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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 430, page id 1815201908:0487
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=487
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 42 lines, status machine
# Lines: 42 recognised, mean confidence 0.86
# 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.

12. b.
DE. ducancurq; HII, NO parallet D, LII quidem secce parabolas in
Iet L, lineas A D, AB in K _E M, reCtA VETO NO, OCCUTTAE DE, BC,
lincis in P e R, parabolis in  d O.
ROPOSITIO CLV
Dico eC VE LM ad R O, Sic IK
2dOP.
Demonstratio.
LTHAd LH SCDF ad B P, CCdFEDF
ad BF, SIC KITadMFL, isitur ve LH ad
L HI, SiCR TTadMEF, _ TK ad LM, DCTH
2d F FI; id est vE D F ad BF. Sed VED P ad
BF, AC ON quoque est ad a NF, _ PN ad
R N. igitUF vE ON ad O N, HC P N ad R N
OP ad O F, veO DFadO DF, id est DF ad
BF, id est ex demostratis LR ad L M, X pet.
mutando DE TR ad OP, SIC LM ad R9.
Duod erat demonstrandu.
PROPOSTFIO CEVI
DArabolx duae ad cundem adem AC constiture communem habeane
apiCem A: policaG; ad aXCM Ordinatim C D E, IUMGAHNEUT AD, AF,
et recta dueacur Ls patatela C. P, lecans parabolas in l e R, rectas
VeTO AD, AF, in C & Il.
Dico C F H rectangulum ad rectangulum l F I eam habererationem,
quam habet FC linca ad lineam C D.
Demonstratio.
AbeanE ABC, A D E parabolx communem axem AF, policilque
Lad illum ordinatim lineis F es C F, iuNgAnEIT AB, AD, BC,
2d lfR rellangulum duplicacam ha-
bec racionem eius quam habec linea FY
acio rectanguli OF H adTFK, re.
etanoulum composca est ex rarione
FC ad FI, CCX HFad LK. Cn aurem
veFCddtL.hc2 LCaCB Cte
adFR, AIC FR ad C P; ratioigieur re-
etanguli GFII ad rectangulum IFK.
compolica est exracione FI ad C D, et
ex FK ad C F: sed. F R eA ad CF, Vt
F Test ad C Directangulum igiturOFH
b 2bid. F C. bFB CD proporrionales TunF. Duodtuir demonttrandum.
ad CD: id est rectaneulum OFHL Ad XF K rectangulum, eAt VE F C. ad C D, quia
(  t      e  1.   te   t  .      A 1     . H  t .   t     e        et  1   d st  1  .    t.    A. t At s p p 1  1  1