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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 23, page id 1815201908:0080
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POTFNTI A.
Demonstratio.
Voniam AnguIUS AB C. ponitur rectus, et B D normalis, CrUNE ABD, A BC
Leriansula limilia, e AB ad BD, ve AC ad CB, inde ABC 2 rectangu- a 17. SexrI
lum aequale rectangulo AC, BD, Scd AC, BD rectangulum, est ad quadracum
AC, veBD linca ad lineam b AC; igitur ec ABC rectangulum, eAt ad quadratum b L. Sonti.
AC, ve BD linca ad lineam A C; estaurem quadrarum AC, aquale quadracis
AB, BC. igitur rectangulum ABC, est ad cria lacerum AB, BC. C A Guade2
ea veidem rectangulum, ad quadratum A C bis sumpeum; id est ve B D line a ad AC
lincam bis sumpeam. Sed A B C criangulum, dimidium est rectanguli ABC, igicux C47. Primi.
criansulum ABC, ad AC quadracum bis sumprum, id eA ad eria lacerum quadra-
ca, illam habecrationem, quam BD linca, ad quadruplum linex AC. OuOd CFAE
demontrandum.
PROPOSITIO XXIV
IIdem positis, diuidatur BD bIFa
ariam in L.
Dico AB C criangulum, ad quadra-
cum BC, cam habererationem, quam
trabet FD linea, ad lincam DC.
Demonstratio.
Voniam BD linea in P diuisa est bitariam. C ABC criangulum, aquale
Lrectansulo AC, D B; nam in praecedenci propolicione olletum est, rectangu-
lum AB C; aequalerectangulo super AC e BD: rurtunt Cu ALBC angulus sit
rectus, et BD normalis, exic AOD rectangulo, aequale quadratum BC; quare
AB C errangulum, est ad quadracum BC, ve A C DF cecatontum, ad rectan-
sulum ACD; id est ve F. D linea, ad lineam D C. Quod erac deb andum.
P RODOSIFIO XNI
Aceri AB, anguli ABC, aequi-
distet DF. OpOrTCE peF F pun-
ctum inera angulum DEC, rectam
POneTC AG, VE AD ad FC, datam
habeaerationem FI ad l, 
Constructio ess demonstratio.
VCaCF FC, quae aequidister ip( AB;
_ Aac ve II adI, SCB P ad C C: dein
BONAEUE C F A. DicoFactu quod requiris
EUF. CUIM eNIM AIC eam E B ad AD quam
COad F G, vEF G ad D G, (Ob A B. E D, C F paralletaS) CMM AB adt A D, vE CG
2d F C; ee permutando AD ad F C ve BF. ad C C; id elt Pel constructionem rE
FFad I. isicur ec. Ouod erac Faciendum. IHc
P R O P OSIT IO X XV V
N dato criangulo ABC, parallelam vni
lacerum constiruere, recta DF: Vequa-
dracum E D, aquale sIc AF C, rectarigulo.