OF LONG AGO
About three hundred years ago there went to school in Japan a boy named Seki (s k ), whose teacher had recently learned about an improvement which the Japanese had made on the Chinese abacus.
So Seki learned how to compute on the soroban (so'ro bän'), which is the Japanese form
JAPANESE ABACUS
Japanese abacus, or soroban. This instrument is used everywhere in Japan to-day ofthe suan pan of China, and this instrument is used everywhere in Japan to-day.
Seki grew up and became the greatest mathematician of Japan, and his name is known everywhere in that country and is also familiar to many mathematical scholars in other parts ofthe world.
Many Japanese can add and subtract more rapidly with the soroban than we can with pencil and paper.
NUMBER STORIES
About four hundred years ago there was born in England a boy named Robert Record (rek'ord). When he went to school he was taught to use the Roman numerals, and he added, subtracted, multiplied, and divided numbers very much as Caius had learned to
Ten thousands
Five thousands
Thousands
Five hundreds
Hundreds
Fifties
Tens
Fives
Units
PLAN OF A COMPUTING 1ABLE
This plan shows the arrangement of lines on the kind of computing table used in most parts of Europe in the Middle Ages. It was still extensively used when Columbus made his voyages to America
do when he computed with the aid of calculi about fifteen hundred years earlier.
Two important changes, however, had been made in that length of time. Instead of having places on the computing table for only units, tens, hundreds, and so on, the spaces between the lines were used for fives, fifties, five
OF LONG AGO
hundreds, and similarly for all other fives, and the lines were now horizontal. We do not know when these changes were made, but they came in what are called the Dark Ages. Because Robert cast the calculi down on the board, he spoke of " casting an account," and
HOW ROBERT WROTE 1922 WITH COUNTERS
This shows how Robert Record represented MDCCCCXXII, or 1922, by counters. We sometimes see the number written MCMXXII, but this is not the old way of writing it. The cross was always placed on the 1000's line so as to aid the eye in reading the number. It finally suggested the use of the comma in writing a number like 47,256
this expression is sometimes used to-day. The board on which he counted was generally called a counter." We buy goods over the counter to-day, not thinking what the word originally meant. Robert also called the calculi counters," and if you have read Shakespeare you may have seen the expression " a counter
NUMBER STORIES ADDITION. Mater.
heeasiestway in this arte,is to arte but two fummes at ones togfther: howbeit, you maye abde mo e,as Iwil tel you anone . therefore whenne you wylic adde two fummes,you hall fyifte let downe oncof them,it forceth notwhiche, andthen by itd aw alyne cro e the otherlymes,And afterwarde fette dounetheotherfumme , fo thatthat lyne maye bebetwent them:as ifyou woulde adde 2659 to 8342 , you mustletyourfûmes asyou leè verc.
And then if you Ipft, youmaye adde the one tothe other inthefame place, or els you may adde thin bothsrohither.in a.ucw place:which way,bycau eitis mostplyuc
This page from Robert Record's " Ground of Artes" was printed nearly four hundred years ago
caster," meaning a man who could calculate only with counters and not with pencil and paper as we do. We sometimes use counters to-day in keeping the score in games.
PAGE FROM ROBERT RECORD'S BOOK 3