De amplificalione campi apparentis in telescopiis. 747 



20. Quod si hic pro M substituamus valorem , erit primo k — M= ^^ , tum vero • 



w»-i- 1 r m -H 1 



r __ 4 (2 - §) m 4_ (10-6S — 7H-e^)m _ 3 ^ __ 2(l -^?)m 2 



(2_,)(mH-l) m-»-r (l_5)(2_^)(m-4-l) m-Hl' « " (i_,)(^^i) -»" ^^1^1 ' 



PonaQUis ad abbreviandum : 



2_, -^' (l-5)(2->?) -^' '"" ^-*^(l-5)(2-,)' -737- = ^' 



... , *m — 4 Cm — 3 ^ , i)m -f- 2 



mn-l m-Hl <♦» m-^i «^iH"*^ 



m -t- 1 m-*-l m-+-l 



m-*-l m-Hl m-Hl 



I^DJbus valoribus substitutis consequimur: 



^ 4 (5m — 4) a > n (5m — 4) a 



'— ^(m-t-1) ' m' ^^ *m' 



^_ 4 (Bm — 4) (Cm — 3) a 4(Bm — 4) (C — 5— 1) a 



(C — l)(m-Hl)[(£H-l)m — 3] m [{B^ l}m — 3] B {€ — i) m 



4 (^m — 4) (Cm — 3) (Dm -t- 2) a^ ^^ 4 (^m — 4) (Cm — 3) (C -h Z) h- 1) a 



(fl-t-2)[(5-Hl)m-3][(C-f-l)m-2](m-Hl)'m' [(£-«- 1) m - 3] [(C-i- 1} m — 2](C — 1) (Z)-i- 2) * m' 



(Bm — 4)(Cm — 3)(«m-+-2) a rip, (Bm — 4) (Cm — 3)(Z)m-4- 2)(i[) — 2) a 



" ■ -L/ri* = ftt: — ,-. ^._ ^TTTTr TT— r — • — > 



[(l?-4-l)m— 3][(C-+-l)m— 2][(Z)— l)m-4-l] m [(5-i-l)m — 3] [(C-Hl)m — 2] [(Z)— l)m-t-l] (Z)-+-2) m 



t pro loco oculi EO = -- — t. Hicque — denotat distantiam focalem lentis simplicis aequivalentis, 

 uam posuimus = k. Notandum porro est litterae B, C, D ita a se invicem pendere, ut sit: 



BCD-*-QBC—5BD^kCD^ikB — SC-^kD-^S = 0. 



21. Fractiones ergo ^ et ?? unitate minores arbitrio nostro rclinquuntur, quas autem ita accipi 

 porlet, ut ne lentium intervalla nimis fiant exigua, quam ut ob crassitiem tam prope sibi invicem 

 djongi queant. IJinc patet neque ^ neque ij evanescere posse, quia iilo casu intervallum BC, hoc 

 ero intervallum DE in nihilum abiret: intervallum autem CD non evanescit, nisi ulraque fraclio 

 el tj unitati aequalis accipiatur, quod ergo probe est cavendum. Cum igitur ncque utramque 

 imis parvam, neque ambas simul unitati fere aequales accipcre liceat, nonnullos casus, qui ad praxin 

 lonei videntur, evolvamus: 



:r 



irih' 



• 



^ 22. Casus 1. Sit ergo primo ^ = ri = \y atque habebimus B = h, C=9 et D = 6, hinc- 

 IH^ pro constructione telescopii ponendo — = k, determinationcs sequentcs: 



b 



