718 L. EULERl OPERA POSTHLMA. Phjma. 



-1 ^ k, oaihq Jm » y-^ AB = a — k, 



6 (m — 1) (3m - 1) ■ p>^ 2 (m — 1) , 



r. (m-i-l)(5m — 3) ' 5m — 3 



_ 6(m — l)(3m-1)(3m-+ 1) , .,^ 6( m — l)(3m- t) ^ 



* (m -+ 1) (5m — 3) (5m — 1) ' (5m — 3) (5m — 1) ' 



__ 12 (m — l)(3m — l)(3m-Hl) , j^„ __ 6 ( m - l)(3m — l)(3m -i- 1) ^ 



{5m — 3) (5m — 1) (om -h 1) * (5m — 3) (5m — l)(5m-i-l) 



Haec intervalla lentium satis sunt magna, ut earum contactus non sit metucndus, unde hic casus ad 

 praxin eo aptior vidctur, quo formulae inventae sunt simpliciores. 



23. Casus 2. Casus etiam notari meretur, quo ^=1, unde fit B = ^^- ^ C = oo et 

 T) = - ~*~^\ quos valores notasse sufficiat, ex quibus habebitur: 



^^- 4(m-2-^^) ^ ^B=a — {2-rj)k, 



4m (Bm — 4) , r*^ 4 (m — 2-*-?) . 



(m-Hl)[{B-i- l)m — .3] ' (BH-Dm — 3 



(1 — 7i) [Bm — 4) (Dm -H 2) , ^^ (1 — ;r){gm — 4) , 



* (m-*-1)[(i?-+-l)m- 3] ' {B-Hl)m-3 



(Z?m — 4)(Z)m-i-2) , rkc ^{i^m — 4) (Dm -i- 2) , 



ft, L)lL= ——-— — — J7— — TT«. 



I 



[(fi-i-l)m — 3] [(D— 1)m-+- 1] ' [{/?-+- 1)m — 3] [{O - 1) m-i- 1] 



Cum crassities cujusque lentis sit ferc pars dccima sexta distantiac focalis, patet nisi rj capiatur infra 



\ nihil esse metuendum; commode autem sumetur ??= j, eritque B = ^ et D = k, unde fit: 



_ 4{3m-5) . AB - a — -k 



'*'*'' 16m(3m-5) , p^ _ 20(3m — 5) . 



i;»i..Ji:iffci 



(»n-^-l)(l7m-15) ' 3(*7m- 15),:;,'yjy,- ciianiJc( 



16 (3m-5)(2m-Hl) , ^^ 8(3m - 5) , 



^ ~~ 3(m -+- 1) (17m - 15) ' ^^ ~" 3(17m — 15) ^ 



' .'■" '^- "■ - _ 8(3m-5)(2m4il) y>''''^^^^f- ^' •^gjj^j^'^ 8(3m - 5) (2^-4^'^-' Y ^>"'''''^''" 



aJ'3'j;7n? icf;?. ^.^rsr! ~ (17m - 15)(3mH- 1) ' ^ 3C17m- 15) {3m-H 1) -:*.•;■ ' 



Pro loco oculi est semper EO ==■ —. — t. , 



Am ;,Ufil|f«».t'^ 



De lentibus ocularibus quintuplicatis f quibus campus quintuplicatur. 



2k. Sint lentium B, C, D, E et F distantiae focales q, r, s, t et «, indices autem aperturac 



7T, Tc^, tt'^, n^'' et n^^ , e.\ quibus cum sit semidiameter campi cp=. ^ > quo is 



maximus evadat ponamus :np = ctj, n' z= — co, n,'^=(o, n^'^= — oj et n" = co eritque (p = —^ 



