# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0065
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0065?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 8, page id 1815201908:0065
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=65
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000065.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 51 lines, status machine
# Lines: 51 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.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

Y. LN E A R V MI
P R O POSITIO XIV
Seo ABC trianguli balis
A C, bitariam dunila in D:
Junctilqs BB, agatur per B li-
nea BE, parallcla rectae AC,
ducaturq: C. l, Occurrens linex liB in R.
in qua alumpro pucto quonis
E, ducacurrecta LC, _ CxC
erigatur linea C F orchogona
rectX AB, OCCUErENS F. BlineX
in C2; dein ponatur L F iNCCF
secans BD in 1, _ BC in II.
Dicolincam EB in G _ V, diuilam extrema de media ratione pro
Cortionali.
Demonstratio.
Gratur per C linca Y. NI, paraHIela reCIL A B: OCCUTeNS FK in M. Ouoniarri
Lainea EC, per constructione Hormalis est ad rectam AB, crune anguli
AF L: sSiCur reliquus aSus OF L aequalis est reliquo GFR; rurIum CuM LM
linca aequidisterlinex AB normali ad rectam GC, cruneanguli F CL, FCTM rC-
eti; isicur cumtam anguli E GTM, FCFL, quam GFM, GII. linc incer sc xqua-
Les, _ FC linca communis, crune F C+M, FOT. criansula, adeoque ex lateraL. C
CM incer sexqualia. OuarC VE F B ad L C, lic FB ad GM: Sed est vE FB ad L G
sic BF ad E C, ex ve EB ad GM, hC BK ad RC, isitur vE B E ad F C, lic
BK ad K C. Ouod erat demonstrandum.
ROPOSITIO XV
Onsticuane AB, DC scccumangulum, _ AB maius HClalitC BC.
oporrer A lalus producere in D, vriuncta DC. hancproporrio
Constructio es demonstratio.
normalisipt A C, ex alia queda Cu
angulum DCB consticuat duplum anouli
C AB. dico factum eNc quod pecitur. Fri-
ganEUT ex D lincx D E, D C; _E D Fquidem
aequidistet ips F C; DG vero, rectX CP.
Duoniam angulus ACF per constructio.
nem rectus elt, ex CB linca normalis ipl
A F, CrUIHE ABC F B C. criangula similia,
ex
ddia
GF R, GF B rectis elt aurem anguluS RE B aequalis a angulo BFL, id est angulo
nales DC. AD. _ C B. AB.
Vat a C A, demiteatur ex C linca C F,
de angulus L. C B aequalis angulo C AB;
guare _ angulus D CB, recta C. F. bitara e S. Nurtum cum DC linca,
per Censtructionem aequidister recrx BC; et F D linca, ip(i F C; crit angulus
OD C aequalis angulo DCB, e angulus FDC, equalis anoulo P CD; adeoque
ODC drioulus, recta FD bitariam diuisus; sune aurem de an du DH∞, DLC
recci (cum FD linca ague C; Hoa ad A C) ec LDlinea communis,
cut cllatoccua aLEi alate cllatico dte   tacuo latelt e
aequalc.
  e   1 e. .  1 1 .  1 1  e  ti       . .  .  u    e    u 1. . 1 . 1  .     . . 1  u pu  p  11