Positive and Negative Quantities. 7 



or his capital suffered a diminution of $200. If his original 

 capital was $1,000, then the first transaction increased it to 

 $1,500, and the second transaction diminished it to $800. Thus 

 an addition of $500 followed by a diminution of $700 is equivalent 

 to a single diminution of $200, or 



$i,ooo4-$5oo— $700= $1,000— $200. 



Hence $^00— $-] 00 whe7i joined to $1,000 may be replaced by 

 — $200 joijied to $1,000. 



Now, as any other original capital would have answered as well 

 as $1,000, we may neglect that original capital and write 

 $500— $700= —$200. 



Thus we see, by this illustration, that it is fiatural to prefix the 

 minus sign to the $200 to indicate a resultant loss of $200. 



13. We might have used an illustration involving some other 

 kind of quantity than money, as time, distajice, etc., and have ob- 

 tained an equation similar to the one just written. We may then 

 make an abstraction of the $ sign and write simply 



500— 700= — 200. 



14. In Arithemetic we are concerned only with the quantities 



o, I, 2, 3, 4, etc., 

 and intermediate quantities, but in Algebra we consider besides 



these the quantities 



o, —I, —2, —3, —4, etc., 

 and intermediate quantities. 



15. We may represent these two classes of quantities on the 

 following scale, 



—5.-4, —3. —2, —I, o, I, 2, 3, 4, 5, 



which extends indefinitely in both directions from zero. 



The sign -f perhaps ought to precede each of the quantities at 

 the right of o in this scale, but when no sign is written before a 

 quantity the -f sign is always understood. 



16. Quantities to the right of o in the above scale are positive 

 and those to the left of o are 7iegative, or we might say Arabic 

 numerals preceded by a + sign or by no sign at all are positive 

 quantities, and Arabic numerals preceded by a — sign are 7iegative 

 quantities. 



