230 THE POPULAR SCIENCE MONTHLY 



" Book of the Abacus," while " Algorithmus Linealis " was applied to 

 numerous works explaining the reckoning on lines which was a slight 

 variation of the abacus idea. 



The beautifully printed Calandri arithmetic of 1491, the first in 

 De Morgan's list, differs from its predecessors in having the traditional 

 problems co]3iously illustrated. The slow-moving snail, who climbs up 

 by day one seventh of a foot and slides back by night one ninth of a 

 foot, is seen here with his head just emerging from the fifty-foot well 

 and looking remarkably active after a climb of 1,575 days. The title 

 page presents Pythagoras as " Pictagoras arithmetice introductor," the 

 wholly erroneous but wide-spread notion being that this philosopher was 

 the originator of the science of numbers. 



Of the eight or ten arithmetics (two being parts of compendiums) 

 given by this catalogue as preceding Philippi Calandri's treatise the 

 three following are of general interest. " Prosdocimi de beldamandes 

 algorismi tractatus " (Padua, 1483) contains probably the first refer- 

 ence to a slate ; Pietro Borghi, one of these successful text-book writers, 

 wrote the most elaborate of the early books on the subject and more 

 than any other set a standard for the arithmetics of the succeeding cen- 

 tury. This text-book for the use of merchants, written in Italian, 

 appeared at Venice in 1484 from the press of Eatdolt. Widman's 

 German text of 1489 employs for the first time the -f- and — signs, 

 but simply as warehouse symbols of excess or deficiency. 



One of the rarest of the catalogued treasures is the " Arithmetica " 

 or "Compendium of the Abacus" (Turin, 1492) of Francesco Pellos 

 (Pellizzati). It appears that this native of Nice came very near to 

 the invention of decimal fractions, writing almost a hundred years 

 before the first complete explanation of the subject in " La Disme " 

 or " The Decimal " by Simon Stevin the Hollander. Pellos actually 

 used a decimal point to indicate division by such numbers as 100, but 

 its full significance did not dawn on him. 



The first printed discussion of arithmetic in the English language 

 is a chapter of Caxton's " The Mirrour of the World or Thymage of the 

 same" (London, 1480) ; the section begins "And after that of Arsme- 

 trike and whereof it proceedeth." An interesting sidelight is thrown 

 on early American history by the announcement of the discovery in 

 Madrid of the first arithmetic printed in the western hemisphere. 

 Extensive printing was done in Mexico in the second half of the six- 

 teenth century, and it was here that Juan Diaz Freyle published in 

 1556 the Spanish " Compendium . . . with Certain Eules of Arithmetic." 



Of necessity many works apparently unrelated to arithmetic are 

 introduced. The fine distinctions between the sciences did not then 

 exist, so that an astronomer, a geometer, a philosopher or a writer on 

 the Church calendar would not hesitate to bring into his subject a dis- 



