# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:1138
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:1138?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1081, page id 1815201908:1138
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=1138
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00001138.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 50 lines, status machine
# Lines: 50 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.

GONOIDES HILLLRDOLLOrM
82
Demonstratio.
A FBCFTEDEXCCdentis proPOLICOIS ProBramma AEquE WXEa 17 J. = L alum-
LLPEOTOS RLO hyxerbola, qCHin conoD F F. Ottensum est quod quadra
tum ID excedit IFI quadeacum aeguali excessu, quo quadracum MO exocdic qua-
drarum NCS. lcdquin X P est alympcoros hyperbola R M C, eriam quiadratum I L
excedic aacum IO aquam excestu quo quadracum OP, excedie quadedeum
OM cum quadrata lP X O P, excedanc quadeaca PC et OM, rectangulis sub YC
dc duptâ YI; e (ub PM X dupla P O, guae per 18. hyperbola aequalia lunc. lgieur
excellus quadrari IY luper quadraco IFI, aequalis est excestui quo quadracum OP
excedis quadracum ONV. Sectioigicur BNII axi parallela, est hyperbola.
Ouod auce similis sichyperbola B N FT, hyperbole A B C que per axem facta cA, p2
tec ex eo, quod BNII hyperbola alimproris claudicur ijsdem, quibus claudicur hy-
perbela KL C, ve ostensum es supra. Fre0 per 17 4. huiushyperbola B N E axi par al-
lela similis est hyperbolx per axem. Ouod crac demonstrandum.
Corollarium primum.
Mnes sectiones conoidis quXe axi sune xouidistances angulum ast po CoM.
Corollarium secundum.
ine crtam manifectum est, omnium sectionum minimam ese ayperbea PL
axCH, Comparetur cum Elavis hyperbola qua sic eidem sectioni parallela,
cum enim ostentum sic omnes illas hyperbolas alrinprocisrei, qui sunc eiusdem an-
suli. lsicur quo maiores cudent diametrieransuerta, co criam maiores cundenchy-
perbolae: diamerer aurem cransuerla, minima illaCIt quA PCFAKCMM ETANEIE, VE PaECE
curioluis has materias consideranci.
eROTOSLTIOLLLXXX.
prelciulum aquate ConinenC. Pacec ex 177. huius.
DEcetur conoides plANO PEF AKCM ex-
Dhibenshrperbolam: inuentis aurem
huius sectionis alymprocis, hacsectio co-
noidens alteri alzmprocon parallela.
Dicoparaboraac scerione producis
Demonstratio.
Ec ABC platum per aAcM L B L conoidcos
hyperbolici, exhribens sperbolam ABC.
cuius cenerum F, a Pbci vero F C F FI. POL-
es deinde recta BD que aequidistet alymproco
FC. hac per eam lectio B  l recta ad planum
ABC VicotSTaBDF CHC ParabOla ad FBR
axem comme conorucos a sectionis ABC
constieuantur oramatm ICCl L MI, que produ-
etx cuntalympeons d cum sectione concurrars
ponancurq: B lalimptolo H aequidistans, et
XBScansenssectionem AB C in B. Denique
sectiones AanE L R V, que sinc rectx ad plamit
per axem quarum commanes sectiones NR
cum plano B R R, 19. vndec. _ detinic. 3. vndec.
recte erune ad lineasF. D, BD. quoniamigieur
FC, BD xquidictanE P N aquales exunt SB
   p e e   es   e uui s e e es qe es ee u e ee se ete s te site u e te  r   u   p te u   (    qu et 1 e e s  1. te e   e  e  . at H 11 11