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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 519, page id 175905688X:0541
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=541
# Source image: https://digitale-sammlungen.gwlb.de/content/175905688X/jpgs/default/00000541.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 70 lines, status machine
# Lines: 70 recognised, mean confidence 0.77
# 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.

DCD
et
detu
es
ducu
ependi
iden
eo cor
DEi
C, d1
inCF
_ P
a, Yb.
C, A,l
F prallit
sins
1n5d1. 1
DE PR ANSMUE. CURVAR. LIH. IW RECT. 519
in Beec, ed in iec d; denique ex S ducacur S L parallela linea
AF, Producaturqueransens TS ulque in H.
Proprer rectum angulum NC Q, erit C. M ad C Q, UEMN
ad NC. AEqui M N est ad NC, UES X adST. OuareeriES Z
ad S F, uE CM ad CO. EF quia C M est ad C O, uF Z ad M I,
eric X SZ ad ST, uE Z ad MI, ac proinde rectanousum sub
S X lire YZ d MIsire Y b aequale rectansulo (ub S I _ Z. F0-
demmododemonstrabitur, rectansulum ce esse xquale ∞lo lub
IV_E, _D d F ∞ D VF, 2, _ ∞ a Y ∞ ∞lo subRSC2.
Ouapropter omnia haec rectansula simul Cumpra aequalia crune
rectangulo (ub 2 _ alia recta aequali omnibus cansentibus Cunul
Sumpris. Unde cum illud rerum sic, quorcunque rectangula at-
que cansentes extirerine, ec figura ex parallelogrammis con-
sans, E eorum numerus in infinitum augeaeur, delinae in super-
ficiem AOHITKLF, ac cangentes similicer in lineam curram
ABCDF, liguet superFicieM A G FI TRL F xqualem esse re-
ctangulo sub 2 d recta aequali currae AB C D F. Ouod erat
demonstrandum.
Ouomodo autem hinc longicudo datxe currx linex inrellisari
vortic, lequentibus exemplis patebit.
Sit primo curra ABC D F. ejus naturae, ue, sumpro in linea
A F prolibicu puncto M, duetaque perpendicuiari M C, Si A. NI
VOCetUT N, de M C rocetury, semper yy (it ∞ =. Deinde posi-
Eis A9 ∞S, CO ∞V, d MI∞Z: erit QM ∞s=X, _ ejus
quadratum ∞ ss - 2 (X- F xx. Cui (i addatur quadratuI CX M C,
hoc eA, y y live = invenietur (s - 2 (X F ∞ X L = ∞ VV.
Propter duas aquales radices
mulc. juxta meth. Fluddenii per
_ InVeHiCTUT  2 (∞ F 2 N N -1
Unde A O sive s∞ X F
InanCBIEMO D
3XX
Xe d
taa
X 3
∞ O.
. a qua sI SuBEFAHaEUE A HI D K, FC-
X 2
ra cujus quadratum est.
seu =, e provenietH C O∞
ad CQV
X
63
a
D X 4
44a 
Xe 3
+aa. cui addCH C N
23
. PrIEjAI UE CNV.
ira cognita aliqua linea, puta ; a, (licet
enim