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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 621, page id 1815201908:0678
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=678
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 68 lines, status machine
# Lines: 68 recognised, mean confidence 0.83
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

Derbo.
I: pe
nE p
dito
Bolam
erian.
OH
dina.
iuII
niam
de
icu
situr
aEu
nou
acum
HIX P E R BOL A.
AAE ad YE, id eA IF ad dE, vE LB ad cB, id est B C ad B Y. est aureim etiam
622
vE FT ad TR, AC B C+ ad CF, GuIa LR. CHL in l a L. bissectae luNC, ex COn-
permucando OVl ad N=C ve OEI ad NBC. id cl HLLM 20BL, per
anee demonstraras similicer ostendemus, si residuis segmencis OT, II icem N X,
XC criangula insecibancur maxima; criangula Cegmentis OT, T PMMcMpCa CHC d
rrianoula leomentis NX, X C inseripca, vE F MII criangulum est ad crianpulu
116. D
BL C. Ouod crm heri possiehine cermino, constat a lesmeneum LFO esse ad (e- progressions.
smencum eXNV, ve PMI criangulum ad criangulum BP C: addicis igleur crian- bus.
sulis NVCFI, ORI quae proporcionalia octenla limeeriangulis BI. C. LM L. Palel
semitrperbolam NX CII esse ad semihyperbolam OTIFI, re BL. C crianou-
lumad erianiguluim F. M l: quod propolicum fuic.
P. RO POSITIO CLXXV
perbola dd eandem applicacae diamerrum e communi gaudCHTeS
ranluecca, Candem inter se habentrationem, quam ordinatim poli-
Demonstratio.
lc. AB diamecer cransuersa communis hy
perbolis BED, BF F: posiraque ordinarim
ad B C diamerrum, linea F D C, bisecCTUEBC
in II s_ HIOF ducacur aequidictans F DC,
iungancurque puncta BD, BB, F FG FB, GD.
EB: ve AELB rectangulum ad rectangulum
ACB, EcbHIC quadracum ad quadracum DC.
_ F HI quadearum ad quadracum F C; igieur de
H C linea eltad D C lineam, ve FII ad F C,
_VED CAd BC, siC FF C ad TTF: lCd VEDC
3d B C, sC HIK elt ad IHI, recte igicur HIC
F TI proporcionales (UnE FIK, TII: quare ve
EIG ad FTF, lic OK residuum ad residuum
FI: CRauceM VE GK ad FI, sIC BCR crian-
sulum ad eriangulum BF (, ad eoque e BO D
2d BFF, criangulum isitur BGD ad BFF,
criangulum est vr CHI ad F HI, id cl vED C ac
F C: Similicer R relidux BII, HIC biseceneur,
ee a sectionum punctis ordinacim ponantur lineae, hancque triangula ve prius, olten-
decur criangula reliduis segmentis BCD inscripea, cAc ad criangula scomeneis B F
FP inscripca, ve DC linca est ad lineam F.C: quod cum semper heri ponie; ly
perbola BDC est ad hyperbolam BFC ve BDC, criangulum ad criangulum
BF.C. idcuDC linca ad lineam F. C, hyperbolae igicur ad eandem applicace dia
merrum, ec. Ouod erac demonstrandum.
Sructione; ioicur d B~ al pE, ve Hd ad dR, id elt B= ad A O , H F L al LS.
e BO 2d OX, Ve FS al 3L, eMCF SA SF, HC OBL ertanoulum est 24
criansulum PTO, e HeB dd X. HC BC criangulum est ad criangulum
NXC, criangulum ieu BC  1XC CarLOIadOII ctasulum; de
ex candem habences alcicudinem.
Varum hyperbolarum concauarum ebe alteu.
PROEBSITIOCEZXVI.
IE lE H 1
Constru-
   u  e       e   s   p   e  e pe      e 1 1         l f  a  1  e