296 Barnabae Torxolijni 



G3_hMG^ — (TIN-h2KL)G-i-(K2 — MN)H-hL-N=:0 (1). 

 in qua brevitatis causa ponltur 



G = A'D — AD', 1I = A'B — AB', K = B'D— BD' 

 L = A'C — AC, M = B'C — BC, N = G'D_CD'. 

 In nosiro casu, pro coefficientibus cluarum aerjuationum ha. 

 betur 



A=:1, B=— 3(j-h;). C = ?>(j^-{-z-—1jz), D=— Cr-4-2)3 

 A'=1, B'=— 3(U— ^r), C'=3(U-^-+-x'-+-7U.r), D'=_(U_.r)^ 

 unde valores G, II, . . . . facto P=U — x, Q=y-+-z, erunt 

 G = P^—q\ II = 3(P — Q), K = 3PQ(;P^ — Q-> 

 Lz= — 3fP-— Q'-)-9Ua:H-9>j] 

 M=:9[Q(P--t-9U^) _P(Q'2_9jz)} 

 N = 3[P'(Q'— 9j2) — QHP'-+-9Ua:)] 



et facta substitutione in resultanlem prodibit aequntio noni 

 gradns quoad U, et per consequens vigesimi septimi quoad 

 R . EvoUuio oinnium terminorum fit simplicior si polius ac- 

 fipianms duas aequaliones jam statutas 



• S3=j-t-i-f-3S|/'y7, S'=U — X — SSi/lJ^ 



in quibus non adest secundi termini coefficiens, ita ut pos- 

 sumus scribere 



S-^—^]/y~z.S—{y^z) = 0, S^-f-3|/U^.S_(U— x) = 

 quae comparatae cuoi duabus generalioribus 



Ao'-<-B»^-+-C«-4-D = 0, A'o''-HB'a''-HC'«-+-D' = 

 praebent 



A = 1, B — 0, C = — 3i/jz, D = — (j-t-z) 



3 



A'=1, B'=0, C'=:3i/Ux, D' = — (U— x) 

 unde resultans erit 



(A'D — AD')^-l-(C — C')(C'D — CD') = 0. 

 Ilinc ex snl«titulione oblinenms 



(1) Hacc acquatio in pliiribiis algoLrac libris referlur , ex. g. Viile 

 Lotteri Inliod. al Calcolo lom. 1. pag. 125, 12G. 



