134 ^^ PARTITIONE 



acqualis fiat idi cxprcfTioni : 



s:=:{ I -\-xz\ I -+-.r's)( i -+-.v'ir )(i -4-A*i:)(i ^-a';;) etc. 

 Hiinc in finem i^itur pcrptndendus c(l ncxiis , qui inter 

 has diuis cxprefTuMies intcrccdit , ct qucm ad modum altera 

 immutari dcbcat , h in nltcra mntntio indituntur. 



§. 13. Qiii.i vtriusc]uc expreirionis idcm eft valor/, 

 ambae inter fe mancbunt acquales , fi in vtraquc loco si 

 lcribatur quaccunquc alia qu:»ntitns. Ponamus igitur in vtnique 

 xz loco x:,etva!orvtrinquc rc(iiitnns vocctumf,eritqucprimo: 

 t—i -+-Axz-\-Bx' z" ^f- Cx'z' -f- D.v* z*-^ etc. 

 tum vero altera exprelfio transmutabitur in hanc : 

 /— (i -^x'z){i-{-x'z){i-^x*z){i-\-x*z) etc. 

 qui pofterior ipfius / valor , fi cum pofieriorc valorc ipfiuj 

 j comparctur , quo ernt : 



j— (i-+-.v2)(i -f-A-'c)(i-t-.v'5:)(H-A-*2) etc. 

 mox patebit c(re s-z: {i -\-xz)t. Qiiac rclatio cum ctiam 

 in altcris valoribus ip(arum i ct / locum habcrc debeat , 

 nobis praebebit hanc acquationem : 



j — I -f- Ag H-Bg' -i-Cs' -4-D~* -+-ctc. 

 ( I -\-xz) t ~i -f-AA:s-f-BA-'s'-|-Cv^c'H-l;A*3* -t- ccc. 

 -H xz-\- k a'x:'-h Bx'c ' -f - C.v*s* -h ctc. 

 Vndc tcrminis homogcncii iuter Ic acquandis , flct : 



A— _i_ 



Tl- Afl £! 



" — ,-Jt» — (._*)(, _i«) 



i« 



(,— *X'— '»X' 



^ Bi» ij 



, '0 



^ CX* A^-^ 



*" — ^-** — (.—*X'—*'Xi—*'X. —*♦/-*♦) 



ctc. 



§ H' 



