741 L. EU.LERI OPERA POSTHUMA. Physka. 



— b 



Tum vero pro his tribus lentibus ponamus B = ^-^^ > 33 = — 6, C= — 1, 6 = c», D = oo 



et 2) = 1 , unde nanciscimur: 



33n; — (p = — {b~t-M)GJy ^Ti^ — jT-i-cp=z — (Scj et ^n^^ — 7r'-t-;r — 9^ = (3 — M)(o, 

 et destructio colorum praebet hanc aequationem: 



1 1 1 



= hincque b-h-M=Z — M et 6 = 3— -2^/. 



6-f-^ 00 3 — Jlf 



ik. Quodsi porro distantias focales trium lentium i?, (7, D designemus litteris q, r, s, erit: 



bM ^ ■# b M 



" 6-f-Jlf* 1-1-6 l-t-63 — J»/' 



et lentium intervalla: 



at pro loco oculi est distantia ^^ = 337^* Substituamus ergo loco 6 valorem inventum 3 — 2i»/, 

 ac reperiemus has determinationes: 



__ (3-2itf)Jtf (3-2itf)itf _ (3-2itf)itf 



9 — 3-J*f "' '^ — 2(2-Af) "' * — 2(2-J»f)(3-Jf) " ^^ 



^D 3-2Jlf p^_ (3-2J»f)Jtf ^ /^n _ (3-2Jtf)tf ^ 



/^ = THF "* "^ — 2(2-J»f)(3-itf) "» ^*^ — 2(2-J»f)(3-J»f) "» 



existente /c = — • 



m 



3 



15. Cum nunc sit M= ' , > ideoque 3 — M = ^//w, erit: 



tn H- i * 



3(m— 1) «^ 9(m— 1) _ 3(m — 1) ^ ^ 



9 — mn-l *m* ^" ~" 2 (m-i- l)(2m— 1) "' 2(2m — l)'m* 



.„ m — 1 n^ 3(m — 1) a ^y. 3(m — 1) a . 



m * 2(2m — 1) m 2(2m — 1) m 



et pro oculo DO = „"*" 5 = J^Z~ «v • — • • Ac si introducamus distantiam focalem k lenti 



*^ 3m 2m(2m — 1) m 



simplicis aequivalentis, habebimas: 



3(m — 1) , 9m(m — 1) , 3 (m — 1) , ^^ pr rn « 



quae formulae, si multiplicatio m sit satis magna, abeunt in: 



g = 3^ ky r = -rfc — ^k. s=-rk-^ ~kf 



» m ' 4 8m 4 8m 



quas tres lentes ita jungi oportet, ut bina intervalla BC et CD sint distantiae focali lentis poslr 

 mae s aequalia. 



