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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 255, page id 1815201908:0312
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EL. L. IPST. S.
Demonstratio.
ECCE ABC elliphim diameter quxe cunque BD, ducan-
Diurque ex B e D, incra sectionem parallela AB, CD
dico illas incer se ese aequales. InHCNEO a CenETOF, &
AB bisecta in F, iunse FE, e produc in C. ex quoniam
F. F diamecer bisecat A B, bisecac eriam DC ipA AB, Pa-
rallelam. Deinde quia limilia lunc criangula LB B, D F C,;
CFIE D E adD C VE EB ad BF: 8 PermutandO VE D P
ad F B, sic D C ad BF. Sed DF, BB RGUAREUE. CrZO QE
BF, D C, que lunc, reiam ostendi, iplarum AB, D C dimi-
dic. Ergo eE cOTE AB, D C aequales lune. Duod crat demon.
Atrandum.
Corollarium.
InCtEgLIEUF IUNEtAS A E, R C ese in directum: cum enim laCCTA A F, F L X=
ralia line duobus laceribus C G, GF. e anguli ae qualibus laceribus conten-
aequales. paret AFF, CC F criansula esse inter le x qualia, ex angulum AB P X-
rualem ansulo CR. Cm 2dc0que A B BC lincas in directum.
P R O POSTTTO XXI.
Inee per excremicates duarum parallelarum inequalium in ellips
hducte, conveniune in eodem puncto cum diamerro, ad quam Or-
dinacim poluxe lunc parallelE.
Demonstratio.
n
ECCHE F CD ellipum due queuis paralletae in equales AC, F. F, ordinarim pon
ordinauim Cbe Puncio Conene. ubia bimuacu ponntur ca sil.
F. P ad alametrum BCh amba bilecancur in C, e Hl. vnde AC, ad 6C v L,IL
sitam ad diamerrum D B. dico iunccas B A, F C cum B D diametro quam sCCANE
at TIF. ec permucand  AC ad LIL, HOCC ad HIF. Concaac tam F A cum
diametro in I allera vero C  ll. Cueson1et al 211, C211 ad 12. ll
etiam ve IC 2d LF HC AC de AL, eA enim R C ad RF, VEC C ad F HI, hoC
eAt, ve ance oltendi, De AC ad FFI, hocCRvETC ad IFI. ergo puncta L _C R
erac demontraiaum.
eadem lunc; ergo pu L.L13 L. abU
LRC.