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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 813, page id 1815201908:0870
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 35 lines, status machine
# Lines: 35 recognised, mean confidence 0.87
# 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.

l
.
ais Biosota Lanotum inter se ductu seu multiplicatione.
Esi ex toto huius libri decursu, satis aperee colliei possit methodus,. Quata
 Obseruare debeat 1s, qui in doctrina huius libri se exercere desiderat; nih-
lominus has paucas propositiones subiuncere decreur, maioris lueis erco:
x enim linea recu, secundum vllam propositionem, sive notam, sive in-
cornitam alld ol est, qu selundum eandem divisionem, subseruire possit huius l.
bri areumento. Quod quontum multis paradoxi loco habendum existimarem, operae pre-
eium, imo necessarium duxi, partem hancadiuneere, t hoc ipsum luce clarius inno-
tescat, e Geometria studiosi Oceanum parentissimum sibi derectum aenoscant, cur sese
ruto posse concredere, vel tenuissimo lembo vecti scientia elementorum persuasum
habeant.
PROPOStIIO CLXKKI
VIMETLLS HCa PEOPOECOHaleS AB, AC, AD.
 a ad media AC _ AgGreTAEO ExTremOruM D A,
B A aequari rectangulum sub excremis D A, B A bis Cumprum, una cum
rectangulo sub differentiis BC, CD comprehenlo.
Demonstratio.
Fitat E. A aequalis AB. Ouoniam D A, C A, B A sune proportionales, erie divi-
dendo DC ad CA, VE C B ad B H. eryo rectangulum DC, A B a qUaTUE rC-
cangulo AC B. LCangulum DC, AB bis, aequatur rectangulis AC B, DC
A B. Addicoisicur communi rectangulo C AB bis sumpro, rectangula D C, AB
bis, C AB bis, hoc esta rectangulum D AB bis, aequabicur rectangulis A C B, D C, 21. secunat.
AB, C AB bis, sed duohuius summx rectangula C AB, A CB b _ QuaNEHE qua- b +. secutuo-
draTO AC. ergo rectangulum D A B bis xequatur quadraco A C cum rectangulis
C AB, D C A B. quare verique lummx addarur reclangum DCh, crit rectangu-
lum D AB bis cum rectangulo D C B xquale quadraro AC, _ rectangulo C AB
id CA C AF, vna cum DC, AB, D C B rectangulis: hoc cA quadratO AC, _ rC
cangulo C AF. vna cum rectangulo DC A, sivC ACD. Sed quadratO C A, _
rectangulis C A F, AC D aequacur rectangulum AC, F. D, hoc cK rectangulum su.
per AC _ AB, AD eanquam rarecta; ergo rectangulum sub AC X AB, AD
regnatur rectangulo D AB bis cum rectangulo D C B. Ouod erat demonstran-
dumm.
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