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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
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9. DC
islo
b77. Mottis.
L. LIPS
30
Constructio es demonstrario.
Inc ABC cllipis axeS AB, C D: Cenerum F: racio
vero daca maiOrIS A minus E ad C, quam non ma-
iorem esse oporcecratione axium AF, P C. C rario da-
ta aqualis est axlum racioni; res pacec: sminor, luman-
TUE HLT, TK lincx, tectis AE, F C equales, ponan
curquead ansasum rectum HIIK: ductaque HK, e
divila bitariam in L, cenero P inceruallo L. HI circulus
deseribacur FTIK qui cransibic per puncta Lex K, in
Segmento dein HTIR inclinentura dux linex HIFK ha
bences datam rarionem F ad C. Ouoniam igiturFIM
eAtiad MR vEF ad G7, eAtque rario F ad C, minor
ratione axium, hoc est ex constr. rarione TIL ad TK,
pacet punctum MI cadere incer L _ FI, adeoque re-
etam FTms minorem quam FTI, hoc est quam R A, rC.
etaM VeTO MI K maioreni quam IK hoc eA quam P C
centroisieur F inceruallo FIMI, descriptus circulusle-
cac elliplim in puncto aliquo NT inCeF A _ C, duCATIF
igitur diamecer NF, eiq; coniugaca R O. dico NL,
OF diamecros sacistacere pericioni. Juoniam quadra-
tA NF, O F b sunexgualia quadraris AF, F. C hoc est
FTI, TK hoc est quadraTIS FTM, MIR S SICAUECM ANF
lincaxqualis recta FTM. Crit _ OF linea xqualis li-
REx MK. IsIEUT VE AIM ad MR; id cA ve F ad 6, IC
Demonstratio.
PROPOSITIO CVIII.
N daca ellipli diamerros exhibere coniugatas in darararione.
NF ad OF. exhibuimus ergo, eec. Ouod cracFaciendum.
P R OP OSITIO OIZ.
LECCE A C D elliplim guauis diametrorum coniusario AB, BC. a(-
aCumproque inperipheria puncto quonis D inFeF A _ C, aGAEUF PCF
D contingens EF, quae cum AB, B C lineis COnCUETAEIN F. _ F, cud
percentrum utut aa 2.
Dico DF, BC, D E. lirtedsete Ia conrinua analo 8la.
Corol. 60.
: 102. hs -
crune similia, ac proinde DF cs ad BC, ve DH 20
niam ex hypothes DF, BC Tune paralleIX.
riangula DF LL, BFTC, re ex elementis paret
FIC: hoc est verriangulum D HB ad crianguluBL1C
Deinde, quoniam B C percencrum es eangenti DP
Parallelas liquer cam coniugacam ese diametrum ipli
DB: Cunc vero extiypocheli etram AB, BF conivga
tx. Ergocsectores BDCC, BADC, adcoque d es
criangula BDG, BA C aequantur: Ouorum bales
DO, AC, cum cproporcionalicer sinc diuila in II d I,
sc xquulla. eCum priusoctenderim DF esc ad BC
DE D FT sic ad FTG, Sicur C T est ad IA, ConstAE Ex
elemenris triangula BFTD, BTC _ BFIO, BIA el