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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 249, page id 1815201908:0306
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meter
calerip
cum
int
ExO
eunes
n
CCM
B
Pit
H.
etoc
pest
D
F L. LIP SIS.
DO ad CiF, hoc eAVE DG ad CK, sic G P ad RF. ErgO punCtA DCF TunE
in directums (ed eciam puncta DCO, lune in directum, cum ex Hy porcn DC.O
siclinearecto. Vnaisitur cademque recta TunE DC B, de DCO. Aequi, DC R. bi-
secta est in C, (cum enim ex constr. C+F, F C sinc pacallelae, cric ve D F 2d F C, (c
DC ad C F.) Ergo etiam D C O bilecta est in C. Ouod erac demonstrandum.
P R O P O, S L, F, L. O oV IIL
Aea Ecellip(IS A DC FB, cuius diamerer SIC BHI; OcaInatIm NIO aa
diameu aPPIICATA L PR: cenerum cllipleOS G. DVCTA AUFO CIE
percenerum C, recta AC. C. ordinacim applicaca parallela.
Dico BH, AC diamerros elso coniugatas.
Demonstratio.
Vmacur in AC quoduis punctum MI, per quod duca-
PEUE KD diametro BFI parallela, occurrens ellipli in
punctis D _EK; ex quibus dUCANEUE DFR, RNL.
ipA IR parallele. Ouoniam igicur VR. NEparalle
logrammum est, rectxe DF, RN, adcoque e quadraca
DF, RN aequancur. Duarc cum 2 rectangulum BF II
Cic ad rectangulum B NFT ve quadracum DF ad qua-
dracum RN, rectangula BF PT, BNII eriam lunc X.
qualia, ac proinde, vrostensum in praecedenci, B F X NTII
EquanCUT. TUNE VerO _ B CF, FI C aequales. UrgO e reli-
que FG, N C aquales sIIMC, Sive FN bilecta est in C.
Eroo dRD parallela diamerro BFT bilecacur in MI ab
AC. Smilicer ostendam quasuis alias diameero BF Pa-
rallelas bilecari ab AC. Dugro cum eriam b AB BilCCCF
DE, L, R coceralque omnes quae sune ordinatIm POCEX
ad BHI. _ Parallelae ex hypochehi ipsi AC; Pacec exde.
finicione cBH, AC diametros esse coniugatas.
Corollarium.
Va per cencrum 2d ellipleos axem dacum perpendicularis ducieur, est axis dato
Laxi coniugacus.
Exdilcursuiam allaco Facile sibi lector demonstracionem huius reieliciet.
PROPOSITIO 1X.
Atalic ellipus ciulque diameter BHI.
Oporceat diametro BHI coniugatam diametrum exhibere.
Constructio e demonstratio.
eacur recta aliqua K D parallela det BFI, ee veraque DR, B IL dsuisa bitariaru
in M de C, Per M d C, duCREuT AC
Dico AC, BHI coniugacas cAc diamerrOs.
AC primo quidem reCFaM AC CNCAAIHCCEMIH PACeL CL G. CtiuS. eF B FI diameter
est exhypochelis amba igitur sunt diameeri. Onod aurem sine coniuracx sic osten-
c defin
d0. Ononiam AC diamecer est ex bisecat R D, erir dF D ad A C ordinacim appli- d definit. v.
eata erro d reliquae ipsi RD Pacanera, ctam aa A C ommaum applicatae, hoc ele
Cz diamerro A C bitariam lecabuneut. Lea DR ex Constructione cum libi paralle. c ibid.
IS, Palaela cMad alametrum B fl. ergo diamerer AC bilccac diamerro BII p a-
Callelas. Ducancur deinde DP, parallela diamecro, AC. es L _, Parallelar eAta D H.
Facal.