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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 239, page id 1815201908:0296
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AD SBCTTONES CONI
ISITAEM E, ad FT GS VEAM ad A FHS hOC CS DE AN Ad AL, HOC CAVE MK ad L I.
Jeaque permucanido, MI F est ad NK ve HI ∞ ad. L. I, adeoque eoquadracum N F ad
quadracum NK reguadeacum FI C ad quadracumr P. I. sed quadracoTIC aequale cAt
BHIC rectangulum, de LI similicer quadracum ae quale rectangulo B P C. Igitur
MF quadracum cA ad NVK quadratum ve BFFC recrangulum, ad recrangulum
BL C, est aurem velBH C reccangulum ad BPC reccangulum, ica rectangulum
DM Fad DNF rectangulum, cum exii dem rarionibus compolica HnC, isituF qua-
dEaTUM MIH est ad. NK quadeatums vereccansulum D MI Fad DNF, reccanguli
lam rerO D MI est ad BFT, vE AM ad AFI, hoc CAVEMF: 2d FIG. ergopermucando
DM CItAAME, VEBII ad HIO. (Cd BFI, HIC CunCaequaleS, CrGO _E DM, MP aequa-
les lunc lgicur quadracum DM, hoc estreccangulum D M F (nam cum B C scbise.
CFA in FI, CFIE BE D P IN M) EQUAEUE QUAAEAEO MIH. OMARE CUMI GUAAEACUMIME, ve
lupra octendimus, SIE ad QUAdEAEUM NR, VETCCEaNGUIUM DMF, ad reccanoulum
DNE, criam reccangulum DN F, aequabieur quadrato NK. Denique cum DF, BC
sinc parallelae icemque GFI, P M, ec vna CII licnormalis ad vnam BC, crie aleera
F. Mnormalis ad alceram D F; similicer octendam R N normalem esse ad DF. ICa-
que cum normalium P M, K N quadraca equalia sine reccungulis D M F, DN F, (C.
EciO D E, B F circulus elt. Ouod Euic demonstrandum.
Corollarium.
X diccurso demonstrarionis liquec centrum circuli D E F eNC in axIS pUNCEO F, in
quo nimirum axis occurrie recex DL, qua est communis seccio criansuli per
Xem _ circUli DPF.
P R O POSITIO XVII.
N conolcaleno circulum exhibere qui bali x quidistansnon (IC.
Constructio es demonstratio.
CalenuS COnUS PONatuT ABC. (C-
ccus plano per axem proterence
crianoulum ABC minimum illorum
quae per axem heri postune erie illud
scalenu, cum omne icalenum sc quod
Per axem Ac peaecer maximum per Cor.
2. Oct au_; angulus isieur AB C minor
ponatur angulo AB C: quarC HaL an-
sulo AB C aequalis AC D _E PCFFECTA
DC duc planum rectum ad crianoulu
ABC: Dico sectionem inde nacam
DLC esse circulum. Ducaneur enim
duo alia plana bal parallola F LC,
TTMK, quorum communes secciones
cum planO DL C. GINERCCEX F L, INI.
ex7. huius parec batim coniad minimu
triangulum AB C rectum eAC. ergO e
alia plana parallela FPFI , HIMK (
ctiansulo ABC recta crunc: sed e
planum DI. C criansulo reccum est.
ergo communes lecTIOnCS L F, M I,
receae lunt criangulo, adeoque e lincxe
DC. Ouoniam AUCCM FL G, FTMK,
circuli lunc per praecedentem, _ FL, IM normales DC, eric cam rectangulum
F F C aequale quadraro P L, quam rectangulum FITR, quadraTO TM, quia vero
Similia suncrriangula DIFI. e IKC, cum anoulo ACD, Sc ex constructione X-
qualis AB C hOC eA D HI: CruNE punCta LID K C in eodem circulo: Similiter
octendum