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‘ARITHMETIC
PRODUCTIVE SYSTEM.

ON THE

ACCOMPANIED BY A

KEY AND CUBICAL BLOCKS.

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BY ROSWELL C. SMITH, A M.,

ADTHOR OF PRACTICAL AND MENTAL ARITHMETIC; THE PRODUCTIVE GRAV

MAR; THE PRODUCTIVE GEOGRAPHY, ETC.

STEREOTYPE EDITION.

PHILADELPHIA:
J. B. LIPPINCOTT & CO.

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HARVARD COLLEGS LIBRARY

BY EXCHANGE
FEB 12 1932

Adopted by the BROTHERS of the Christian Schools in the Uni: TED STATES.

“IT IS NOT EASY TO DEVISE A CURE FOR SUCH A STATE OF IJINGS, (THE DECLINING TASTE FOR SCIENCE :) BUT THE MOST OBVIOUS REMEDY IS TO PRO

VIDE THE EDUCATED OLASSES WITH A SERIES OF WORKS ON POPULAR AND

PRACTICAL SCIENCES, FREED FROM MATHEMATICAL SYMBOLS AND TECHNICAL TERMS, WRITTEN IN SIMPLE AND PERSPICUOUS LANGUAGE, AND ILLUSTRATED BY FACTS AND EXPERIMENTS WHICH ARE LEVEL TO THE CAPACITY OF ORDINARY MINDS."

QUARTERLY REVIEW.

"THE FIRST THING TO BE REQUIRED IN A SYSTEM OF POPULAR INSTRUO TION, IS, THAT IT SHOULD BE INTELLIGIBLE; THAT CHILDREN AND YOUTH BHOULD UNDERSTAND WHAT THEY LEARN. UNDERSTAND WHAT THEY LEARN IT MAY BE ASKED; WHAT ELSE CAN THEY DO? WE ANSWER, THAT THEY MAY COMMIT IT TO MEMORY, MAY REQITE IT, MAY EVEN MAKE A FAIR SHOW OF KNOWLEDGE AND YET KNOW NOTHING. WE HAVE NOT THE LEAST HESITATION IN SAYING, THAT TWO OR THREE YEARS, IN THE EDUCATION OF ALMOST EVERY INDIVIDUAL IN THIS COUNTRY, HAVE EEEN THROWN AWAY UPON STUDYING WHAT THEY DID NOT UNDERSTAND."

NORTH AMERICAN REVIEW

Entered according to Act of Congress, in the year 184),

BY JOHN PAINE,
in Who Clerk's Office of the District Court of Connecticut.

ARITHMETIC:

PART FIRST:

BEING A MENTALS COURSE FOR EVERY CLASS OF LEARNERS.

NUMERATION.'

D Recite by the Questions. 1. 1. Number, which shows how many are meant, is represerted' by letters, by words, and by characters called figures, as: One ....1....1] One hundred ................... 100 Two...,11...2 Two hundred ...... .......... . 200 Three...

...3 Three hundred .....CUC ..... 300 Four. ...

Four hundred ...... cccc ......... 400 Five....

Five hundred ... ... D or 157...... 500 Six...

Six hundred ....... DC or 15c ....... 600 Seven.

1... VII. . ..7 Seven hundred . . . . Dcc or 15cc ..... 700 Eight ... VIII ..8 Eight hundred . . . . . dccc or 150cc....800 Nine.... IX*...9 Nine hundred ...... dcccc or 15cccct.. 900 Ten .... ...10 One thousand ......Mor ciof...... 1000 Eleven .. XI ..11 | Two thousand...... ii or mm. ...... 2000 Twelve , , XII. . 12 Three thousand .... III Or MMM...... 3000 Thirteen . XIII . 13 Four thousand ..... TV or MMMM.... 4000 Fourteen . XIV . 14 Five thousand ..... 7 or 155 ....... 5000 Fifteen . . xv.. 15 Six thousand ...... VI or 150M ..... 6000 Sixteen . . XVI. . 16 Seven thousand .... VII or 135MM ....7000 Twenty .xx..20 Eight thousand ..... VIII or 109MMM... 8000 Thirty. , . XXX . 30 Nine thousand ...., 1X or 150MMMM ... 9000 Forty . . . XL* . 40 | Ten thousand ...... X or ccioof.... 10000 Fifty....L...50 Twenty thousand . . . XX or cciocciɔɔ. 20000 Sixty . . . LX .. 60 Fifty thousand ..... 7 or 1333 .... 50000 Seventy . Lxx. . 70 One hundred thousand. cor ccciɔɔɔ . . 100000 Eighty . . LXXX.80 Five hundred thousand. 7 or 15005.... 500000 Ninety . . XC* .90 | One million ....... Mor cccc15590.1000000 * Or, for 4; VIII for 9; xxxx for 40; LXXXx for 90; and cm for 900,

1 Every o annexed to 19 increases its value 10 times : as ro, is 500, 105 is 5000: in like manner the prefixing of c and the annexing of o to cio increases it 10 times as ciu, 1000, CCIO, 10000; lastly a line over any number increases it 1000 times: as, D, 500, D, 500000. NOTE. L. stands for the Latin language ; G for the Greek and F. for the French. I ARITHMETIC, [G. arithmétiké.) Computing, calculating or reckoning by numbers 2 MENTAL, (L. mentis.) Pertaining to the mind; intellectually. 3 NUMERATION, IL, numeratio.) Numbering; the method or act of numbering. 4 REPRESENTED, Exhibited ; described ; personated; to supply the place of. 6 CHARACTER, A mark; a stamp; a letter reputation' a personage.

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