55 DE EXTRACTIONE RADICFM 



V pracfigendo feptcm radices nequationis x T -iro 

 aflignare. At fi has radices in fbrma fimpliciirima exhi- 

 bere velimus , indagare dcbemus , an ex iftis quantitati- 

 bus /"/> — 4 , qq — 4- , rr — 4 actu radix quadrata ex- 

 trahi poflit. Cum igitur fint p , q ct r valores iplius 

 u ex hac aequatione : 



if - u* — 2 u -f- 1 — o 

 ponamus V (uu — 4) ~ v , atque hic valor pracbcbit 

 valores pro V (/>/>— 4 ) ; V (^</ — 4.) ct V (rr — 4). 

 Pofito autem V (uit — 4.) ~ <y feu uu — vv~\-^ habc- 

 bimus : 



( v v -f-a ) V ( v v -+- 4 ) =: v V -f- 3 hincquc 

 c 6 -f- 7 i? 4 -4- 14 1> J -f- 7 — o. 

 Iluius acquationis ponantur (ecundum §.29 faclorci 

 i> 5 -f- p v~ -f- # v -+- r zzi o 

 v' ~- p v'- -\- qv — r — o 

 atque ad dcterminandos cocllicicntcs p,q,r prodibit ac- 

 quatio : 



<7 4 — a8# 5 -f- 5<Sq — o 

 ex qua prodit q — o , r — V — 7 , ct p — V — 7 ; 

 it.i vt i? definiatur per has aequatioues : i;' -4- q; 1 V - 7 

 -h V - 7 — o 



§. 45. F,x hac duplici aequatione fiifiiciet altcram 

 fantum refbluifTe , cum alterius radices flnt negatiuae ra- 

 dicum alterius aequafionis , atque iam fiipra figoa radica- 

 lia V (pp- 4) ; V{qq-\)\ V(rr-+) fignum habeant 

 ambiguum. Quaeramus ergo radiccs aequationis huius : 

 v - v V - 7 - V - 7 — o 



quat 



