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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
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ni  
PR O GR F. 3SAOHL.
Corollarium quintum.
TIIdem positis intero quinco: si Fuerir progressio AB, eec. similium magnieudinum
mis. interolat lolao teteo a a Cattabetac e lat plt
cermini AB d d.
icenque alia prooressio similium incer se magnicudinum a. (, y, d, ec. uc similes illae
Tnccerminis alcerius siue dilsumtes; il duce ploslemoreraque ciuldem proporcio-
152
Demonstratio.
eto
1
DEr Corollarium secundum series A R, est ad seriem B K, ve AB ad B C: Scd ex
BVPOTheR AB CK ad B C; vea adB; ergo series A K est ad seriem BK, ve a ad 6,
hoc estper idem corollarium ve series aZ ad seriem βZ. Igicur per conuersonem ra-
tionis series AK es ad AB, vescries aZ, ada: e permutando series AK est ad (e-
riem aE Ve AB ad a. Quoderac demonstrandum.
Corollarium sextum.
l Quamquam hactenus solum aMampserimus progressionem planorum, corpo-
rumve similium Cmilicer que poncorum, non est camen quod existimet lector, que
hactenus demonstraca sune non subsistere, E planorum aue corporum non similium
Racuatur progressio, eadem quippe verobique, ve cuilibeerem expendenci manite.
Rum est, et vericas est _ vericatis demonstrario. idcirco aurem Aguras similes aNu-
mere placuic, quod ex rlus earum frequentior, ee magis unc ad demonstrandum ac.
commodaca.
Ex his hunc in modum demonstracis manifectum est progressionum proprierates,
secunda parte explicatas progressionibus magnirudinum in directum policarum, quas
deinccps prolequemur, non minus quam aliis convenire: ac proinde propoliciones
superioris parris in quibus ille tractancur, prorsusrniversales esse. Juare has deincep.
vei revera cales in sequentium cheorematum demonstracionibus citabimus. n
PROPOSITIO CXXIV
cit.
TALR CINE PFONOTCHHALES EDHCMUX AB, BC, C:Vd, _c. 8 Cuper ij5
constructa plana limitia
Dico plana esse in conrinuaanalosia: ex si plana deneur concinue pro.
Portionata.
Dicoetiam bales Fore continue proporrionales.
Demona
  . u  t is  t s      e t       e it e   1. e t e  e    i    p    t           a  u a  a l 1