Rem. 3^ — -a^if +6^ — -9<: +i6^* 



Rem. ~i6^^ * —6d^ — 2a;" 



10. II. 12. 



From — i2A?v 5^7;^* 5<i*+3^Ar+i4 



Take —12x7 2^.v*-f-4 «*-t.2^;v — »io 



Rem. *. 3^^'^ — 4* 4^*+ ^Ar+24 



13' 



* The ten foregoing examples of simple quantities being obvi* 

 ous, we pass by them ; but shall illustrate the eleventh example, 

 in order to the ready understanding of those, which follow. In 

 the eleventh example, the compound quantity 2^^* -{-4 being tak- 

 en from the simple q\iantity 5^*;^, the remainder is "^ax^ — 4, and 

 it is plain, that the more there is taken from any number or quan- 

 tity, the less v/ill be left ; and the less there is takep, the move 

 will be left. Now, if only lax"^ were taken from Sax'^^ the re- 

 mainder would be 3^7x* ; and consequently, if 2ax^-{-/^, which 

 is greater than zax^ by 4, be taken from 5^ai*, the remainder 

 will be les3 than ^ax^ by 4, that is, there ^yill remain ^ax^ — 4, 

 as above. For by changing the sign of the quantity 2<7."c*-{-4, 

 and adding it to ^ax'^^ the sum is ^ax^—2ax^ — 4 ; but here the 

 term — tax"^ destroys so much of ^ax^ as is equal to itself, and 

 so 5flx* — 2^^* — 4 becomes equal to 3ax*— -4, by the general rule 

 for subtraction. 



