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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 31, page id 1815201908:0088
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 73 lines, status machine
# Lines: 73 recognised, mean confidence 0.81
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# After the first blank line: the recognised lines in reading order, one per line.

B
m
ri
tis
n2
d.
1-
Ca
M
i5
12
ca
e
.
2
1C
1i
POLLNTIA.
InECE Se requaleS: UINC AUECI F. C,
FC duo lacera, aequalia duobus
Laceribus AC. C Biigitur reliquum
lacus crianguli CR B, reliquo la-
ceri crianguli ABC est aqualei
unde punctum P elt in recta FIK,
e PKC rriangulum, aequale
criangulo ABC. Fodem modo
ostendicur criangulum ABC ∞-
quale criangulo DL A, ec pun-
Ecum D esc in directum cum L P
producta. Rursum cum D L lacuS,
equalc sE laceri C K, HOC eAR FI,
eE FL aequale ipA AB, id est F K; crir relignum lacuS FHT, aequale reliquo DF3
est aurem angulus FOD (ob BF, L A parallelaS) aequalis angulo D AL, id eA
LAC, id eltansulo PIFI; ec angulus E FII, aequalis angulo D FC, iBiEEDFC
FFIL criansula, d VO, LF latera sune incer se xequalia. Tcerum cum arguli AD L
CAC sinc incer Le aquales; de AC, AC lacera, aequalia laceribus AD, DI, erie
ID A criangulum, aequale srransulo C AC; vnde dempro communi eriangulo
ABC, erir ABC criangulum, aquale Trapezio IBODI. Isieur cum criangu-
lum ABC, id est ER C aequale sic crapezio IBGDI, _ DF C triangulum,
aequale criangulo F FTI, reliqua veto sine communia, crit A F quadratum, lace
ris rectum angulum subcendentis, aequale quadratis AF, C II, laretum rectum an-
culum concinentium. Ouoderac demonstrandum.
Scholion.
emonstrat hanc Clauius ad 47. primi Elemens. Pripliet alia he d do; secus quam Pele-
carius fieri posse existimauit: copiae ramen, non necessitatis ergo, etiamnos illam, alia
via demonstrandam a ssumpsimus, maxime occasione sequentium duarum propositionum.
PROPOSTTIO XLIV
Sr0 ABC criangulum amblyconium, ex laterum quadTaEA A D, AF,
CF. ducacur q ex C linea C H secans orthogonaliterin LI ee l, linegs
AB, KF.
Dico A D quadratum, SuPCTarC QuadTATA AE, C F, rectangulo AB FY
bis lumpto.
Demonprario.
L M aet MICASCB
EF, ex super A C: ve diamerro de-
scribatur lemicirculus AIIC; 2 er 2(1-
biris PeF FP_ L. Iungancurq; pun-
et2 AC, CK BD, BN, dein exB,
recta demictatur BO, lecans ortho.
Conalicer inO P, lincaS AC, DN.
Ouoniam AM, CGlinCX, PeF CON-
Aructionem aequidistanE, exiE, ACC
criangulum aequale dimidio rectan.
buliCL: eodem modo criansulum, lic
CAR, aequale est dimidio rectansu
li AI. Rurlum cum anguli A BF,
CAH. per conttructionem reci:
u adao commumaisuto B A. C ceinlira ris. 
crunc anouliB AN, C AK incer sC
aequales; sunc aurem AB, AE lacC-
1
ari AN
Veacur ex Alinea AM secans in