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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 334, page id 1815201908:0391
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27O. hu
LLIF5IS
PR ODOSITIO CLXKII
erum circuliin H, C F vero ellipleos diamerum F. D in C.
Sicoiunctam CH aGuidittare BF.
Demonstratio.
DOHaTUE PEF F, linea TK aequidistans B. B.
iunetilque punctis FD, ex FY recta duCacVE
HC, Parallela IK, occurrens FD linex in I.
_ F. D in C. Duoniam TK aequidistacrangenci
F, B, 2IF, F K linex incer (e aequales lune; quare
e FFO, linca aequidistans PK in L, diuila quo-
que est bitariam. E iam punctum C non sC com-
mune lineis FC, F D, FIGI, OCCUTEaEHI C ipSFC
in M: Ouoniam ergo FEM aguidictac R B adeo.
que AC, vE AD ad DC, SC FIL ad LM,
cur C e MI, rnum idemquelune: onde C commune lincis Fi C, F. D ae quidistanti
isitur FIC, BF. Ouod crac demonstrandum.
rirculum ABC cuius diametri AC, BD se ad rectos decultent in
LsD, contingat in B linea BF, ducta deinde per A _ C ellip(IS AF. C
continsens BF in F, occurrat circulo in F, e polita ex contactu ad cen-
trum recta F D dUCanEuT AF, et e A F quidem lecans BD diame.
quarCMEI in L diuisa est biFariaM: Se d _ FIO, in L bitariam est diuila; punctaigi
PROPOSITIO CLLLIII
ircidum AB C cuius diamcte (C, BD sese ad rectos decuNanE, COn-
in II, occurrens diametro AC, in C: dein ex HIponacur HI, parallela
BF occurrens cllips in l, iunganturque 16.
Dico lC lineam conringere elliplm in I.
Demonstratio.
scingat in Brecta BF, ductaque ex E recta linca F. D, de lcribatur ellipsIs
AF. C, ContingeNS F F, in P: ponarur quoque F.C contingens circulum
Dnaeur La aequidulcans LD, Cu IIla O.
dinacim posira ad diametrum AC, cum AC,
DF diamCtEI SnE COnIugaTE: CX R vero cri-
SaCUE KHI, Parallela BD, ocCurreNS FI li.
nex in FI. Juoniam tam IIK, BD, quam IR.
dracum HR: led requadracum L D ad qua
dracum TR, sC AD C rectanoulum ad re-
etangulum AR C. reigitur rectagulum ADC
adrectangulum ARC. HC BD Guadrarum ad quadratum FIK. Ouare punctum H
in peripheria circuli est: isitur cum ITK sic normalis _ FTC contingens, ve GC
ad CR, SiC CR ad AK: est aurem TK ad diamerrum AC, ordinatim poltA; et.
veattia 30 Clb linca est Cansens. Guod erat detohlitatiaum.
F. D aequidistane, eric ve quadeacum F D ad
quadratum TR, SC BD quadratum ad qua-
D. BH1115.
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