2Z AUITIIMETIC, 



2. Begin at the right hand, and multiply the whole mul- 

 tiplicand severally by each figure in the m\iltipiier, setting, 

 down the first figure of every line directly un^er the Eg- 



ure 



tens ; the pro4uct roast hz ten times its simple value ; and therC:^ 

 fore the first figare of this product must be placed in the place 

 of tens ; or, which is the same thing, directly under the fig- 

 ure we are multiplying by. And proceeding in this manner sepa- 

 rately with all the figures of the multiplier, it is evident that we 

 shall multiply all the parts of tlie miiltiphcand by all the parts of 

 the multiplier ; or the whole of the multiplicand by the whole of 

 the multiplier ; therefore these several products being added to- 

 gether will be eq^al to the whole required prodoct. Q^E. D, 



The reason of the method of proof depends upon this propoe 

 sition, " that if two numbers are to be multipUed together, either 

 of them may be made the multiplier, or the multiplicand, and 

 the product will be the same.*' A small attention to the nature 

 of numbers will make this truth evident : for 3X7=^2irr7X3 i 

 and in general 3 X 4 X 5 X 6, &c. =4 XSX6xSi &c. without any 

 regard to the order of tlje tern^ : and this is true of any number 

 of factors v/hatever. 



The following examples arc subjoiaed to make the reas(>n of 

 she rule appe-ar as ylzisi. as possible. 



(I) ' (2) 



375^5 I3754.3X 



5 4567 



» ^ 



25 zr S"^^ 9628045; = 7. tiiEcstUcinul* 



30 = 60X5 8252610* = 6otimcs dp. 



7,5 = 500X5 ^^^'17^75 = 500''imes dcr. 



35 nr 7000X5 5501740 =4000 times da. 



15 = 50000X5 



187825 = 37565X5 



628x611545 ~ 4567 tuiic* do. 



Beside die preceding method of proof, th.ere is> another very 

 convenient and easy one by the help of that peculiar property 

 of the number 9, mentioned in addition ; which is performed thus :, 



RVLE 



