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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 77, page id 1815201908:0134
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 59 lines, status machine
# Lines: 59 recognised, mean confidence 0.84
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d
2
E
3
GF O N E TRIC A.
Construmo e atmonstratio.
Aex sinc duc linex AB ec B C, quarum
alceram lcilicet AB, oporreat diuide-
e In D puncto, DE AD, DB, BC sinc in
corinua analogia. pro constructione, (upCF
BC diamerro describatur circulus, icem
super linea AC, compolica ex duabus da-
eis AB _ BC. qui linE BF. C _ AF C,
ex ex puncto B crigatur perpendicularis
BF, ad rectam AC; duCAEUEqUO EX F
puncto, linea FI. Per cencrum minoris
circuli C; hac denique rectae CF, X qualis
CD. Dicotactum esse quod imperacum fiic: quonsam quadrato F B tam aequLaTUE
rectangulum AB C. quam = F FI, hoc eA BD C, crunt BBC, ABC LCCHOI erc.
aequalia incer se: Ced AB C rectangulo aequantur rectant a ADBC BC; a
BDC rectangulo aequarur rectangulum DB C, vna cum quadraco DB: dempio
isicur communi rectangulo DBC, manec DB quadrato, aequale rectangulum
ADBC. isicuc AD; DB, BC Canc concinua.
EX linc AB, CD
quarum vna CV
Iea Cecanda sIE in F,, VE
AB, CB, P. D sinc in
analogIA COMFIHUA.
Constructio s a
monstr alo.
SIUIPEA LEr MIICd
LLmaiori quam AB.
hac super FGeanquam
diamerro circulusLiICr
deinde (quod ex cle-
mentis Facile perHCI
cur) rectangulu GHIF
aequale Aat rectanenlo
ABCD; _ expucto FI
ica duCAEUE FIRL, vE
Aliter.
RI aequalIS SE A B (quod ab aliis Factum, et nos libro nostro de circulis alia aeque
alia methodo praestabimus) denique ex R crecta normali RL, aequali iph CD,
praescindaTUF ex K L. (ostendam enim cNemaiorem) linca KN, aequalis ipAI HIR.
Dieotactum quod pecebatur.
Nam rectangulum b IF R aequacur rectangulo CHIF, Id est ex constructione rC. B 36. Sentio
ctangulo AB C D, id eAt rurlum ex constructione PRL, ergo ve III ad KI, ica eAt
reciproce RI ad R II: acqui IEI maior cA quam IR, ergO e I. R, quam K HIma-
ior erie, quoda umpcum fuerat in constructione: perticiancur iam rectangula ITIR,
TK L. ductis per N _ L parallelis ad H I, ee normalibus HIME, IO P. Ouoniamisitur
rectansula TN, TE aequalia lune, ablaro communi KO, roliqua OL, KMt xqualia
CEUNE. DUaFC CUM KMI (VE Cx ConStruCtIOHC PATCE) NICGLadFAEUI, CFUINENO, RN.
EN cres concinue. Acqui N O est K I, hoc est AB; _ N P. eA C D. Factura igicur est
quod petebatuE.
deno.
11
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111
LIIIII