# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0659
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0659?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 602, page id 1815201908:0659
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=659
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000659.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 50 lines, status machine
# Lines: 50 recognised, mean confidence 0.79
# 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.

ATY P ER BOL A.
PROEOSIFIO CXZZVI
Acer duas dacas quoclibet medias proporrionals dele Coce.
Constructio es demonstratio.
TIN, IO, RP, PO esse QuattOr que requiruneur. Osendimus
cructione, rario F C ad MI F. quincapcala estracionis F. C ad FTN. isiEuEHIN, IO.
PK. L. Q Cunc quari Ca et asitata L C, M P. Ouod cracpraestandum.
AAtOSTEIOBALXVIII
Tirculo AB Crectangulu e DC Dinscribatur a sumprilque rectis
AB, B C inalzmprocos, pet M eoldem describatur hyperbola
F. D occurrens circuloHenuo in F, ex quo demitrantur rectae F. IL, FF
no. hr
BI29. BM
alsumpea hyperbola cuius atympeot C, C. E ponacur C F aequalis A et xquidi
sans CD; ee hac ve B ad A, ica C C 2d C P; _ crigatur P M aequidistansFO
que parces aequales in FI, I, K, L. _ ACMIETANEUE IIN, IO, KP, L. 9 Parallela
asymproco: dico
ergo cum FC Mquancicas concana, ala lic in quinque parces aquales cciam quan-
cITAS E GFMI per parallelaS FTN, TO, RL, TO in cocidem parces aequales, divila
eies b quancicas F CFF. M continet quanaem F CENTFI, hoc est quinguies ex con-
Ine A, B dux dacXe: oporceat inter illas quaruor medias proportionales assignares
e ductis C F. CM: divila ponacur quantitas FCM, concaux lyperbola, in quin-
quancicates LCFI, IICL, eec. 2 xequales ese quanciracibus FONTI, NFIIO, dec
eric: ereocum rario LC ad MF, toriesmulciplicer rationem F C ad FTN, quo-
huius.
d EX 73:
161s.
CCorot. 1).
alymprocis aguldictances.
Dicobe,  aldo CeeMa B, BC.
Lobtbnstatet
Depuncta F e D agacur rect
ITLC Ponacurque BB: erir
igicur IF, cae qualis Id C: , H K
aqualis L C ALB, LG
triangula HIRB, D C, Cd aequalia
sincincer (e, de similia; quia vero
circulo AB C inleriprum cA re.
ctangulum AD C, Cndemverique
Ex ila-
heneis.
tEx cto.
mense
cerit diameter; quare angulus BE. D, adeoque _ angulus FIF B rectus est: quare
eum FK aquidister AD laceri rect ansH AD CD, recta FK normalis cA ad
HIB: Vndeeres sunt in concinua analogia LL IB, K F, K B: scd HI K R quAEUE AB, &
RF aqualis est B Fs vei _ R B ipsi L L, iEIC AB, BF, FF proporcionales, sune
deinde cum rectansvlo AP C. B a ute  ulum R F, F; NE A B ad B P, iea est
iF ad
a e a pat u te u t ee t u te e t te ta e ta et tet t  et at  t e t a   ti  ite d e  e te te ut et it t tit  a t   t e      ste   dib