hers by fairs i you (hall create a rank of Numbers .whofe 
differences are equal and if by ternaries, then the 3< differen- 
ces of thofe Produfls fliall be equal. And how to find the 
greateft Produdi of an Arithmetical Progreflionof any number 
of terms having any common difference aflign'd , contained in 
any Numberpropofed, isfliew'd by PalcaHn his Tn£t Tri- 
angle Arithmetiquey where he apply's it to the Extradicn of 
the Roots of fimple powers. 
4. It appears, How this rank may be caried cafily by Ad- 
dition , till you have a Refolvend either eqiiall or greater or leffe^ 
than that propofed, .vjmoi irM / 
5. When you have a ii^^j»; and AfiW, you may interpole 
"iSs many more term es. in the fArithmietical Progreffion as yon 
#ill 5 that is to fay , Subdivide the Common difference in the 
Arithmetical Progreffioa, andrenderitleffej and then renew , \ 
and find the Refol vends, which are eafily obtained out of the i 
Powers and their Coefficients , which are fiippoCd knowne, and 
may bereadily raif d from^ ia l/Skoi^njArts a^dGn^^jrjBcc. with 
which kind the meader may be furjiimc id Gddivi iCt^trobaryca 
and Bahingtons Firemi^ks ^By.this' means you may obtatndivcrs 
Figures of the Rootj and then the General Method oi Ficta ^ 
and Hdrriot tuns away more eafily 5' and. is foifar.improv'd^ 
that aft^r arqf Bgute is. plaffd iS) thd^BLoot , ..mofticertain Gbar 
rafters are given to fenow by aide 6f the fubfequent Dividend \ 
and Divijor ^ Whether the figure before affum'd be too great I 
or too fmall : or laftly it may well be concluded, that, as inXo- 
garithmes, when you propofe fiich an one as is not abfolutely 
given in the Canon^ you doe by Proportional Work , ufing the 
aid of their firft differences (when their Abfolute Numbers dif- 
fer by t^;?/>)findthe abfolute Number true to. 5. or 6. places 
further than the C^;?^;^ gives it (the reafon whereof is, that the 
firft Differences doe likewife agree ta about the fame Number 
©f places 5) that I fay, the like may be done ia^ex^quations, af- 
ter divers of the firffi figures of the root are found 5 provided 
there be th^ like agreement in the firft differences of the inter- 
poled Refol vends. 
Moreover we ought hereto take notice ofa more fubtile kind 
of Interpolation;^ common to all gradual Ranks or Progreflions 
©f Numbers^ wherein Differences happen to be equal : Of which 
kind . 
