divisor was a number which had a 0 on the left, such as 013. Then, as was said in another case above, you will consider that Zero as if it were 00: and you will establish it for the Root, yet remember to mark it with ±, because it was produced in a reversed order.

Eighth, if the sum multiplied by the number of the fourth line should be greater than the quantity of the last pyramidal line from which that sum of the word ought to be subtracted, and in addition the number of the divisor was 0, in which case, as you see, two exceptions to the rules are joined together; then so that you may obtain the Root, subtract the quantity of the pyramidal line from the multiplied sum; and divide the Remainder of the subtraction by the same sum but not multiplied: and whatever comes from the division will be the sought Root to be placed in its place and marked with ±. As in the second example, for the seventh sum of the words 76, which led by 5, the number multiplying it, makes 380, a quantity greater than the last line of the pyramid, which is 306. Therefore, the smaller being subtracted from the larger, 84 remains, which divided by the non-multiplied sum has a remainder of 6, which 6 will be noted for the Root marked with ±.

But if that non-multiplied sum, which according to this eighth division ought to divide the remainder of the subtraction, were greater than the quantity to be divided—which I do not deny can happen, whenever the multiplying number of that sum was 2 or 1, both of which frequently vary the sum from the product of the multiplication—then you would cease to use that divisor number itself for the Root, namely that non-multiplied sum, and in such a case it will be the appropriate indicated Root under its own eighth line. As in the example of my brother, you will find the twentieth sum, namely of the word Chesed Mercy/Loving-kindness, which not only when multiplied by its adhering number is greater than the quantity of the last pyramidal line (for the sum is 126, but the pyramidal quantity is 53), but in addition for the Root of this the Divisor is 9. And although according to this given rule the quantity of the pyramidal line, which is 53, was to be subtracted from the multiplied sum, which is 126, and the Remainder of the subtraction will be 73, which according to the prescribed Method was to be divided by the non-multiplied sum—which sum does not permit its own subtraction, but where it was even multiplied, namely 126, it remains because of 0 as its multiplier. But in this case 73 would be divided by 12 (for our value is twelve). Therefore the whole sum, which here is to be taken for the Divisor, should be written in its proper place for the Root, so that it may be noted.

Ninth, if any Divisor, besides the above exception, should be greater than the quantity to be divided, then subtract the quantity of the last pyramidal line, which is smaller, from the Divisor, and the Remainder is as the Root under its pyramidal line, and you bind it with ±. For instance, if the multiplied sum of some word is 199, whose first line (which is always considered for the divisor as it is true) is 88. Then let the quantity of the last pyramidal line be 120, from which when the sum of the word is subtracted, there remains 31, which was to be divided as if for 44. But because the divisor is greater than the quantity to be divided, therefore according to the aforesaid doctrine, subtract the Remainder of the quantity of the last line of the pyramid, namely 31, from the same Divisor 88, and 57 will come forth, which you will arrange in its proper place for the Root marked with ±.

And behold, more briefly than ever, all cases and exceptions that can occur in this second operation are most clearly explained and illustrated with examples (which I commend to your skill), so that nothing is so difficult that the prescribed method does not solve it.

Furthermore, in any other language (except Hebrew) you will observe the same rules conceived by us here for the Latin language, because here nothing new seems to exist. In Hebrew, however, two things remain to be noted.

First, that in the Hebrew manner the words, which the pyramidal lines must effect, are written in a reversed order, just as likewise containing the Numbers for the same words Tav, Shin, Resh, Qoph, Tsade, Pe, Ayin, Samekh, Nun, Nun-final, Mem, Mem-final, Lamed, Kaph, Kaph-final etc., which in reversed order, as you see written, you will mark with numbers, and you will make the pyramidal lines according to the rules thus = 120, 10, 90, 5 = 9, 80, 6 = 500 = 5, 80, 10, 1 etc.

Second, in any exception shown above which ought to be marked with ±, in this most primary language you will note it with no sign: because here the language itself does not permit you to invert the Roots; just as in the second part of these my Labors I have tried to render, showing also the reason and cause, as will be seen there.

CHAPTER IV.

That the Rhomboid diamond shape is a figure in Mathematics that is neither equilateral nor rectangular is known even to beginners. In this our sacred art, which follows like a most excellent and obedient daughter where the footsteps of the Mother Mathematics are, we do not intend to show an equilateral or rectangular figure by the name of Rhomboid; as will not only be seen below, but will shine in the examples appended after the end of this first work. To speak of Rhomboids did not seem superfluous, so that their origin might also become known.

Then, before we arrive at the practical arrangement of numbers in any Rhomboid, it was not tiresome to speak briefly of the mathematical construction of them, which construction is as follows.

The beginning of any Rhomboid is written in only a single cell; but the succeeding rows of the same Rhomboid continue in an articulated order by an increase of two cells. Proceeding thus to increase the rows until the middle of the Rhomboid itself; which will contain two rows equal to each other. Then the figure of the Rhomboid, by going backward or decreasing and cutting off two cells, will form its following rows, until they come to a single cell.

This is also done, and the words will also show us when the cells should return. For if you have five or six words of your query, it is necessary that each Rhomboid contain eighteen cells.

If it is made from seven, eight, nine, or ten words, it does not exceed the twenty-second cell in any construction of Rhomboids.

If indeed it is composed of eleven, twelve, thirteen, fourteen, or fifteen words, you will fashion a Rhomboid with a fifteenth cell likely meaning 15 rows or a specific configuration.

But if it is from sixteen, seventeen, eighteen, or nineteen,