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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 720, page id 1815201908:0777
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11
de
DVCEVS PL AN
ROPOSITIO XXI.
deulnicirculus ABB, inscriprus rectangulo AD L cur a GualeII
Dcoecurum DO ad angulosrectos, semicirculum C F. F concitens
aequalem AB. ducatur aurem eo sicu AB Semicirculus in SCHHHCHCMIUFO.
Diccuperticies oriri cylindrieas, e communem oe
Fore cllipricam.
Demonstratio
crangula F A D suncTCOlCCHA. MI DH= planum clt. agatur deinde quodcunque
deacorum, erune quoque diagonales DB, incer se aequales, ac proinde criangula re-
aPerole.
perticie cslindrica.
VOX, h0
Vcacurcorum rectangulum AD, in DC rectangulum; de ponantur diagona
les D F. quoniam igituE AD, A P aqualeslunc, repoce lacera corundem qua
+. D. et
planum RO FTM parallelum planis BOY, DF Z: Cimilicer, divila superkicie A A
DF Z planis aequidistans. Ononiam OR AUCCLI In RMI, XGUAEUIE R NY in se duccoe
NO, hoc est IS in se ducro, vna cum rectaBGIIO, ALO BIS Sampeo, hoc est ro-
Odia vero elt ve quadrarum O P ad O NT quadratum, hoc cASI, SIC GHAUTAIUIIE
ad X IIZ
bitaria ECCCa O R paraIlela A X, per O R ponacur alcerum planum ijidem D C,Y
menea.
c19. huius: superticiem cxlindricam; H a C Al, TL, hoc estomnes BC, C F, Cunein su-
b Exc Crangulis NS, IM, Simul Cumpris. IgicurfgurE NKL, S. IT quadrarx lunc, qua-
mencis. rum diagonales unE RI, ITI. Oltenlum cA aucem BD duccum in le c producere
quare Y PIZ hoc c d CC, sunc ad candem ellipuim; quae exhiber
Scholion.
PR ad TFI, quadracum (illorum nimirum dupla) estque recrangulum V OX ad
tZRZ ad YHZ, ve quacacum  ad ON quadrarum, (quia
PO. ON normales luncad V X diamerrum in semicirculo V BX) etiam quadra-
EUm P R ad TFT, quadracum eandem habebierationem, quam reccanoulum YRZ
communem incerleerionem planorum B, FG. Quod erar demonctrandum.
Eoposirum sit AB, ductum in C D, adst 
re
actu AB, in se: nam Cn LLD, UHCd fitit
aquales CD, Videtur prorsus tae corpus debere
produci cum illo quod prdaneitur per ductum AB.
in se: lonee tamen est diuersum. sit enim quadras
rum AD, quod diuidat F. F. linea bifariam late
ribus quadrari aequidistans, es descripri sint aequa
les semicireuli AB ex C D, ex ducatur AB, in
C.D V1 proposit. 22. postulabat, orietur sicura cuiu
dime-
ssest stes de e  t. es e   e e t att st lt e   e     ti i t      e it  t         e e  se este  te