OF QUANTITY AXD NUMBER. 3 



Scholium. AH quantities may, in practice, be considered as 

 commensurable, since all quantities are expressible by numbers, 

 either accurately, or witli an error less than any assignable quantity. 



11. Definition. Multiplication is the adding toge- 

 ther so many numbers equal to the multiplicand as there 

 are units in the multipher, into one sum, called the pro- 

 duct 



Scholium. Multiplication is expressed by an oblique cross, by a 

 point, or by simple apposition; axbzza.bzzab. 



12. Definition. Division is the subtraction of a 

 number ifrom another as often as it is contained in it ; or 

 the finding of that quotient, which, when multiplied by a 

 given divisor, produces a given dividend. 



Scholium. Division is denoted by placing- the dividend before the 

 sij^n -7- or : , and the divisor after it ; as a-~-hzz.a \ b. 



13. Axiom. When no difference can be shown or 

 imagined between two quantities, they are equal. 



14. Axiom. Quantities, equal to the same quantity, 

 are equal to each other. 



If azzb and czz5, then azuc. 



15. Axiom. If to equal quantities equal quantities 

 be added, the wholes will be equal. 



If flzzj, then a-\-c:zzb-\-c; if a — &zzc, then adding 6, azz&-f-c ; if 

 a-\-b — czzd, then adding c, a-j-bzzc-^d. 



IG. Axiom. If from equal quantities equal quantities 

 be subtracted, the remainders will be equal. 

 If az:6, a — 0=6 — c, if a-|-&z:&-}-c, azzc. 



17. Axiom. If equal quantities be multiplied by equal 

 numbers, the products will be equal. 



If azzb, 3«=i36 ; if azzb : 3, 3ar=& ; and if amb, ca—cb. 



18. Axiom. If equal quantities be divided by equal 

 numbers, the quotients will be equal. 



If 5anl06, azz2b; and if cazzcb, ai::b. 



B 2 



