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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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B.
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c.
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1
POZL NTIA.
EROPOSFFIO XXXV
Aco puncto A inera anou-
lum BC D; per A rectam
ducere pertingentem ad lacera
BC, C D, vrrectangulum quod
Cub Ceomentis ContineTuT, X-
quale sc quadraro dato Z:
quod oporrer eAe non minus
minimo rectangulorum qua
segmentis linearum per A du-
CLAEUI COHTINCHEOT.
Constructio es demonstratio.
Vadcacum Z vel aequale est mi
Lnimo rectangulorum qua sub
Tegmentis linearum per A delcribi
Possune, vel maius. Si x quale, a8acur
per Alinca B F exhibens R C Perian
sulumiloscelesi pacetper praecede-
cem P AF rectagulum equari qua
draco Z. Sicigicur quadracum Z ia-
ius minimorectangulorum. DucA.
cur per A linca D B re in A divila sc bitariam (quod ROr S duet a ex A linCA RC
parallelalareri C B, hac D C linca aequalislinea GC: d ex D per A recta ducaeUE
DB) dein ducatur linca FIK, parallela rectae FF, a criangulum auferens ITC R a32. Ruiuii
aequale criangulo BCD, cricq; HIC K quoque ilosceless ec, FII quadrarum b quo d b33. Ruins
Ec a dimidia linex FIK, aequale rectangulo F A F: quod per hrpochesim minus est
quadraco Z. duplaigicur rectx Z maior eric linea TIK, Porericque auterre criangu.
lum isosceles sub angulo C, maius criangulo TTCK. DUCAEUF CFGO L.M, dupla re-
ax Z, auterens crriangulum P. CM aequale rriangulo TIC R; e per A rect 2 292- c,2. Xuius.
cur NP, Parallela linex P.M. Dicolactum eNe quod pericur. cum enim recta BD
in R dinila sic bitariam, e per a ducta quaedam NYP, cuius parallela P MI, crian-
sulum auferr aequale criansulo EICR, id et per constructionem xquale criangu- dy3. Huins.
I0 BCD; cric N A P reccanoulum aequale dguadraco dimidix ipsius L NI, id est per
constructionem quadrato L. duximus ixicur per Alincam; ex c. Duod erac Faciendum.
PROPOSITIO XXXV1.
Sco A BC criangulum Ccalenum ductâq; ex
LC, linca CD, ad oppolirum lacus; quae
angulum ACD aqualem Faciac angulO AB C,
ducatur ex D linca DE, Paralsela ip (iC B, quam.
in FI secent recta quorcuriqué FO parallela
ipsi CD, Occurrenees C a D erianouti laceri
Dus in F, _C
HC) t etC)
DicODHE rectangula, aquari rectangulis
FHC.
Demonstratib.
Lxqualis angulo A B C, id cA AD F: sunc aurem e
anguli PHD, E. HC ad vercicem opposir incer se
Noutus, A O FidCA ACD, per ConRrcciorem est
aequales.