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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 88, page id 1815201908:0145
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# Lines: 50 recognised, mean confidence 0.80
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# After the first blank line: the recognised lines in reading order, one per line.

s . e n B2, B P I
PR. OCR ESSTON LS
 1dBCt 55~ L CIL B EeE.I
lis t A CELeSCAS CslS
ti.  CCorollarium. sleE BR  M Clvel e, CBE
etocum perpranam huius, etiam continue proporcionalium, disferentix sne
in concinua at210gi2 luorum inceororum; manifectum est rectangula quoque
ABOLBCLR, CDKI, DE L. M, e c. ese concinue proporcionalia.
. PROPOSITIO LX.
Ine in contindaanalogia AB, AC, AD.
Dico reclangulum ABC, ad AC D rectangulum, suplicaram
astatione eius, quam habet AB ad. A C lincaminoy , e pe
d. . 2 8 i _M5. i  LL B5. 2 d BL Ir A (5i1 133 leB E B  aMLWBMER
 L 15 1 D SuC 13IEDP CLIBHOM. Demonstratio: .1 2L1 1 B32 A et L.5 cil L. 1I
cst BorG,d. CaVIBC. Ba
Voniam D A, C. A, D A ponuneur continue proporcionales, erie DC ad BC.
ve C A ad B A, et errendo BC aAl C D, ve AB ad AC: icaque cum rectan.
b23. Sexti. fullarum AB C, bZLCD racio componatur exlacerum racionibus AB ad A. C, et
BC ad C D; que La ostense lune aequales, constat eam esse duplicatam, rationis
AB 2d C. Subderas demonstrandums
eR OP OSITIO LXI
Dico ABC rectangillum ad rectangulum A DC, eriplicaram ha-
bere lacionem etus sam habet AB ad AC.
et 
racti Demonstratio.
 datisrario A. B ad A D, duplicara estrationis A B ad AC: RE DE PAFCE Ex PEX.
cedence ex per primam huiusrario BC ad CD, aequalis est racioni AB ad A C
ergo racio composica ex racionibus AB ad AD, e BC ad CD, criplicaca est
rationis AB ad AC. Quare cum rectangulorum ABC, ADC ratIO Ex PFOPOT-
Nonibuslacerum AB ad AD, _ BC ad CDc componatur, paree caim ese eri.
plicacam racionis AB ad A C. Ouod exac demonstrandum.
LR OP OSITIO LX
aT. FIHIUS.
IIdem politis:
et clot ilises oei
Dicorectangitunt c. FI, de L. Drectangulum, criplicatam ratio.
nemhabere eius, quam habet BC rectangulum, ad rectangulum F C.
Demonstratio.
DOnaneur dux series quaruor concinuarum A, B, C, D; eC E, F, G, H.
um lub L. _ D, cacio es compolIcu dexra
tone A ad D, d II ad B: racio vero recranguli B Cx, ad rectangulum FC
compalica est exratione B 2d. C, ex C7 ad F: rarin aurem A ad D, criplicaca eAt
P
3. Sensi
sub A _c FI, ad FCCLAH
rarionis B ad C, ex rario FI, ad. F eriam eriplicara est racionis  ad F; igitur racio
reccansuli AEI ad D P criplicaca est racionis eius, quam habet B C reccangulum,
aC. uba po at.
R0.
i  e   1. . . t      e          p     1 . e p     mu muad