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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 338, page id 1815201908:0395
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1 1 . 111
236. tersi. M F R, hoC est rectanguI2 2 N FR, I_ CH L RTT. CrGO reCtAnGUIIA FK TT sunE ad
POSLTIO CLXXX
E L L IPSIS
3d
se invicem re quadrata F. L id est quadeaca J. I. Quod erac demonstrandum.
Demonstram.
eca LLLCParaIICla ipAI AB quxe cir.
Dico AFF, AElB segtenta esse aequalia.
Airculum A B C cujus diameri AC, B D le decultane ad rectos, con-
scingar in B linea BF: descriptain ellipli per A, C puncta qua
contingat BF. lineam in L, iunsancur puncta AC, AB.
culum concingac in El ducacur exI
linea FFO, paraHlela ranseneI B R OCCUT.
teelliph in Li ex rectis AB, Al. L. B,
BD in N, PP, B Oiunsancurq; pucta BII
AFI, FF, F A, dein per s ducatur siMCa
FL aequidistans ip(i AP: Duoniam tan
FIK cangens aequidictat rectE AB, quam
E L ipA A F, CED aucem dE IL cangenS,
CFUNECAEIB, A F F. criangulorummaxi
maque leomentis AFTB, AF F inscribi
dicta triansulorum ncpCo. Aritque semper aequalium de maiorum dimidiis se.
Bmencorum snC cermino concinuari poliE, sesmEntA B AHB, AF. P. xqualia sunt.
Duoderat demonstrandum.
Corollarium.
Lenim Ccortiencum ATIB octenlum aquale sCgMENEO AF F, Cunc aurem criangu.
la AB D, H F. D Cuper eadem basi e inter ca(dem parallelas costicuca incer le equa-
lia, isicur quadrans circuli AB D Equalis est quadranti ellipsis AF. D. ergo semi-
circutus AB C. Equalis est semietlipa AF C. Quoderacoltendendum.
nectu a cans DE, parallelam diametro AC: secet
aurem AF. C ellipsis circulum ABC in F, ducancurq. linex AF, CF.
Dicolesmenca AIF, CC F esse xqualia.
Paret
13. g 42.
vins
43. bu
i15.
us
F43. buint
haius.
3174. 1
PONunE; dac proinde plus quam dimidia suorum segmencorum. Rurtum cum
criangula ABD, AF D sinc super eadem basi _ intra caldem parallelas Con-
RITuCa, _ FTM linca xequidistee basi AD, crunc OI, NM lincae c aequales; sed
170. hu- 8 cOEx FII, FM, sunc Exequales, Suu e relique HIO, FNinter (C xquantUr: Oua-
eecam criangula TV (D B, NF. F, quam criangula HI A O, N F A, adeo que tora crian-
316. ero Sula BHA, P F A sune xqualia. eodem modo s residuis Cesmentis criansula inferi-
rss. siuel.2. Bancur, ostendemus criangula reliduo circuli inscripea xequari eriansulis residuo elli.
Breosinscripea, _e veraque maiora amenss esse luorum legmeneorum. Ouare eum
Iidem potitis sequicur semicirculum A BD Equalem esse Cemicllips AF. C; est
PROTOSICIOCLRKAI
AbCANE A BC Pemicirculus de A F C semiellipsis communem dia.
Demon.
ttus u  ite hti te  e ate  te  t  tet  e et   e te  e  e p e te et t e ta te ete t ei t te u t u e pe i e ite    e 1 1  1 l