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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 203, page id 1815201908:0260
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ele
BV
de
11
ertin
a
les li
ND
AI
ncta
et
cet
A
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ud
CIR CYLVS
in quo circulus A EB secabar recam QC. Ount cum circuli K G H diametex
aequalis sic rectae OL, diametro circuli BL C O, sequalis quoque crie rectae IC
circulus igieur R GFI cranlic per P. Aequi eciam lupra oltenaus cenerum eius df-
Cc in recta OC tranlcunto percenerum circuli A E B; CFFO CITCHIUS R OLL CalIZHL
circulum AF B C. Ouod crac demonstrandum.
PR O P OSI F 1O
per ABC crianguli laceribus semictcus calibantur ABL, BIC.
RGC, QuOTUM CCHETA SINED, E, F, cemtris aurem F vel P, circuli
Construancur HC, KN, qui circulum AC C Concingancin C d H.
Dicocoldem, quoque reliquos concingere In. L, L L.
emonstratio.
TCaNEUE FF, DF G, DF. quoniam
diamerri AB, CB bilectae Cune in
Cencris B, _ F, erie P E parallela AC.
ergove AB ad EB SC AC adt F F. quac
ec cum AB dupla SIC F B r eFIC AC du-
ola quoque EF. Ergo AD dimidia iplius
a C, hoc est CD, aequalis eric F F lmi-
licer quoniameres diameeri AC, AB, BC
bilecta sune in cenerIS D B, R PACCE
ED; BC, _D F, AB essC Parallelasip2-
Fallelogrammum isicur est R BF D. ergo
FB hoc est FL aequalis est DF. OuarE
CHIM EOTA F P EOti GD, _ ParS FF, parti D F. xequalis sic, rehiduum quoque TF
aequale crirresiduo C F, Hoo est circuli diametro CF, siue F. FI, quare punctum 1.
commune elt duabus peripheriis OII ec BIC sive puncta FI ex I omnino cadem
sune incer se. Vnde cum. R. F Per cenera circulorum ducta per Lpunctum eranteae,
manifectum est in eo concactum heri eodem pacto de alcero circulo cenero F de-
Ccripio demonstracio proceder.
PROPOSTTIO LXV.
Netiansulo ABC, sinc in continua analosia BD, B A, BC: d per
puncta A, D, C describatur circulus.
Dicocum rectam AB contingere.
Demonstratio.
Tonam ADC. puncta in perime.
lunc circuli, igicur sinon concingae
ecta AB, circulum, occurrac eidem in
alcero puncto F: igicur rectangulu AB R,
aequale erie rectangulo DBC, hoc est
perhypochelim quadrato B A, quodb eAt
absurdum: quarenon occurret B A, cir.
Monikiin A.
P ROPOSITIO LXVI
1 super AB C rrianguli laceribus segraenca circulorum similia deleri-
Peatuerint,
L X IV
Dico