— 352 — 

 La terza specie di soluzioni, pel caso che stiamo lisolvendo , conterra 



) '.^ li =■ 1G soluzioni diverse, ciascuna con k — 3 •= 1 fattore 



1.2.3 



comune con la ^ , e saranno quelle che sieguono 



Xi = 

 •vj" = 



.vj'^- = 



X3'' = 

 •Vj'" = 



.vj^- = 

 a:3'" = 



A-3XU = 

 X3XHI= 



(a I '-»-/) 1 

 [ai'-hbt 



[a^-i-b; 



. (rt3'H-)&3' 



. (a3'-t-63' 

 = [ait'+bi 



;'— 63') [ («,"— i&i')(a,^ — 62') — ita.ajiib. ■i—Uaibz{aia3—bib^)(a^bz-haJ},) 

 ;«,," — j&,^') [ (a,' — /i,')(«a' — i6/) — Ita^a^bibj. ] — 4a4i&4(aia, — h^b,){a,b^-^a.J),) 

 'a^^—bC) [ (a/— i&/)(a3'— /»3°)— 4a3&3a=62 ']—l^a!fi!,[a^ai—hJ}^)[aJ)i-^aJ}^) 

 [aC — 64') C («," — /'i''](a3'' — 63")— 403630,6, ]— /ia464(«,a3— 6,63)(a,63-Ha3Ai) 

 (a-= — 6-=) [ (a,' — b,'){a.^ — 62'') — 4a,6ia>;, ]-+-4a464(aia2 — bj):,){aj)^-^aj)^) 

 (a4' — 64") [ (rt/ — 6/)(a3*— 63'')--Aa363aA '\-^ha!fii^[ajty-^bJii){aJbi-^a!,b^) 

 (04' — 64^) [ (o." — 6i'')(a3'' — bi'')—liaibzaibi ]-t-4a4A4(a,a3 — bfi.^[aj).\-^aib) 

 (03^—63^) [ (a,^— 6,^)(a2^ — 6/) — ha,b,aj)^ :\-h!taihi(a,az—bJ)^){a,b.,+a^h,) 

 (a4'— 6,,=) [ (as""— 63'')(a.^— 6i')+4a363a.6, ]— 4ff464(aia3-t-6.63)(ai'&j— i&.«t) 

 Ki'— 64') [ (fl/— fr/)(«'3— &3')-t-'4a3^3a:='&2 ']—^a!^bi(a,a3+-b^b3){a^bi—a3b,)' 

 («,= — {,4") [ («,' — 6.'')(a3^ — 63=)+4rtj6ja,6i ]+4a464(a,a3-t-6,i,i)(a,63 — 6, a.) 

 (a4-_64') [ (a/— 62=')(a3=— 63')-f-4a,i63a26a :i-h^a;M{a2a3-hb:,b^)(a^bi—ajb,) 

 (ui'—bf) [ (o,^ — 6.=)(a/ — 6/)-l-4a,a2&.6j 3—40363 (atau-^bib:,){aib^ — 0261) 

 (04^—64') [(0i'—6i'')(a/—62')+4a.a,6.6,]— 40464(0,0,+ 6,62)(ai6.—rt26') 

 (a4=_64=) [ (o,'— 6,')(o/— 6/)-t-4ai026,62]-)- 40464(010,-+- b,b.)(aib, — O26,) 

 — 63') [ (0/ — 6i')(a/ — 6/)-l-4o.a26i62 ]-4-4a363(oi02+6i62)(o.62 — 0261) 



