4i CAROLI JOHA.XNIS M IT T IIE S , henr. Fit. 



Eodem modo : 



•^ {a+b'jib+cj '^ ^- ac J ' 



fjui valor hoc modo trans/oi-mari potest : 



Est X' = J' Xi{'ia+b-^cfbc'-{a-irh+c){h-^c—a){a+h){a+c)'](G-i.iovva..k.) 



at liabemiis : (^2a + b + cybc =:.ia^bc +^abc (b -\- c)-^bc{b -\-cy- 

 et (fl+6+c)(i4-c— a)(a+6;(aic)z=[(i + c)' — a==] x [a'^ -^ a (^b -{- c') -\. bc'\ 



= _a4_„3(i^f.) + a=(Z-+cf— a=6c+a(5+c)3+6c(6+c)» 

 ergo : (aa+i ■|-c)='ic — (a+6+c) f i+c — a) (ß+6) (a + c^^=a*+a^(J}-\-c) — a'^Ci+c)' 



+ 5a-bc — n(i + c)3 4- iabc{b + c) , 

 quem valorem si poi.amus S, erit : 



cui si demseiis : 



(a^. i_j_c) (a+ c — Z») (a + i) ^«3 — ^3 _|_ ,^2^ — ai^ + sa'o + ac» + bc^+iabc 



vesiduum eiit: 



S „ 



(^a+ b + c){a + c — b){a+b)= — c3 — a'^c — 2ac^ -f- bc + abc 



a 



huic iterum si abstraxeris : ir (a + 5) := 6'c + abc 



o 



restabit : \_{a+b+c)(a+c—b) + bc] x{a+b)^ — a^c — 2ac'- — c=-^ — c{a+cy 



ide erit : S -^ a^^ [^^a+b-^c){a-if-c~b)+bc'\x{a-\-b) — c(a+c)=\, quosubstituto valore, 

 [(a M- Ä + c) (a + c — b) + bc'\ (a+ b) — c(a -f c) 



[(n+ b + c)(a + b — c') +bc']{a + c) — b(a+by 



, , ,. , , Ua H-b+c){a + c—b) +bcl(a+b) — c(a-\^c)'■ 

 hahehl^ms : x^ = abc X '-^ ^^ ^ >r,-T^ -' ,, ' ^ . . . . (B) 



sive : x- = cic X 



(.a + ö)»(a + c)- 



Simililer : r^ = abc X ti--!: — ^ ' ^ , -^ ^V^ — ^^-^^^ — .... (B') 



sive- y^ _.^. M^+l>'t-c){o + b-c) + a r ]{b + c)-a{a+by 



Est 



