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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 594, page id 1815201908:0651
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AXPERBOL A
ROPOSITIO CZXV
NTeF alyMPEOTOS AD, A C
Lcur quaenis dux parres rerminata rectis DF, P CB a sII, LC, qua
aequiamtene alymproco AB. sic aurem Cuperticies D F Ql C
Turabitis plano HIC. K:
Dicoluperhciem D F. OP e
ries concinere supersiciem LL LC , 4u
nsticuta sic tixperbola; ex qua assuman-
ciesratio linex DF. ad P CSlationem HIL ad R C.
sicbi
e
Voniam commensuraponuntur quancirares DP OB, HTIC K, Cam in-
2sdecimi. Lcer serationem continene, aquam numerus ad numerum: Sicisicur DL O P ad
B2sB. hu. Quancicatem IYTC K ve quacuor ad inum. Finneque de HII ad RC, sIC F. D ad
FC. Toirur segmencum FIICK scgmenco b DBOF est xqualc. Factaicecumta-
cione FG, ad LMI, de L M ad NO cadem, cum ratione DF ad F C, criine
sCgmenta POML, C MOWincer s0 xequalia, ee singula aequalia segmentOD R C P.
hoc cA HICK segmenco. Porrn cum luperticies D P. O P ponacur quadrupla su-
perticies HITCR, crie quaneItaS NOO P quarea pars quanticaris D F O P. pro.
indeque NOOP seomento HIIC est sequales isitur est NO ad P 9, ve linea
TII ad R C. eHt aurem rario D P ad P Y, compohies ex mulciplicacione racionis
DE ad F C. hoc CA HI ad KC, de exrarione P G ad LM, hoc est HII adK C.
de racione L. M ad NO, hoc cA HI ad R C, e candem exrarione NOad P.
Igitur rario DF. ad PO, composira eA ex rarione D R, 2d F C, quadruplicata,
sed etiam quadrupla ponicur quantieas D P. O P scemenci HIC K. ipicur cories
mulciplicarracionem HII ad CR. racio DF. ad P, quocies contince luperticies
DF9. Supertciem FIIC. Quod Fuir demonstrandum.
eROPOSITIO CXXMI
1
VInE AB; CD, E F, parallela asyMpEotO HTC hyperbOLZ ACF, et
supertcies ABD C incommenturabilis CDF F; quantitas aurem
ExId. CB L, Guolles porest, Tublara a luperticie s ABD C cermineturin lin
int.
sims.
nea R L:
t 1
quories luperticies K L. DC conriner planum C DF. L.
Loraiodem K Lad C B coltespe alonem C d , +.
Demoi.
a eeac e esarre ero oeoaer  eaisee e