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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 440, page id 1815201908:0497
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=497
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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 0.84
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

P A R A BOL H
2. I L tt.  L E1e153, sC1 5. V
oHCd.P O. S.F L. dC WIX. X IX.510IC
ordinarim ponancur lincae CF, C f: allunspeoque in AF. puncto quouis
Ci ducarur ex C ordinarim linea, Gl, lelans AB C, AD C parabolas in
B _ D, aet 2 95 per Id diamerro D HI, qua AB C parabola occurratin II,
aucacur per Hlordinacim lineca IIE, Sccans A F lincam in l.
+Tdd IK.
se at L 135. VL diroir 3 aenriliqin.
Demonstratio.
Acio C B ad TFT, id est C D duplicaca est
acionis AC ad AI; scd AC ad AI, du.
plicatam habet cacionem C D ad TK, id est
TII ad IK, racio igirur OB ad CD, qua-
druplicaca cslacionis IFT ad TK. Ouod erat
FIO CLXZX.
Dicorationem OM ad D L, quadruplicacam eAc rarionis D L. ad HE N.
demonporalio.
EScenim ratio OM ad D L duplicata racionis A M ad AL, id est GB ad ITP:
Lid est quadruplicacarationis AC adt AL, id est L. D ad N K. Quod erac de
monstratidum.
deper A e B parabola B F A Cuus axiS B L, de continoens BD, ducatuE
ad BD quauseama linca HC, occurrens parabolis in C, F, FI; e
Demonstratio.
Ectangulum CDT, eequale est
La quadraco HID: Sed FI D qua-
dearum aequale cA quactraro ID, id
cAbrectangulo ID B, vna cumcre.
ctangulo FITC; rectangulum igitur
CDI, aquale est rectangulis FDC
TTIC. est aurem idem GDT rectan
Sulum, aquale quoque rectangulis
quale rectangulo C.DIl. Suodetac dehcchaum.
35. 13 ly o2
DArabolas AB C, A D C communem habences verricem, contingane
in A lincx A E, AF, Secentameme parabolae in C puncto, ex quo
Dico CB ad CD quadruplicacdus abere rationem cius quam habet
demonstrandum.
dem AD C parabolx in O.
DRoducta HIDdoncc A F linex occurraE in L, demitTAnEuE ex B ex H
L diameErI BMI, IE N OCCUErENTES A F. linex in MI, de N, X BMI qui-
u
FIC
CLKXKI
AtabOla ABC cuius axis B BCoMsac in B linca BE, in gua alTuM.
peo quovispuncto F, demictatur ex P. diamerer F. A: descripea dein.
BD, BA, E. A lineis in D, 1,C.
Dico HIIC rectangulum, aequari rectansulo CDIF.
067. hurus.
C5. securidi.
FDC GDTE: rectangula igitUIr FDG, HIIC, aequalia sunc rectanoulis FDC.
ED LF. demproisitur communi rectangulo FVEr, ManeE FTIC rectangulum X
   .  s  A e.  e   te    (AI. Ae    . . Ae  1r A  1 1. i  . M u  . A. t 1e.   1     u V 1 p       1 p    1 ur u u s p p ini1