jfyfifcellanea Curiofa. 1 87 



f orients of the Letters which compofe ^em Jhall 

 always be the fame with the Index of that Power. 

 Now this is the Method I ufe to find eafily 

 all the Produ&s belonging to the fame Pow- 

 er of Let m -\-r be the Index of that 

 Power, I confider that the Sum of the Ex- 

 ponents of the Letters which compofe thefe 

 Produ&s mull exceed by one thofe which be- 

 long to ni^\~?~~}^ now becaufe the Excefs of 

 the Exponent of the Letter b above the Ex- 

 ponent of the Letter a, is one, it follows 

 that if each of the Products belonging to 



^fe r T"i is multiplied by b, and divided by a, 

 you will have Produ&s the Sum of whofe Ex- 

 ponents will be m + r j Likewife the Sum of 

 the Exponents of the Letters which com- 

 pofe the Products belonging to z, m ~\~ r exceeds 

 by two the Sum of the Exponents of the 

 Letters which compofe the Produ&s belong- 

 ing to ^+ r *~ 2 ; Now becaufe the Exponent 

 of the Letter a is lefs by two than the Ex- 

 ponent of the Letter c, it follows, that if 

 each Product belonging to z, m ~\' r -^ 2 i s multi- 

 plied by c and divided by a, you will have 

 other Produ&s, the Sum of whofe Exponents 

 is ftill m-Yr\ Now if all the Products be- 

 longing to ^ WI "t" r — ' 2 were multiplied by c and 

 divided by a, you would have fome Produ&s 

 that would be the fame as fome of thofe 

 found before, therefore you mult except out 

 of 'em thofe that I have call'd Products of 

 the firft CUffs^ what I have faid Ihows why 

 all the Products belonging to ex- 

 cept thofe of the firft and fecond CUffs mult 



be 



