# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0540
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0540?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 483, page id 1815201908:0540
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=540
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000540.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 74 lines, status machine
# Lines: 74 recognised, mean confidence 0.78
# 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.

Cib
1
PiPC
uI.
hea
111
V19
181
ean
VIM.
atum
est 2t
FB,
I1.8
et V.
1Mori
AC
sine
nsti.
sinA
AB;
AB
Aal.
MIb
11
eit
ebl
i
PA R A BO
R O POSITIO CCLXXV
Teparabolae AB axis BD, ad quem POa Ordinacim E. F, CFI,
_IIF, R S: aucch cinde diamettis L. L, lMI. Mecsique conicuris
N, MO inter OL. L. LL, _ AN, M C, deCcrIbAnEUFCIECA AxeSEL, IM
Dicoparabolashas xquales esse.
a pricta e L Patabolae F. L N, IP
8
demonstratio
remattet pet S. L. dempto quacr.
deacoV P. sed cum ex constructione R P, PG. lS linc continux, rectangulu R P S
deaco P O. lergo B Filarus rectum est parabolx IO P. Acqui eodem plano discur-
lu B P lacus rectum cA parabola B NT.  xequantur igiur parabola. Ouod erat de- 2 desin
monstrandum.  ib loctn
OSITIO CCLXXVI
buius.
IE B F lacus rectumL aXCOS
BV. eric ergo rectangulum
VBV aequale quadrato. V R.
e rectangulum XBF aequale
quadraco XI hoc est quadea- i1
10 V P: icaque à rectanguloiticrit
V B F pdempio rectansulo
ZBT remanoc rectangulum.
VXBT, aquale rectaigilo2 A e t
R P S, quodlex quadratOlVK
aquacur quadeaco P. O. rectangulum isieur V XBT, hoc est IPB T aequatur qua-
R
ile
Mnis parabola patavola limilis est.
Duplici modo supersicies duas euruilineas dici similes: Primo, quando similes fia
a in in-
finicum illis inscribi possunt: es hôc sensu archimedes ex Fuclides, Similia esse curuilinea quae
dam ostendunt. Secundo similes dicuntur sizus a Curmunea quarum essentiales proprietates ea
dem sunt. Nos duplicem hanc sune Parabolio nesse demonscrabimus.
monsrabto.
DONaNEUT ABC, DFF parabolarum a
BC, F Faequales laceribts  rectis
EE peF G_ FI, ordinatim RC, D F: IUngANCUEqUe ABC, D E F. Ouoniam L LL,
BClinexe laceribus rectis aequales lune de A C, D F ordinarim polIce, reatX P II. D FI,
icem AG, BC aequales suNE: e quia AC, D FT ad axes ordinarim applicantur, adgu-
si DTTE, AG B recti sunc: vnde criangula DFTE, A G B, aC PTOIndOFOFADF F, ABC
Cmilia Tunc: Rursum diursIS A G, F FTlineis proportionalicer in ICK, ponancurpet
L_ R ordinatim L ML, NT O: IUNGANCUEGUC L BM. NF. O. Ouoniam igitur ve BI ad
BC, GC P K eA ad P HI, vE P. Iquadrarum ad quadracum AG, liC N K quadrarum eA
         e   o     g    at 1  1 6   l 0  3 e6  5       t a o  5 1