HISTORY OF ALGEBRA. 169 



factors together, and call the excess above 10, tens. Multiply together 

 the two differences of the factors from 10, and add the product to the 

 former number. For example, to multiply 8 by 7, add to 50 the product 

 of 2 into 3. 



II. To multiply units into numbers between units and 20 ; add the 

 two factors together, call the difference of the sum from 10, tens. From 

 this result, subtract the product of the difference of the simple number 

 from 10 and of the compound number from jo. For example, to mul- 

 tiply 8 by 14.. Subtract from 120, the product of 2 into 4. 



III. To multiply together numbers between 10 and 20 ; add the units 

 of one factor to the other factor and call the sum tens: add to this the 

 product of the units into the units. For example to multiply 12 into 13, 

 add 6 to 150. 



IV. To multiply numbers between 10 and 20 into compound num- 

 bers between 20 and 100 ; multiply the units of the smaller by the tens of 

 the greater, add the product to the greater number and call the sum tens. 

 Add to it the product of the units in both numbers. For example, to 

 multiply 12 into 26, add 4 to 26 and call 30, tens. Finish the operation, 

 it is 312. 



V. To multiply numbers between 20 and 100, where the digits in the 

 place of tens are the same ; add the units of one factor to the other and 

 multiply the sum by the tens, call the product tens, and add to it the 

 product of the units multiplied by the units. For example, to multiply 

 23 by 25, multiply 28 by two. Call the product 5.6 tens, finish the 

 operation ; 575 is obtained. 



T * 



