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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 63, page id 1815201908:0120
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GE OMET RIC A.
PROPOSITIO XII.
Eneur reslinex in concinua ratione AB, BC, CV, ad veBC sic
Demonstratio.
MI POnACL U COMEMU2 analoBia A B; BC, CD, iditur erie ve B Ca aa C D a L. Huin.
Ita AC, hoc est ex constructione BF 2d B D. Frgo diuidendo nDD daDC.
ita F D ad D B: _ inuerrendo vei CD ad BD, ita le habet BD ad D F. OuAFC
BBD qUadrATM RQUATUE F. D C rectangulo; quadrarum autem cB F, aequale cA c q. Secuni
7. Sext
quadratis BD; DB, ∞ rectansulo F. D B bis lumpro: acqui rectangulum ABP D
Eequarur iisdem: nam rectangulum. A B F. D; EguaTuF F D C srectansulo(hoc est, ve dL. Secundi.
octendi, quadrato BD) ex rectangulo F D AC (hoc es rectangulo BE D, id est
rurtum e quadrato F D cum rectangulo F DB, _ rectan sulo inUPEF FDB, rC. c3. Sccundi.
ctangulum icaquo AB F D, oum iildem e quale sic; sequabieur B P Guadrato: pacet
sicur AB, EBB, BD eNelneoncinuaatulbsia. quoddehohsratidum Fuie: t l. lE17. Sexii.
maior AC, _ hacrecta AC aequalis BF.
Dico AB, B L, F. D esse proportionales.
La
DOnaneus AB, BC) C, lres linea in conrirsua propoitione; e Hac
Dico AL, LC, C L   Concinua analogia.
Demonstrario.
ondoquidem ponuneur este Con CmuX BLoporcionales linex AB, BC, CD, cC
Liam erunc continuxe proporrionales RB, DEs C Di et B C. medixe equalis D L
Crir quadrarum D E rect angulo AB C. D _ ualO, quadTALH AULEI SC P XGUAEUFCD, 5 +. Secun-
BC aequalis DFC.
DF quadraris, e rectangio C DR bis lumpio. Gurous ciam a quatuErectanoU-
Ium AE CD. nam rectangulum AF CD aequacur F C D rectanoulo (hoc est qua-
draton C D cum rectansulo CD F) ec rectansulo D C B, hoc CA (quia ex constru. h. 3. Secun-
atione BC, D F aquantuT) icerum rectangulo C D P. ex rectangulo in uPeF AB CD,
(id est, vemodo ostendimus, quadraco D E) quare rectangulum A P CD cum ijsdem
equale GE, quadrato C P. aequarinecessc CA: ad eo que CD, C P, P. A esse in conci-
noa analogia. Ouod erac demonstrandum; o
INE AB, AC, AD, in continua analogia; ee hacve AB ad BC, it2
eam ceADdaDe; HCB Mat 2aF.
F lit
DicOF _ F cNcinter le aquales.
Demonstratio.
Voniam supponuntur concinux AB, AC, AD, A Aac D G a qualis B C, CFUHE
Lconcinux AB, BC, C C, ergo cum ex daris eriam sine in concua rarione, 13. Ruius.
AB, BC.