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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 281, page id 1815201908:0338
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 53 lines, status machine
# Lines: 53 recognised, mean confidence 0.86
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EL L IPSI
BF A minorem lectore DF. C, quem cum axe facic did.
MCTEE DF.
Ouoniam igicur sector D F. G maior est sectOre BF A
AaEleCEOE FF C aequalislectori BL. A3 _ FL occurrat et
lipsi in C ducacurque BO C; sector BF A cquacur sectori
Fi P C ex constructione hoc est: sectori ad vercicem AF. C.
Ergo DBC. bilecta estm O ab axc A C. anguli ergo adO
recti lunc. pacec ergo angulum BE A aequariangulo AB C,
hoc est angulo FF C, hoc estminorem ese angulo D F Ci
liguecigitur ex primo BF. qua sectorem facit cum axemi
norem axi propiorem eAlc quem D E, quae MaiOTEM.
PROPOSITIO LXLII
Ectangulum sub dimidiis axibus aquale cle PX
Crallelogrammo sub Cemidiametris coniugaris.
Demonstratio.
2InE ABC elliplisaXCS AC, BD: cen-
Derum E, e guanis semidiameeri coniu-
SaEX EF, BG. actilquE PEF F eE G can-
sencibus qua convenianein FI, X axi AC
OCCUTrAHEIN T_EK: ducaneur ctiam per C
e B linca quae ellipsim concingane in C
_ B: CONVENIANE AUTEM In MI: _E FTR, PF
secenem O, L. N: cum iunctis punctis F. O
agacur per Acanigens, secans F. N lineam
in P. Duoniam cam NO, R F. clince quam
OK3 NE. Sbi muruo aquidistane; crie
NOKF paralleloprammum, diamerro
OF dinilum bitariam: sune aurem eriangula d F OB, F O C aequalia, igitur _E rC. 838. Duius.
liguarriangula PBN, P OK InCCF LCRQUANEUE. Rurlum cum C A P, C. L lineX  is huius.
xquidistene, _ AF, C F lineae sincaequales, crie F. C L criangulo xguale crianou-
lum E AP hocEC CF. IF. Ouoniam isitur eriangulum F. C K sequacur criangulo (70. huius.
E BDT d rriangulu TE F crianguloF C L, provortionalia crune quatuor illa erianou.
lai sune vero eciam similia incer se, nimirum F. C R ipA IF F, _ F BN ipA F CL.
ergoreCA KE, P L, N Fs F L, proportionales CUME. quare cum super propOrtIO- S E2. savel.
nalibus indirectum politis consticura sunc eriangula PF F, F GK, IFIKincer Ce simi-
lia ex criangula C L F; P. BN, L M N incer Pe quoque similia, re sunt duo criangula n60. de 163
TFE, FCK ad duo criangula L P. C, PB N, ica hi ctiangulum F HIR ad criangu. nei:
Ium LHNI: Acqui duo triangula PF F, F CK aequancur, re ostendi supra, duobus
TCP; F BN. ergo criam eriangulu PFTR criangulo LMN aequale est; ac proinde
dempris aqualibus paralleloorammum G F P ET sub semidiamerris coniugatis, x-
quacur rectangulo B F C FI lub dimidiis axibus contento. Ouoderat demonstran-
dum:
Corollarium primum.
 eMlucutacllipaaua quanilucalametcocala Conu altolco e en latis
PF, F. C. criangula TuPeF F A, PB, P. F, P C in angulis AF. B, FF O, eNcin-
cer se aqualia: lunc enim dimidia pacallelostammorum ae qualium.
Corollarium secundum.
Cquicur secundo patallelosrammalub cocis alamccti Comuzalio celteellea
qualia: cum linc quadrupla eorum que hac propolcione octeula tuneaqualia.
i tt 
c 13. Bt1.
t t  is p  tr ee p