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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 731, page id 1815201908:0788
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Du
1
e
CN BL A N, V M
Demonstratio
Vin enim AD minox ponacur dupli ipsius GFF, pacec AF Ecclalisatum in2.
ius elle reliduo FD: similirer ob eandem rationem. GF maius est quam
FNHT; _ F K MIUS ipIO RM F, aC. vnde AII, OF, PK, TC. Fixurx simul cum
Pra, maiores lunc cmisio Rgurx mixrilince ABC D. Ouoderac demonstrandum.
Scholion.
Ora: si eadem construc s p cCdeha methodus servetur I resolluis fieuris OHD.
iN FI, exc. patet Tectangula illis inscripia, simul sumpta, maiora esse acmali peurarum
DFID, EN EI, Cc. adeoqe per similes ablationes tandem residuam relinqui. ex tota ficura
mixrilinea quantitatem, datâ minorem.
PROPOSITIO XXXVII
Se AB C Rgura incercepra duabus lincis AB, A C rectum angulum
scontinencibus, perimerer vero C DB concaua lic, divisâ aurem AB
bitariam in C, ducacur OD parallela AC _ DN aequidistans AB: dein
ND bitariam dinila in FI, ducacur HI F aequidistans AC X F O, ip(I
AB aquidistans, e hoc lemperhac.
Dico rectangula hoc pacto ablaca concinere plus dimidio heurx mixri.
linec ABC.
Demonstratio.
Delticiancur rectagula Be D, DHIF F IF, aL. erun
illa aequalia rectangulis A D, N B, OF, 8 c. ob sub.
dinisionem lincatum Ber aequales parces: sed OL. HIK
LM reclangula maiora sUnE RGurIS mixclineis BDO.
DE HL. P. F L igitur _ rectangula AD, N B, OF, _C.
Sitrul Cumpeamaiora sunc fguris BD C, DF FI, F F L,
ac. id est reliduo fixure mixciliniex ABC. Quoderat
demonstrandum.
Sed ABC Agura incetcepta Fecris duabus.
laotoseta
+AB, BC angulum ABC reccum conci
curuicacis.
menribus, e AD C perimeca aa AOquadritariam in HI, 65,
I: ducancur HD, GF, lF. fucalicta BC; uK, CL, FM, aequidistan-
res AB, ica vereccangulis A  ac
1c
Dico HH. CV. 1M, asulad  pras maioreo esse dimidio F
poraBC.
Demonstralio.
Vancitas FIK maior est EguTa HI A D; ee
LKL maior CRipsA D R Eidein e LMm~L
For quam P. L. F: parec aucem IS maiorem ese
BACA MI F C, IBICIE HIK, GL, IM AguTA A.C
Muaaao suc maiores Aguris HI AD1
DRF, L.L. L, FMC, id est residuo hgurx
ABC, Saur de maiores dimidio hgurE ABC.
mubnen AC
u a du.
1