338 AtOirSII CASINELLt 



7 = 3,7320547, 

 et idco 



x = 2,7320547 

 qui a vero diflerl mimis 0,1 000000 . 



Pro seciindo valore iucognitae y habeblraus 

 112 5 14 42 132 



4 ■ 64 ' 1 024^ 1 6384"" 2021 44 "" 41 94304^^071 08804 "^ ^'''" 

 = 0,2079453, 

 et ideo 



x = — 0,7320547 

 qui et ipse differt a vero minus 0,1 000000 . 



Eodcm calculo, quo radices aequationls x'^ — px — <jr = 

 habentur scriebus ordinatis secundum potentias coefficienlis (jr, 

 haberi quoque possunt seriebus ordinatis secundum potentias. 

 coefficientis p. 

 Posito igitur 



x=a-i-bp-^-cp'^-i~dp ^->rcp ^'i-fp ^-i-gp ^■^hp'^-\-kp ^-¥-up ^-t- etc. 

 habebimus 

 a '^-{-2al>p-i-Zacp ^~i-2adp ^-{-2aep '*-^2afp ^-^-Zagp^-i-2ahp^^-+. etc . \ 

 — ^ — a p -^b'^ p^-\~lbcp^-^'lbdp'^.^2bep^-^2bfp^-^lbgp'^ -+-elcl 



— bp'^ — cp^ -^-c"^ p*-^2cdp^-^2cep^-^2cfp'^ _(-etc.|=0. 

 — d p^ — e p^ -i-d'^p^-^-Zdep'^ -+-etc.| 

 — //jS — g p^ ^-etc./ 

 Hinc 



lab — a =0 

 2ac-|-62_-i=0 

 Zad-if-2bc—c=Q 

 2acH-2i</-4-c2— </=0 

 2af-+.23e-t-2c(/— e=0 

 2a^-t-2^/-+.2cc-|-^2__/-=o 



Zak-\-2bg^2cf-ir-2dc—g=.Q 

 2ak-i-2bfi-^-2cg-{-2d/-^c2—h=0 

 etc. etc. etc. 



Ex proma aequatione haljcmus a = ±: |/ </ . Sumpto autem. 

 o = [/ <jf invenicmus 



f 



i 



i 



