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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 70, page id 1815201908:0127
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. 1 . t t 1. 1. 1 1
P R O GR FSSIO N FS
emonsratio.
217. Sexri.
16. SeX1
similirer rectangula BCTK, _C D RL, aem incerse, quia eidem quadrato N,
EX hyporhesitincx AB, NI. HTE lunc concinux proporcionales; icem B C, NY, YY:
Leroocam rectangulum ABFTI quam rectangulum BC IR a Xequatur quadrare
NI. ac proinde rqualia luncincer se rectangula; ergo ve AB ad b B C, SCIK adIII,
aequalia lunc; igicur re B C ad CD, siC RBKI: acqui ex daris BC est ad CD, ve
A P ad B C, hoc est, re octendi, sicur IR a LLL ergOR L, cstad TK, ve TK ad TIT.
continux lunpropooalessu  , R L. Quoderac demonttranaum.
Ke votii
X L LV.
3. Seriio
continue proporrionaliu caaorum bales LInE in CoMCHua
plosia: erum e alltlidires in conrinuald proportione.
Demonstratio.
EINE AB, BF, F C, GB LL, intupeF _ rectangUIA AB CD, BE DF, E O F H _C.
in concinua analogia. Dico eriam C D, DF, EFTXC. ellecontinue proportiona
les. Rectanguli enim ABC D proporcio ad rectansulum BF. DF, C CompOnIEUE ex
rationibus AB ad BF, de CD ad DF: irem rectanguli BF DF proportio ad
FC FHI rectangulum, componitur exracionibus B B ad F Ci ec DI ad FII: qua-
re cum ex hypocheli rectangulorum AB CD, BF DF, L G F FI, xquales sive eedem
PFOPOETIONES HME, CrunE quoquerationes AB ad BF, _ CD ad D F, simul sumpex
aequales, sivc exdem cum rarionibus BF. ad E. C, _ D F ad FHI Simul Cumpeis. sune
auTE ex hypochesi eciam aequales raciones AB ad B F, _ BR ad F. G; OuarCS ab
aequalibusrationibus, nempe a composica exrationibus A B ad B F, _ C D ad DF.
icemque a compolica ex rarionibus BF ad F. G, _ D F ad FHI, auferas xqualesra-
ciones, AB ad BB, e BF ad P C; Pacet reliquas proporciones CD ad DF, _
DF ad F FI Forc aequales: ve constae ex definicione compolicionis proporcionum.
continue lunc igicur proportionales CD, DF, FHI. Simili dilcurlu cciam reliquae
TTK, RM. XC. cum praecedencibus oandem concinuabunt rationem. ConstAE eryO
quod propolicum exar demonstrare.
Corollarium.
Odem genere discursus, s rectangul2 A B C N, BF DN, F. GFN, eec. icemque
pases AB, B P, F. C, exc. sine in concinua analogin, demonstrabimus eorum alci-
cudines CNY, DN. F.NI, ec. concinuam quoque seruare analogiam.
E R OPOSITIO ZXV
Suantur denuo AB, BC, C D proporrionales, vei criam Ll
(7. GFI; _LacIo L1D al L F, concinuetur quomodocue iu 1
RR. P: _MIIMIMet TACO DC a FC producarur in L, NI, O: e rario CD
adCitl, pergacim l,, t, clc.
Aled eltato tofuteo d tenc  edtui corteltluate tlanitla
tOHCtIL.
Demot
   t s. i . 1 . p . 1. 1. 1  .  e  1 i u  . 1   u. p 1   u t ie   t.  s   1  tt. 1 1     e   11   et