^An Account 
Comrnmg the Refolution Equations in Numbers^^ im- 
fdrted by Mr. lohri Collins. 
This Account fliould have been annex'd to ivhat was dif» 
courfed ofMonfieur Skfius \\\$ Mejolak in the precedent Tradlj, 
if then we had found room for it. For, the Reader having 
there tinderftood , how farr the Gemctrick part of Algelpra is 
sdvanc'd by that excellent perfon? 'twas likely ^ he would 
be inquifitive to hear fomewhat concerning the Excgefis iVj- 
msrofA^ or the Refokitionof jEquatiooi in m mhers. For 
whofe fatisfadion herein , we lhall here inferc t he Accotmt 
then omitted , being part of a narrative/ formerly made by M, 
lohn Collins touching fome late Improvements of Algeqra in 
England^ upon the occafion of its being alledged ^ that none 
at all were made fince Des Carm. 
t. It hath becn oMcrVd by divers of this Nation , that 
in any iEquation, howfoever affefted, if you give a Root 
and find the Abfolute number or Refolvend (which calls 
Bomogeneum Comfaramnis) and again give more Roots and find 
^ore Refolvends , that if thefe Roots or rather rank of Roots 
be affum\i in ^ri>*i»e^/V4/ progrcffion j the Refolvends ^ as 
to their firft, fecond orthird differences, &c. imitate the Laws 
©f the pure Powers of an Arithmetical progreflion of the fame 
degree 5 that the higeft Power orfirft term^ofthe Equation is 
of. e. g. In this Equation aaa— 3 aa-f- 4 a^^' 
10 rXhen N. or th^] 740 
If 4 be — -9 1 Abfolutes or Re- {,522 
^^folvends will be ^ 
\ found to be l^^ j" 
ai8 
170 
128 
92 
48 
4i 
3^ 
6} 
To wit the 3d. differences of thofc Ahfvktcs m equal^asj 
in the Cubes of an Arithmetical Progreflion. 
'i. To find , what habitude thofe differences have to theC^?- 
ef^cient ^ of the Equation, 'istbeft to begin from an Unit, 
3, In^any Arithmetical Progreflion 5 it you multiply Numi» 
Pppp V ber* 
