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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 194, page id 1815201908:0251
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# Lines: 50 recognised, mean confidence 0.88
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et    p u e 1 e1 11
IR CF L VS
P R O P, OSITIO,XLVII.
ectam D BF. Poneres eua recta, aqualem BF. consticuat.
Constructio ex demonstratio.
DOnanEuE AB, C B concingences in B, circulos
ABD, BP. C; occurrences perimetris in A e
C: dein per A, B, C, circulus delcribacur ABC,
quem in B concingat D P: dieo Factum quodpo.
Culacur. octensum est enimlesmenca, ADB, BEC,
ABC esse incer a le Cimilia adeoque DB
tangencem in B diuisam bbifariam: poluimus igir
cur per B rectam; _C. Duod cras Faciendu.
PROPOSITIO ZLYTII.
Ecencinnicem repriuscilculi duo ABC, AHB in A de B. Opor.
ceac ex B rectam educere BF. F, ve E Fperimerris incercepra sic data
Construitio e demonstratio.
Onsticuneur BC contingens circulum A HB in
B. oporcec dacam lineam D, hac concingence ma.
iorem non eNC; iunetis A C AAE VE C B, ad AB, ita
D, ad C. Dein ips C Hnc aequalis AF, d iuncta BP
perringat in B: dico factum ese quod perieur. Ducacur
enim AF. quoniam angulus AF B cam cum angulole.
smenci AHIB, id eA ABC angulo (ob C B cangen.
cem) quam cum AF B, duobus rectis cA xqualisi dem.
Peo communi AF B remanebunc equales anguli AFP,
AB Cisunc aurem e anguli ACB; AF B cidem inf.
Rences areni equales: similia igicur lune criangula A P P,
ACB. vndo AF est ad FF. ve AB ad BC, id ct
per constructionem ve C ad D: de Permutando ve AP
ad O, sC PF ad D: quare cum AF, _ C aequales
POHANEUT, CTUHESE PF, D linex aquales. Pertecimus
isicur quod postulabatur.
PR OPOSFFTO XL. IX.
Ndato segmeco circuli A BC, ex A, ex C duas
lincasinclinare, Pele inperimetro decussantes:
quae datam incer se racionem contineant G adH.
Constructio es demonstratio.
Tuisa in D rectâ AC, seomencum subcendente, se.
cundum racionem C ad FI; bilCCCET AFCUS ARC
In F3 _E PEF D ex E, rECtA PONAEUE FD B, iunganEuE
AB, BC: Dico AB, B C ese quelicas. Cum enim an-
Suli ABE, P B C aequalibus arcubus insIsenEeS equa
c3. sen. Les line, eriec AB ad BC VE AD ad D C, id est per constructionem ve C ad FI.
ClRCV.
Neerlecent seleinuicem duo cireuli AB D, BF C in B. OporreaL per B,
2II. huiu5.
ta Amiuia
Equalis.
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