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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 316, page id 1815201908:0373
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ar2y. hriios.
LlipSeoS axis SE A, C, poli D, L, ex quibus ductx SInEDB, PFO
Mormales axis ellipsim aurem canSac IL B I in B, occurrens axi in R,
recta VerO OF in L, iUngaTuTqUED F.
LL LP SIS
POSTFIO CXXXVII
Dico rectangulum F LC quadcaco D F aequale esfe.
b120. hucines.
Demonstratio
Voinam DB, L. B auc
clcte Fetio del rlcabu
aBut ABB, LBL 2 xqualc
Mmeote suta DB.llparalle-
lae anguluskBD angulo L lB
aqualis CIt, Xquanturigicur au
Sct LBR, F lB, C130BR, II
xqualeslunc. Dende quia le
ctangulaC L. LL, C DA baqua-
unexqualia, ad eoque _ rectae
LF, DB a. quales. Juare cuu
lia Cune, ccra quadraca L. L, DB
2x. huiu
OB, BHCXgu LL3LL
etiam BP. D F Xquales erunE.
Algur BF onca eC equalIS
EI. erso e DF CAaequalis F I,
e quadracaproinde DF, B IX.
qualia sUnE. Sed quadrata DP.
E F, aQUanEUE quadratO DP3
_, quia OF bilecta eA in P ci-
que adiecta FP, rectangulum GLF cum quadrato P. F aquacur quadraco FI.
quadeata ergo DB, B F aequantur rectangulo GTF cum quadrato F F. Dempro
isicur communi quadrato P. P, remanene xqualia rectansutum C PF ee quadratum
DE. Ouodera demonstrandum.
EROPOSITTO CXXKVIII
AIACH pOMIS AMCantur quorcunque alix O, FL, R, MI, normales aXI.
Dicorectangula HI, Q, M, quadraris DK esse aequalia.
Demonstratio.
Lcans M IIO, dIC In 5. quoniam NC, TC, OM luncnormalesaxi, aequi
distanc. erro per ca quae propol9g. huius demonstrauimus, rectanoutum F LE, aequa-
tur quadraco SI; de rectangulum IIO M quadraco O aquale cA: quare requa
dracum IS ad quadeacum O, hoc est requadrarum S B ad quadratum OB, hoc
elt ve quadeacum F. D ad quadracum RD, ita rectangulum F. PC ad rectangulum
EIO M, e permucando vereetangulum FLC au quadracum P. D, ita rectangulum
HIOM ad quadratum R D, sed rectansulum F PC Per praeced. aequatur quadra-
EO F. D. Ergorectangulum quoque ITOM a quatur quadratO RD.
Similicer dem onstrabimus ad alceram parcem poli D, rectangula ITOM qua
draris KD elle aequalio. cansar enim ellipum A P, in A occurrens rangenci in P, d
cactus iungac AB sCCAnS O MI in R. in crianoulo BCN, Ducatur aliqua O, Pa-
rallela NC normali ad axem, ira sc habens ad O B, Vr O R ett ad OB. cricixicur
PETU.
GLLIpSIM FANEAE CN in C, OCCUrTENS tanBCnEI BN in N, ducarurque BC le
u e e  e e u 1 s e e  . s e  et  e u1t t e e   t p t.   e u  e e e e 1e te    e e t   e   e   e te e ut  s  1 e e e ss