CUTHBERT LEONARDO JOHANN CHAPTER
VI
HOW CUTHBERT AND LEONARDO AND JOHANN MULTIPLIED NUMBERS
" So you wonder how people multiplied numbers, do you ? " asked the Story- Teller, as the Crowd marched into the room, and George put another log on the fire, and the Tease stood wondering how it happened that the story was coming so easily . " Well, you see they just multiplied, and that's all." e But how did they do it ? That's the question ," said the Tease. " How could anyone multiply with the Roman numerals , or how did anyone ever learn how to multiply, anyway ? "
" When Ching was a boy no one could multiply at all," said the Story-Teller .
" I wish I could have gone to school then," said Fanny.
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NUMBER STORIES
" There were n't any schools ," said Charles.
" So much the better, " remarked the Tease.
" As I have told you , those who did not go to school had to work all day, and how would you like that ? " asked the Story- Teller.
The Crowd agreed that, after all , schools and multiplication and arithmetic were easier than digging and planting all day long, and so the Story- Teller continued :
" When Caius and Titus multiplied they did not use the Roman numerals ; they used calculi, or counters, as they did when they added numbers . This story is too long, however, so I shall only tell you about the way in which the world learned to multiply as we do. Listen then to the story of Cuthbert (kuth'bert) and Leonardo and Johann (y hän )."
When Leonardo of Pisa went to school to the Moorish teacher on the northern coast of Africa , over seven hundred years ago , and learned how to write the numerals which we now use , the first great advantage that he found was in multiplying. Some of his boy friends in Pisa were probably using counters , or calculi , for this purpose , but his old Moorish
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OF LONG AGO
schoolmaster could multiply much faster than any of them . He used the numerals that had come from the East, and so Leonardo was anxious to learn the new way.
If you have never seen a modern calculating machine, you would be interested to see how it works. You would watch the setting down of the multiplicand on certain keys , then you would see the multiplier set down , and then, on one of these modern machines , you would simply touch an electric button and the machine would make a little buzzing sound, after which you would read the answer upon it.
Some such curiosity and interest must have been Leonardo's when he first saw his old Moorish schoolmaster multiply one number of three figures by another number of three figures. With the counters this would have taken him several minutes, but his teacher did it in only one minute. Can we wonder, then , that Leonardo was anxious to learn what seemed to him to be a wonderful trick in the multiplication of numbers ?
How do you think the Moorish schoolmaster proceeded ? Of course we do not know exactly, but we know how Leonardo gave the
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