POLYGOXORVM RECTILINEORVM. 105 



Simili riUionc ob 



flcof. A -f- Z^ coH ( A -f B) 4- rcof ( A + B-f- C)+^= o 

 ^cor.C-H«cor.(B+C)+^cor,(A-fB-i-C)+<;— o 



miilriplicata priori aequatione pcr d ^ pofleriori per 



c et fiimta difftrentia conlcquemiir 



adco[.^-bccolQ^bdco(.{k-{-B)-ac<:o{'{l^-\-C)-^dd'Cc-o. 

 Ex priori fit ficla euolutionc tcrminorum fin. (A + B), 

 fin. (B + C) : 

 {ad-bc^[bd-acyoi3ySv\ A+fin.C)+i [ad-^bcMhd+acYoL Byfin . A.-fin.C > zz 

 + Ufl'z>-dr^) fin. E (cof. A +cor. C)- ^JZ^ + ^fXcol. C -^cor. A)z: o 

 fiue 



L (fl^-^^-l-(^^/-^f)cof.B)fin,|(A + C)cor.,'(A-C) 

 + («^ + /?£-+(^^+flir)cof.B)cof i(A+C)fin.^(A-C) 

 + (6^-tff)fin.Bcor.UA + C)cof^(A-C) 

 -(^^ + ^i-)fin.i(A+C)fin.ifA-C) — o. 



Ex pofieriori autcm euolutis tcrminis cof. (B + A), 



cof. (B-j-C) confequcmur 



IL (^^/-^<r + (^^~^t:)cor.B)cof.KA + C)cor.,'(A-q 



-(^r/-f ^(.' + (Z;^+flf,cor.B)fin.^A+C)fin.^A~C) 



~(rf'^-a^)fin.Bfin.:(A+C)cor.^(A-C)-(Z'^/-itff;fin.Bcof^:A+C)fin.:(A-C) 



-i~dd— cc— o. 

 Fadis vero ifiis combinationibus 



L fin. ■ (A + C) H- II cof ^A -f- C) ^ • ■ 



l. cof. I (A + C) - IL fin. i (A -j- C) 

 ad fcquentes pertingemus aequationes : 



{ad-bc-yjjd-ac) co(. I^) cof. \ ( A -C) - {b d^ ac) fin. E. fi n i (A - C) 



-^Cdd—cc^coi.l-iA-^Oj—o 

 (ad-{-h + ',b'd+ <rf)cof B)fin !(A-C)+ (^^/-«^ ) fia Bcof.^fA-C) 



-1- (<; t' - (/^) fi n. ^ ( A -f- C) z= o. 

 Lx 



