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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 396, page id 1815201908:0453
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# Lines: 54 recognised, mean confidence 0.87
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it n ei i1 .1I
P A R ABOL A.
17. D. cerciam duplicata estrationis C D ad F. C, id CA F C, ad F. G: CsL AUTeM VEDHL
broeressio ad C D, SIC FIC ad CHCL VE F C ad P FI, AC FP ad F L, racio igicur (LC a0
b1 Depro. C. K, duplicaca es lacionis FF 2d F. L. Quod erac demonstrandum.
PROPOSTFTO LXXIV.
Irad AB C parabola diamecrum AD, ordinatim polIFa D C: crectaq.
ID exC diaeirOC F, iunsacu C A, ponaturque ordinacim quaevis FF.
occurrens parabolae inB, e A Clincta in C. cum ex B demils a diametros
quae A C lincx Occurrar in LB Ponacur per HI ordinarim linea l L. Occur.
Dicolineam GB ad DL, duplicatam habere rarionem ejus quam ha-
nibus.
gressionibus.
390
bec HK ad KL.
rens diamerro FC in L, de sectioniin R:
Demonstratio.
Voniam EaM FP, BF, cOF linex, quam L I
KI, LLL lunc proporcionales habences xquales
primoscerminos F F, L. I, racio C F, ad FTI, cerrie
adcerriam, id estrario GF, ad BL, id cAt d C+B ad
BF; duplicara est crarionis FB ad TR, scounda
ad secundam, id est racionis TFT ad TR, id cAt
FLK ad RL. Ouod erac demonstrandum.
PROPOSITIO LXXV.
Adem AgUTA MAMCHEO:
Dicorecrangulum F. G B ad recrangu.
lum FP B, criplicacam habere racionem eius
quam haber linea C B ad lincam BF.
Demonstratio.
Q Ectangulum E GB ad rectangulum FFB, rationem habeE Composicam exra
Seo ABC parabola, alum plosu  p
ucria puncro quonis A, duCanEUF reCIA
AB. AC occurrences irerum parabolx: diuilis
aurem AB, AC lineis proporrionaliter in D et
E, erigantur diameeri F. C, DI, Occurrentes p2.
rabolein F _ HI, X actx per A concingenci in
C42. BHF
gressionibu
27. D
rogressie
1. D epr
res
Per ele.
nenta.
EB ad BF. Ouod erac demomucandum.
cione SF C ad P F, id est ex duplicata rarione F. C, ad P B, id est C B ad BF,
nArhuius. (quia P C, h F P, P F sunc proportionales) e ex C B ad BF; igirur rectangulum
E. CB ad rectansulum P F B criplicaram habee racionem eius quam habet linea
eROPOSITIO LZZVI
DiCOGE, DL HnCAS IM F d FL, PFOPOH
nalicer esse divilas.
Dethon
 e ee  e  e s e et  s e e e 1  t 1 e te t et et e e  t  e te et t te s e u 1    u  t e et   te su  e res s e