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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 24, page id 1815201908:0081
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L. IN F A R V
Mt
CUE F D, qux aequidistet ipsi BC. Dico F D soluere problema; quoniam enim
tum, ad CB: hoc csvelinca AF, ad F. C: isitur unc eres in concinua racionc A F,
duplicara sic rarionis A F. linea, ad L. D lincam; eR igicur quadracum D li, aequa.
eR OEOSITIO XXVII.
FIIdem poliris constiruatuF GFL, quae xqui-
distet BaHA.C.
Dico rectangulo C F HI aequari rectan.
gulum FDF.
Demonstratio.
plum GFFF, 2d FD F reccanigulum, rationem habet composicam, ex
EGF, ad F D, hoc es AF Ae F. D; _ exrarione FFI, ad F. D, hoc est
ED; RIgITuE AAEVE F C, ad D, ita F. D ad aliam, erit illa pCF PEXCC
dencem ipla AF: igiCUF VE A F 2d AP., ica rectangulum O F HI ad F D F: paTCE
IIO XXVIII
Aco A. puncto, intra angu-
lum BCD, perillud lineam
BAD ducere, quae dinila (ic in A
iuxta daram rationem P ad F.
Constructio es demonstratio.
DOnatur AE, aequidistans ips DC:
=_E AAE DE F adF, IEa C F ad E B: de-
inde exB, per A duCaEuE recta B AD,
quxe perringat in D. Dico facu qod quaritur: manifectum est ex elementis.
tAOPOSTTIOXXIX.
Daro puncto D exrra angulum ABC.
Prectam ponere qua diuidatur secun-
dum dacam rationem à lineis angulum
consticuentibus.
Constructio ex demonstratio.
Constructio es demonstratio.
Perole-
menca.
le rectansulo AF. C. Uod erar extibendum.
TE AC quadrarum, ad C B quadracum, ica tiac linca AF ad a F C: et erie2
DF aequidistat rectx B C, crit quoque quadratum AF, ad FD, ve AC quadra
F D, F. C. cum ratio quadrati AF, ad D F quadeacum, hoc csratIO A F, ad F C
E
F, C:
isicur aequalia esse rectangula illanet (c. Ouod Fuic demonstrandum.
P R O POS
lalaratio li ad Li, ec cx 6 puncto duca
Cut Guas OTI: Ita VEHE D C ad GIT VE F
CUIA LEcS DC OH: hde e d P. Plalcuimus igirur quodrequituum tuic.
RC
ad F: quo Factoponatur FT A parallela ipS B G. _ dueaEuE D A, OcCurTeNSBC
producta in C. Dico DC ad C A, candem rarionem continere, quae reperitur in-
CClatas F, F. Cum enim aequidistent ILII. C . MMMcin cadem rationc DC, C A,
eu u     uet  e e e  e e e t e ei p  et e ta e  t  e  p   p  ue u   pa u e  t  s  u         p     p  1 1. 1 1