[ 63 ] 



Ip the given number had been 26, it muft then have been 

 refolved into 27 — i, and dividing by 27, the new binomial 



would have been i , and the terms of the feries i. 



m—i ■ ^7 , 3-27- 



, &c. when reduced to numbers would have been 



3-27 



I. ziL . ±-L . ±i_ . ±i_ . ±1L . ±L . +1Z, &c. And 



3.27 ' 3.27 * 9.27 3.27*15.27 9.27 21.27 

 of the terms of the infinite feries refulting, the firft would 

 have been affiimative, and all the reft negative, which is always 

 the cafe when the fecond term of the binomial is negative, 

 as in the follov/ing example : 



Thus, if the limits of the greater quantity be 166,7 '""^ i6^j3> ^nd the li- 

 mits of the lefs quantity be 43,2 and 43,1, then will 123,6 and 123,1 be the 

 limits of their difference. 



4. In diviCon, the greater limit of the dividend is to be divided by the lefs 

 limit of the divifor, for the greater limit of the quotient; and the lefs limit of 

 the dividend by the greater limit of the divifor, for the lefs limit of the quotient. 



Thus, if the limits of the dividend be 33,774432 and 33,7575, and the limits 

 of the divifor be 3,216 and 3,215, then will 10,506 and 10,496 be the limits 

 of the quotient. 



F'Ue Mirlfici Logarlih. Canonis ConflruBio. Edinhurg 1619; vel Lugdimi 1620. 



In the example given above 1,0123488172445 is the lefs limit of the fum of 

 Ae affirmative -terms, and 1,0123488172449 the greater limit. In like manner, 

 ,0001524932859 is the lefe limit of the fum of the negative terms, and 

 ,0001524932862 the greater limit ; therefore according to rule 3^ 1,0131963239583, 

 and 1,0121953239590, arc the lefs and greater limits of the fum of all thefe 

 terms added together according to their figns. And confequently 3,0365889718749 

 and 3,0365889718770 are the lefs an<i greater limits of the cubic root of the 

 number 28. 



of 



