176 r Michael Katz
[And these four—Aleph, Hey, Vav, Yod—are the distinguished ones.
And every squared number where one is added to the square the
same is in its root and the same in its like. And so in the square of
five five and in the square of six six. These four numbers forever
uphold themselves in square, and this is their eminence over all
squared numbers.]The mathematical property referred to here is the repetitive nature of end-
ings of powers of certain numbers. If a squared number ends with 1, Ibn-
Ezra tells us, then so does its root. Put vice versa—if a number ends with
1, so does its square. And by saying “and the same in its like” and then
“forever,” Ibn-Ezra probably means that the same is true for other pow-
ers, not only squares. For instance, the powers of 11, the smallest two-digit
number ending with 1, are 11, 121, 1331, and so on. This holds also for the
powers of 5 (5, 25, 125,... ) and of 6 (6, 36, 216,... ).
While maintaining that this property holds for the four distinguished
numbers (and for no other number), only with respect to the first three of
them Ibn-Ezra states it in detail. Regarding the fourth one, the idea is that
powers of 10 (10, 100, 1000,... ), like those of any number ending with
0, always end with 0. However, Ibn-Ezra doesn’t admit here a name or a
symbol for zero, and we shall return to this point later on.
We turn now to properties signalizing each of the four numbers sepa-
rately. Easiest to handle is Ibn-Ezra’s one-sentence reference to the num-
ber 6.
וחשבון ששה הוא חשבון שוה בחלקיו, ואין בכל מערכת
מספר שוה רק אחד.[And the sum 6 is an equal sum in its parts, and in the whole system
there is no equal number but one.]^8That is, in the system of numbers from 1 to 9 (the one-digit numbers), the
number 6 is the only one that is equal to the sum of its factors (6 = 1•2•3
= 1+2+3).
Next we turn to the number 1, the most magnificent and most powerful
number—the origin and building block of all numbers, Ibn-Ezra tells us.
And then he provides three specific properties of the number 1, the last
two of them tying it to the remaining two notable numbers—5 and 10.