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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 184, page id 1815201908:0241
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. p .  t. te 4 i. 1 .e1 11. 1
Csnoi
IR CVLVS.
verectangulum MIK O ad quadrater k I. Aequi reCtanguIA N L P, NIK O aguaneur
quadracis CL, D R, quod GT, DR sinc ad diamerros NP, M O normales; ergo
quadracum CT. est ad quadracum P. FI ve quadracum DK ad quadratum R Ler.
Borecta GL cst ad rectam F HI, verecta DK ad rectam RI; quoniam isicuran.
Fuli quoque GLHI, DKI, repocc recti ex constr. aequales lunc, crune criangula
GLFI, DRI similia, adcoque anguli HGL, IDR aequales. ergo OFI, D Ip2.
rallelX SUnE. ErgOvE A G es ad AD, SC AFI, ad AI, hoc es quia FTB, IC Cr.
iam sunc parallela, Ve AB ad A C. Ouod crac primum. hmili ratione ostenduneur
iunctx LF, IIE aequidhistare, adcoque esere AHI ad AI, id eA AB ad AC, sic
AE ad AF. Duod erac demonstrandum.
PROPOSITIO XXV.
NIF ABC LCMITCMEIMI MaMCCE RC divisa vecunque in F: descripeil.
DGue TuPEF A E, E C lemicirculis ADE, EFC, crigacuF F B normali-
cer ad diametrum, ponancurque AB, BC, occurrences perimceris in D
_eF.
Dicorationem C. F ad D A, eriplicatam ese illius, quam habet C. B,
dd AB.
Demonstratio.
VnGAnCUE DE, E F. Ouoniam E B norma.
lis est ad A C diamerru semicirculi ABC,
CTUnE AC, CB, C R, ItCm AC, AB, AB
concinue proportionales; Cedve BC ad C B
sCF C ad CF (obF FC, B F C criangula
similia,) _ vE AB ad AF sC A F ad AD
(ob ABF, ADF. criangula similia) ibicur
tam AC, C B, C F, C F quam A C, AB, AP.
AD sune concinux proporcionales: inde
 P. cum verique scriciprima sic communis AC
Aquartam, in criplicata rarione C B 2d A B, sccundx ad
PROHOSTEIO XX
o C lco B, esse proporrionales.
Hi
honibur. Secundam. Ouo d erac demonstrandum L MIL cB
ac Pelerres circuli in pltelis, , d ex A quavis rectX AC, AD.
Deon.
Perimertis OCCUranEIN E, F, C, FI:
 t   ue 1 1    p   5  1. e it  . u i.        1. 1  t  u 1 1  te . 1 1 1  1 t    t ) A