Sopra i Logaritmi. 201 



(cof.f + ren. ?/-i) = log./'— log. -—^ ;- 



4-Iog. (cof. ^-j-fen.f/ — I ) = log. (/^'-f-^')* -|- log. 



( cof. r -\- fen. 9 \/ — 1 ) r= log. (p' -\-']^ )* + ♦ y/ — i . 



Da tali Teoremi in si poche linee dimoftrati coli' or- 

 dinario calcolo finito riefce ora faciliffimo 1' inferire il 

 famofo Teorema del^ Sig. D' Alembert 



m + Hy' — I 

 (P -\- ^ V " nr: P -{- 'iiy — I . Imperciocché 



effendofi trovato log. (/> -|- -7 / — i) = log. (/''H-^')'^' 

 "4~?l/ — ^» pofto <j> per r arco fopra indicato, ne de- 



m-\-n \' — I 

 riva log. (/' + ^V^ — i) z=:^ {m -\- n \/ — i) 



log- (? + -7 /— O = ( m-\-n\l— 1 ) log. {p' + q' y-' 



m . 



+ (?M+Wy/— I )<Pi/— l=:Iog. (/^'-j-^^j^-f- 

 T^V— 1 , 



log. (/>'-{- ^') -\-n}<p\/ — I — ntp . Ma abbia- 



mo dimoftrato 5 z^cof.fA: log. B)~{-k n.(x Ica. 5 ) 



Y/— I , e però (p'^q') — 



cof. (^ « log. (/'^ + ^^)) + fen. (~ n log. {p^ + q^)) \J — i -, 



dunque foflituito quefto valore , nafcerà 



m-\-n\J — I m 



%-(/' + 9V — =Iog. ('/'^4-9^) 2 



►flog. Tcof. (- «log. (/'^-f/'')) +fen. (--«log.O^+<j»')) 



V — ^ j + ^^^V — I — «(p ; e paffando dai logaritmi ai 



, m + n\'— 1 



numeri proviene (p-j-qy — i) 



Ce 



