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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 264, page id 1815201908:0321
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  1 1 11 . 1t. a1. 1
164
ins.
=13. tuiin.
e L.  L.C d2.S
Corollarium.
TIncpatet quadrilatera C. F B A, DCF A, equalia esse, eodem enim diseursi
probabimus equalia esse cangula ABF, AP C, quo probauimus aequa
tROTOSATIO XEXIX
EcentA BC elliplim au quevis parallela AB, C D, junctisque AB.
recta EM paralteta ip I AD, concingar sectionem in F, d exF
ducacur EF, XqCaHS AB, secans AD, C. B lineas in G X FI.
Dico continscillem per P ductam aequidistareipa B C. ui ba
XA ol reit.
Demonstratio.
3+1
VeaneuF ex LcenerO linCX IP, LP OCCUTFeMEOS AD,
CB in K e F: quoniam igitur PM concingens, x-
quidistat AD _ PF diamerer ad contingencem ducta,
secet AD lincam in R, cric A D in R dinila bitariam;
est aurem recta B C in T. divisa sCuE A D in K. recta
enim KT. iungens puncta K, L parallela eAt b ipsIS AB,
DC. igicur _ BC in T. secta est bifariam a diametro
F; vnde e cangenri per si ductae c aequidistat, uod
Tuie demonstrandum.
121is dC
11 311B etseetI A
PRODOSITIOLXI
Alrculus super axe maiore ve olamerro deseripeus ellipsi excerius in
ei ACF, ADO.
Demonoorum.
AB C cllipKB axto BL CnEOque
duobustancum purtelis occurrit.
ilius F MMeccallo F B circulus declibacr
dico illum ellixsi in duobus cancum punctis B e
Doccurrere. occurrarenim si heripostit insuper
inpunctaA, de per A ordinacim ad axem aggtuF
AF. dycaturque axis minor CF. cric isicu r
BF D rectangulum ad quadracum L AHC B P. L
rectangulum ad quadearum B Co: sed BL. D rC-
ctangulum in circulo cA ae quale quadrato F AI
isitur ex rectangulum BF D, id est, quadracum
BF aequale est quadrato CrP, quod heri non
Porest cum B, P. linea maior sic quam OR. ixicur
circulus pum occurric in A: nec in alio quouis puncto, prXTex B e D. Quod
tuic demonttratu.
6
imili discurtu ceabuus circulum circa minore epicos ae acteri.
prum in duobus tancum punctis excremis axeos elliphocCurrCEC, de forum inera
etdesiti
 crutocaosio ut
vtas illa B R O
(51
Corollarium.  d L b~ 1
elliplim existere.
( e e ee.   e e  1 . n  p 1 1 1.  e s .    u  u   .          p       iet