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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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ALDRALVKA CIKCFEI
Constructio Ficurae vnuer als pio sequentibus propositionibus.
IE AB axis parabOIX C A B. Cu equidister diamerer P P Bitariam divila in C.
Sumprisque C CF, CH aqualibus; dini(que GF, FIF in guacuorparces aquales,
ponantur per puncta divisionum Adinacim ad axem, ex perticiantur parallelogeam-
ina BK, L,MI; iceM IN, R O, LL, MO: ex rectangula R, S, F, V, iceme X, ∞Y.
XZnc. Denique ponatur figura patabolica LKE M subalerne in By d a. limilicer
Tubalcer ConsicuaEUE F. C ( N, In P C2 p. Pandem figura parabolica TIF xv
subalcerne ponatur in HFne, vei er Rgura HI FcX subalrerne consticuatur in HL F aB,
de incelligantur parallelogramma rique pertecta.
Constructio Ficurarum particularium.
TT clarius in sequencibus procedamus, cransferaneur rectangula qux in (chemate
onivertali sunc incer parabolam C A, diamerrum B C F, _ parabolas subalcerne
Policas in schema parriculare primum, ee corpora orca ex ductu rectanguli M in (C, I.
inse, K in se, Tin le, irem corpora orca ex ductu rectansulorum R, S, Y, V lingulo-
rum in Ccipla, vocenrur corpora M, L, R, P, icem corpora R, S,T, V. Icem cOrpOTA
qua nalcentur ex ductu rectanguli M in a rectangulum, rectanguli L. in d, rectangu-
li K iny, rectanguli LIn B, VOCENEUT COrPOTAM N, L. S,K V, LB linc addico, vei d COr-
Poragux exturgent ex ductu recransuli R in e, S in O, T IM H, V INM, VOCENEUE COE.
Por2Re, 50, I X, V y.
In SecundUM VETO SCHEMA FeLCFANEUF RCCFangUIAMO, L. P, RO, IN, icem eZ.
Z, x Zi n c ac reccansulo quidem M O in schemacerniverlali, licae quale reccangu-
Jum 9, in secundo schemace particulari: reccangulis vero L P, R O, IN in vmuer
Tali, aequalia sine recrangula, P, O, N in secundo parriculari; icem recrangula X, Y.
Zoaqualia rectangulis eX, 0 Y, dc. Denique reccangulis  n, Ed, vγ, pB; DR, DS.
bT, aV in ruiuertali, aqualia ponancur in parciculari lchemace , E, V, 1; 6, P, V. a-
AC corpora quidem que nalcentur ex dueru reccanouli in le, O inle, Pinle, N in
Sc, irem ex duccu reccanguli Z in (C; Z in (C, Z in lC, WIN LC, VOCENEUF COTPOTA O. P
OH, eC. Irem ea quxe exlursent ex duccu O in v, ex P in 5, O inr, N in pu, _C. Vo-
oencur sinc addico corpora ∞, PE, Ov N p; = B, XD. L. Y, coa.
PRCtSFL1O
L
Llis poliris:
Dico quod proportio qua cA incerrationes corporum Mn ad R e
X XB, ad Da, candem ese cumm proportione quae est incer rationes cor-
porum Ld, 2d50, ∞ YP ad PE
Demonstratio.
cranguli ZadO hoc estrarionerca Mdd k, d ex cactne recranguli d ad pajus
 HOC CsBN ade, F ademisitur es raTH CMIPOTIS M N ad RG, Lrario corporis Z B D Percand
se cum latione quae est incer corpera L’pu P3. Hamcurlus tacto corporis Ld ad50.
componca est ex ratione recranta L alS. d reccanguli d2d0; LaII ducem cOrpO
ris YP ad PZ. ex iildem compolies cponicur enim ex ractene recranguli Yad
P, chocestrectanguli L. act sealsoherecranguli  ad rectats  Hoc C CTerm
recrangulidad0. Cua rtobique rationes exdem sinc, cric proporcio quxe est
inter ratiOneS COrpOrUM MIN, 2d R e, X Xd ad O , eadem cum proportione quae
est incer rationes corporum L. d, ad 58, e 2 ad PE. Quoderat demonsrandum.
per 104.
Tamratio corporis MN ad R P, composica est exratione recranguli MI ad R, et
recranoulin ade. Icemrario corporis Z8 ad O  compolica est ex ratione re-
2d 0 0. Fodem discurlu pacee racionem quae cst incer corpora L de 50, candem es-
MMMM 2
rigura