Enodatto instgms cujusdam paradoxi circa multiplicalionem angulorum. 



309 



24-. Omnino autem notatu dlgna est relatio, quam hic inter nnmerorum ^, B, (7, D, etc. et 

 numerorum a, /?, y, 5, etc. ordines observavi, et quae commodissime ita referri potest, ut sit I 



a-f-^z-^yr«-^.5z«-+-etc. =-^(i-4-^z-i-^z*.-+-Cz8^D2*-i-etc.)*, ^ ^ 



cujus demonstratio haud parum ardua videtur. Operae ig-itur pretium est indolem horum nume- 

 rorum accuratius contemplari: Aenf! . i 



''—•2 — 272-* 



B == i^ — iil 4 



2.3~ 3.3 



^ 6.6.7 6.7^ 



^ —27374-^4:4^ 



D = 



6.7.8.9 



8.9 



2.3.4.5 5.5 



2.3.4.5.6 ~ 6.6 



etc. 



^3 2 

 '^=»(4-T-|-4)=*-^-'^« 



' = ^(l-l-i-i5-n) = '-«-^^-T»« 



etc. 



25. Gonsideremus hanc proprietateln in solis numeris integris, ac formemus has bhias pro- 

 gressiones : 



8=8.9.10.11.12.13 f=g(l-Hi.-HlH-i-Hl-Hi) 



etc. 



etc. 



eritque ut sequitur 

 2 



»1} ,<!»«& in^^^ufi aiu3 



a=2.i^, fc = 39t, c^J^QS-^-e^, t>= 56 -^- 100103, e = 62) -^ 15916 h- 20^, 



f= 76-^-21212) -4- 35936, 



7.6 



9t5) 



7.6.5 



«6 



7.6.5.4 



Seu ^f^^.lS^y^^***- ■ 1.2. 3^-- • 4.2.3.4 

 unde lex progressionis est manifesta. Vel erit 



693 



2.3 



czx 



bz^ 



2.3.4 2.3.4.5 



etc.=4-(l 



7.6.5.4.3 

 1.2.3.4.5 



6t' 



2)91 



7.6.5.4.3.2 

 r.2.3.4.5.6 



6.1, 



3)** 



2^ "*" 2.3 "*" 2.3.4 "*" 2.3.4.5 



-i-etc 



•)' 



