185 



tur aiitem c tanlum ut praegrande et habebitur 

 (3Z — 4)i =: s^ — 6 3 -j- - et 



3 



^^^ — H— 



S2 — 3 as ' 



undc fit 



— 3 as ' »• 



(5-^-z4J_ — /^3_ 6^ _^ 1) /_L + 1) 

 zz — 3 \ 'a/ ^sa ' 2*' 



a Il 



a s* 



Ilinc 



. ,- 3a_, .«a p., I aVS . (^-hV5)(z — V3) 



^ y — T~t~^ ^^-i-T ^ (2 — v' 3) (a -h/ 3) 



Quodsi jam ponatur s izi oo, erit pro casu quaesito 



* — 2/ = — 2 a -V- Ip / l^^J = ~ 2 a -H a ]/ 3 Z ( 2 + / 3 ) . 



Corollarium 1. 



^. 13. Hune valorem proxime investigasse operac pretium 

 crit. Cum igitur sit 



]/ 3 iz: 1,7320508 

 erit 2 4- ]/ 3 zir 3,7320508 



ideoque logarithmus vulgaris hujus quantitatis 



l (2 H- i/3) r= 0,5719475, 

 qui ductus in logarlthmum hyperbolicum denarii , qui est 



Z 10 =: 2,3025851 , 

 dabit logarithmum hjperbolicum 



/ (2 -f- |/3) =3 1,316958 

 hincque -j/ 3 . / (2 -f- ]/ 3) ZIZ 2,281038 

 ideoque excessus quaesitus 



s — i' = 0,281033 a. 



Corollarium 2. 



§. 14. Quodsi unitas per hune numerum dividatur et ope- 

 ratio instituatur , qua maximus quaeri solct communis diviser , quoti 

 continui reperiuntur 3, 1, 1, 3, 1, 3, etc. qui, si forent 3, 1, 1, 3, 1, 



Mémoires de r Acad. T. IX. T" 



