Al-Khwarizmi’s Mathematical Doctrines in Ibn-Ezra’s Biblical Commentary r 183Ibn-Ezra says, the number of all (different) numbers. In other words, in
the decimal system, which lies at the heart of Ibn-Ezra’s treatment of the
letters of Ehyeh and Havaiah, 9 is the largest one-digit number.^12
Now, to show the beauty of the number 9, Ibn-Ezra, in the passage we
are studying, writes as follows, right after telling us that there are nine
numbers altogether.
ואם תכתוב התשעה בעיגול ותכפול הסוף עם כל המספר
תמצא האחדים שמאלים והעשרות הדומות לאחדים
לפאת ימין. ובהגיעך אל חמשה שהוא האמצעי אז יתהפכו
המספרים להיות העשרות אחדים והאחדים עשרות.
[And if you write the nine in a circle and multiply the end by each
number you will find the ones left and the tens that are like the ones
on the right side. And when you reach five, which is the middle one,
then the numbers will capsize so that the tens become ones and the
ones tens.]The circle drawn below, with the numbers from 1 to 9, shows what Ibn-
Ezra has in mind here. And we note that to many people nowadays this
is a well-known game.
At the top of the circle we have the number 9 (9 multiplied by 1). Below
it we have from left to right the number 18 (9 times 2). In the third line
we find the number 27 (9 times 3). This is followed by 36 (9 times 4) and
then by 45 (9 times 5). So far we have gone from top to bottom, and we
have had tens on the left and units on the right. But now we have reached
multiplication by 5 at the very bottom of the circle. So we’ll turn around
and start climbing up. And from this point onward we’ll read from right
to left, so that tens will be on the right and units on the left. In the bottom
line we’ll find the number 54 (9 times 6). Above it we have 63 (9 times 7).
Further up we get 72 (9 times 8) and finally 81 (9 times 9).
We note that the position principle once again plays a central role here.