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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 132, page id 1815201908:0189
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t  . . 1 . 1 12. pe. 1 1. 1
1
PROGRFSSION ES
Constructio ac demonstratio prima.
Gytac DE AC ad AK. RC primum Ceriei planum AHI, ad aliud simile cuius diame.
cer rolbalis sic Z. Dico hoc cori scrici x quale cNC.
Per manifectum propolicionis 126. huius, cora planorum series M K, est ad planum
ABT, VE AK ad AC, id est ex constructione replanum Z, ad AM planum: ergo
planum Z. est ad planum AMI, vecora series M K, ad idem planum AMI. X quancur
igicur incer se planum Z, _ coca eries MK. C uni icaque eriam simile siIE Ex Con-
Structione planum Z, planis seriei daca M R, pertecimus quod in problemate pete.
BAEUT.
Constructio ex demonstracio secunda.
FVmacu A P PrimX A V. ac cerrix C D, basium differencia: Aac que vt A L ad AB,
hcprimam sericiplactum AM, ad aliud sibi Amile Z:
Dico L Planum Cactstacere problemari. Nam FOTA serieS M K cst ad planum AM
De2 AB ad Al. Acqui ex constructione criam planum Z cst ad idem planum AN.
ve AB ad AI; ergo planum Z, ec cora series aequalia sunc. Invenimus igicur dacx pla-
norum similium lerici, planum aequale ac simile. Ouoderar demonstrandum.
Constructio ac demonstratio tertia.
FTac ve AB ad seriem dalu imparium AB, C D, Xc. Sic primum planum ad aliud
amile L.
Dicohoc Ceriei planorum dacx equari. vel (quod idem est) Fiat ve A B ad BC, GC
AF ad FR, reque AB cMt ad AF, Sc planum primum Aac ad aliud simile.
Dico eciam hoc conticere problema: demonstrario eadem est qua primx ac lecun-
da constructionis, cacancum differencia, quod propolicio r26. linius, sic adhibenda.
Dixi aucem sccundum huius cerria constructionis modum coincidere cum primor
eiusdem constructionis cerria, quod ex praecedencimaniteltum Ac, F Kxqualem este
Cerici balium imparium.
Scholion.
Ouerre constructionem illam eriplicem propositonis dcla esti  C Vauer jatto
= (t hurc etiam seriet conventre. Derum quia in procresonibus hulus cenerio. fachltores
subinde ac maxis expedica constructiones suppecunt, visum est opera pretium illas rum hoc locor
sum aussetiam deinceps in medium proferre.
Temma.
n uu q   sat u e  e uie  p    s e  e 1s       1.  u  i  . 1    1. 1.   1    1    tis  1a l