io3 



ex parte sinista piodibit {y. -f- j) (|3 -f- i) (y -\- \) , at 

 ve ro ex parte d e x Lra a [3 + a y -I- 13 y -f- 2 (a --j- (3 -^ y ) + 3, 

 quac formula manilcsto resolvitiir in lias partes : 



(a -I- i) (^3 -I- 1) -f- (a -4- J) (v 4- l) + (Ï3 -H 1) (y + 1). 

 Hac igitar forma siibstituta , dividaLur utrinque par pro- 

 ductum (a+ 1) (j3 -f- 1) (y -j- 1) , ac prodibit 



^ = .--TT -+- .3^7 + ^- • a . E . D. 



5. j3. Ilinc quoque deriv^ari potest ista mcmorabilis 

 proprietas: ^-7 + ^33^- -f- ,^r^ :=: 2. Si enim huic adda- 

 \x\x praecedens aequatio , orietur , ista aequatio identica : 

 1 + 1 + 1 z= 3. 



D e m n s t }• a t i o s i m p 1 1 c i s s inn a. 



E"! e m e n t i s v u 1 £; a r i b 11 s i n n i x a . 



§. J4. Per ptinctum O singalis trianguli lateribus Tab. L 

 paralKLie ducantiir /<^ ipsi BC, g-/] ipsi AC et h$ ipsi S" ** 

 AB, et statim evidens est fore rl-f- "^^ -f- "^- ni 1. Nunc 



A i> Ad a -J 



vero ob triangala ABa et A/O similia erit 



Bf : BA — Oa : A a , 

 sicqne prima fraclio evadit ^^ = g{. Dcinde , quia 

 A^5-\5 .\3 ABv^O, erit A>):ABr:i06:B6, unde ergo fit 

 -^-|r:^^. Denique A/'Ov] cnj A B C A , hinc />) : B A=/.0 : BC, 

 urîde ergo fit ^^^=::^°. Est ve.o /O 1=: B A, hincqiie, quia 

 "irianguhmi BCccNjAfCO, erit °^ — "% unde fit {^zr"'. 



