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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 271, page id 1815201908:0328
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cellet
da
cao
CLLIPSLS.
eR OPOSITIO LI.
Eliplm ABC secent dux quaenis parallela AD, BC, iungancur q
1AB, CD.
Dico AB, C C scemenca esse aqualia, ee si segmenta fuerine aequalia,
dico BC, AD lineas aequidictare.
Demonstratio.
Tuisis A D, B C BiFarIaMIn F eE F, AGACUE PEK F e
F linea F F; occurrens elliph in FP, eric illa diame.
CCF. QuarE BFFI; C FFT Tegmenca a sune aequalia, rUT-
Tumquoniam A E; D F aqualeS (UINE, RE SEGIMCMEA A FI F,
DHTF equalia erunc: ablacis igicur aequalibus seomentis
BHIF, CHTF FCMAMENE SESMENEa AB, FF, DC, FP
aequalia. Deinde quoniani AF, F. D sune aequales, et
alticudo communis paraHelarum BC, AD, CrUNE AF
EB, DFF C crapezia xqualla, igicur ab aequalibus se.
BMENEIS ABFR, D CF E, crapeziis, ablacis xqualibus
manene AB, CD teliqua sermenca incer se aequalia:
Duoderacprimum.
Sineiam AB, C D sesmenica equalia, iunsancurque
BC, AD; dico AD, BC lincas a quidictare: sin vero, du-
catur ipsi B C parallela AG lungancurque CC: erie
igitur perprimam parrem huius segmentum AB aqua-
Delcemento CC: sed _ CD segmentum ox hypochesi xquale est AGMenEO A B.
Tesmenca igitur CD. C. C sunc aequalia, quod heri non porest, cum punctum Gca-
dac supea vel infra D, adeoque CC Termencum inaius vel minus sc legmenco CD:
isicue AC lincanon a quidistar ipsi B C; (0d Sola A D. Ouoderac demontrandum.
DuodEpunctum dacum D idem sc cum puncto A.
duCatur AL cangens. ellipsim in puncto A SIvC D; (TUNE
enim A e D iam ex hypochea bnum idemque pun-
atum) ductaquo BC parallela adt AP iunge 1O.
Dicohane abscindore segmeneum DFO a quale sC
emenco ACB.
Ex contactu dueatur diameter A K, igirue DC qui
cansencix quidistar, est ordinacim b posita ad diatheerum
AK, adcoquebilecta in FI; criangula igitur B AFI.
CA HL equantur; xequancur veric _ segmenica B C AFII
CF AHI. ergo reliqua eriam scomenca BC A, GF A(.
hCCEB EGUAREUT. FaCUM isICUE eA quod pCLCBATUT.
PROPOSTTIC
Ecet elpuim rocta quaenis AB: auterens
CDresmentum, e decur in peripheria
punctum quoduis D, oporter ex D rectam ducere DF, que auterat le-
smencum DE F, aequale seGenTO ABC.
bouint
b13. huins.
C45. htoito
Con-