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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 341, page id 1815201908:0398
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E L. L. IP S LS.
Demonstratio.
Fomencum ABL ad seomentum a ADT es re TB ad FD, vigne cadem LB L 184 B1-
ad TD, ica elt criangulum TF B ad criangulum IR D. ergo ve LB ad FD, ius.
ita eA seCtOr AEB ad sectorem AF D. simili modo oAendemuS seCtOTEM BCOr. 1
T E A ad sectOreM FIF A, ese VE RE ad RFT, id eA, b vE YB ad YD: erGO VEPr. B. B.
IB ad ID, ita esteorus sector BL. L. ad tocum sectorem DF FI, Sed ve IB ad TD,
hoc estminor axis ellipleos ad diamerrum circuli, per 5. Axchimedis de Spher. ic2
est ellipss AB C ad circulum AD C; ergo sector BF I. ad sectOrem DFHI, ve
ellipus ad circulum, e invercendo ac permutando ve sector D F FT ad circulum
AD C, ica cA lectOr BF L ad elliplin ABC, Sed seCOF D F II cA quadrans circuli, c +6. huius.
ergo e lector BF I quadrans ellipseos erir, adeoquec erune BE, E. L. diametri
coniugacxe, ergo, ec. Ouod erat demonstrandum.
Noca idem demonstrari s AD C AE CllipHS cuiuS aXIS A C, SIHEqUC HTF, DC
ipsius coniusaca diametri; si verO D P. II non sic quadrans cllipleos vE sCctOTD RHI
ad circulum, ica erit sector B P L ad Mlliplin, ve ex demonstracione constac.
PROPOSITIO CLXXXVI
A Circuli A BC quicunque sectOT AO C, de ellipsis D F F SectOF
DHE: Sc autem lector ad lectorem re circulus ad cllipsim: ducan-
curque recta AC, DF.
Dico lesmentum ABC eNC Ad sEGMENEUM D F F, vecirculus ABC
estad ellip (I DF F, _ CONEIa.
Demonstratio.
Nueneo CpieosMatoe ACTR deletibaturlu-
per IK diamerro circulus, ductaq; dad axem ordi.
nacim LMI qua auFCraE leGICNEUM L IM ~qu2-
le segmento DPF, occurrat circulo in N et O,
ducaneur que recta LII, M FI, N FI, OFI. Duoniam
Ceomentum MIL aequale eA (CDMOnEO DFF,
eric csectOr L HIMI aequalis sectOriD FTF. Rurlum
Cum sE VE CIlIpSIS ad CirCUIU NOK, SICLTTTIC-
ctor cadlectorem NTII, adeoque _ L FIM (cctOF
ad lectorem NIIO, sicque P. HIMcriangulum ad
criangulum NFT O, DE LM ad NTO, hoc CA sVE
elliplis ad circulum NOK, crie ve ellipas ad circu-
lum NOK, IC T. IM segmencum ad segmencum
NCO, e permutando circulus NOR ad Ccomen-
cum NTO, ve ellipls ad seomencum L. IM. iam
vero circulus ACV est ad sectorem AGC, ex
hypochelircelliplis ad sectorem FTDF, hoc est (Ve
octendi supra) reellipsis ad sectorem L. TIMI, hoc
CA ve circulus NOK ad sectorem NIIO. ergo
ociam hcirculus ACV ad sCOMENEUM ABC, VE
circulus NOK ad segmentum NTO, hoc cst, VF
ance octendi, ve elliplis ad segmencum LIM, hoc
eA (quoniam seGmenTA P. TMI, D F F (UNE ex COn-
Bruct. aqualia) vi clliplis ad segmentum D P. F. igi-
rur permurando re circulus AC V ad elliplim, sic
sesmencum AB C ad segmenEuM D P, F. Ouod erat demonstrandum.
tam vero si tuerir legmencum ABC ad segmencum D P. P, ve circuliis ABC
utlt
d57. BuI.
c59. huin.
E182. B