i6 METH. lyJEG FORM. DIFFEREI^T. RATIOW 



§.13. In Itic mcthcxlo tantiim ad \nicum fiLT:(ircni 

 X _j- px tanqir.uii coyiituni rclpicimiis , atqnc linc ic- 

 fpccln :id icliqiu» ficliorcs limpliccs iJctcrmin;ibimus valorcm 

 littcrAC P pro fraclionc fimplici \n:r ,—.. Pari dcinccps 

 rationc , qua \na fradio fimplcx cft inucnta rcpcricntur 

 rcliquac omncs ^^^> ^Fx c^c. quarum omnium fumma 

 acquctur formulac diffcrcntiali propofitac. Dilccrpamus igi- 

 lur formul.\m ditfcrcntiakm propofitam 



A-f- B.v-f-C.v'-^D.v'-t-E.v*- 4- ctc. 

 I -+-a.v-i- p.v'-hY-v'-i-<5.v*-f- ctc. 

 in cuius numcratorc pauciorcs incflc ponimus dimcnfioncs 

 ipfius .V quam in dcnominatorc • dilccrpamus inquam hanc 

 formulam in binas pnrtcs quarum altcra fit — 7ipi^,al- 

 tc.ius vcro dcnominator crit quotus qui rcliiltat , fi iilc dc- 

 nominator formuhc propofitac pcr i-\-px diuidatur , id 

 quoti vtiquc ficri potclt , cum i-hp.v fit fidor illius 

 dcnominatoris. Ponamus quotum cx hac diuifionc oriun- 

 dum clTc i-hOv-l-bv^-hCv^-h^.v*-!- ctc. in quo 

 ergo maximus dimcnfionum numcrus ipfius .v \nitatc dcfi- 

 cit ab illo , qucm habct in dcnominatorc primo 

 I -H a.v-f- P .v^-hV -v '-V-5 .v*-|- ctc: 



Sit igitur altcra pars practcr ^^-j. , in quam formula pro- 

 pofita rcfoluitur hacc 



91-i-^.v-hg.vM-! ^v'-i - ctc. 



I -5- v -h b v' -i- C V '-h ^v*-f- ctc . 

 \bi ob candcm ratinncm in numcratorc .v pauciorcs !ia 

 bcrc dcbtt dimcnfioncs quam in dcnominatorc. 



5- 14. 



