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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 259, page id 1815201908:0316
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EL L FPSIS
e R O P OSITIO XXIX.
L. Culus aamecer B C, centrum O, concingat AD Occurrens
Lsdiamerro in D, ductaque ex puncto A ordinarim AOF, e iunct a
AC, per B ponaturrecta PBG Parallela rectae AC.
Dico FB, BG aquales esse.
Demonstratio.
G occurrac ellipsi in FI, iungancurque HO, AO
quae erunc in directum. Tum AC bilectâ in I, du-
Catur per I diameter IOP BCCUTTeNS rectX AR in
L, X iungantur puneta L. C, per rectam L C OcCurren
cem ellipliin R, ec recta FTIin M, cCdR verOFTO in P.
Ouoniam AC ex conttructione ordinarim posica
cA ad diamerrum II, rectaque per A e C dupla
occurrune diamerro in eodem puncto L, erit b L K pa
rallela AC. EAverO d B FF Parallela ipS A C ex hy-
Pochel: et Cemidiamerei OB, OTI IcCanE AF, C K in
2 e P. ergo OP equidistace recte BHI, tres isieve
AC, OP, FR Lincpar allela. Ouare cum ex hyporhesi
A F. bilecta lic in C, eric ex CR bilecta in P, ac proin-
de ordinatim polica ail diamecrum A FT. Leaqued CK ∞-
quidictaccangenci A D. est aucem e FM ex hypocheM
Parallelaad AC, ergoc dim aequalis eAt AC, (cd F cF-
iam BHI aequalis eA AC. ISituE FM BH aquales sunc. quare COMMI. dempea
BM aequaneur F B. HM. Acqui eciam s C, B, HM Xquales CunC. icaquC F B, C B B17 huin.
aquales lunc. Duoderat demonstrandum.
PROPOSITIO XXX
Elipsim ABC cuius diameteF B C continsac in A recta AD Conue-
niens cum diamerro in D: ductaque ex A sic linea A F ordinarim ad
diameerum BD.
Dicorectam DC in B e F diuitam elle exrrema de media ratione pro-
porrionali, hoc cst, veC. D cA ad BD, (iCC HI CA ad HIB: ee li dinila Fuc:
ririn B ec I exerema ex mcdia rarione proportionali agacurque per F. Or-
dinarim linea AF ad B C: dicojunctam AD, sectionem contingere.
Demonstratio.
Vrcta AC, agacur per B linca C H parallela roctae A C
Occurrens A F lineae in PI e A D cangenei in C. Ouo-
ntiam RC, B HT lincx aequidistane, eric ve A C ad BII, (iC
CF ad R B: sedVE A C aA B FI, SC A C est ad ∞B, (quia
GB BH TunCh X qualeS) isieurve A C ad GB, sICC F
esad BF: CA aUECM DE AC ad GB, sC C D ad DB
(quia C B, A C aequidittane) igitur ve C P ad D B, sICC P
ad F. B. Quoderac primum lic iam ve C D ad BD; Sic
CTT ad PVB, S per F ordinaum agaeur AP: dico
surctam AD sectionem comcingere in A. TI enim AD
tron tanoit, ponarur pera eangens quae BD diamerro
occurrarin K, cricigieur ve CH 2d F. B, SCCK adRB;
Sed osve CF ad F B, AC CD ad D B, igituE VE CR ad
RB, Hc C. D ad D B, e lliuidendo re C B ad B R, siC CB
ad B D, quod fieri non porest, cum punctum K Cupra vel
intra D cadac. ixicur AK non est cangensnec quauis alia praecet AD. OuodFuit
Bi5. lnitis.
C28. biviuio
d1.
ins
13. Buins
19.
R
demonstrandum.
ba
Corol